Q51. He kept going ___________ his dreams, despite the many obstacles in his path.
(a) up
(b) before
(c) out
(d) after
(e) around
Answer: (d)
Solution: To “go after” something is an English idiom meaning to pursue a goal or ambition. The sentence describes a persistent pursuit despite obstacles, making “after” the most natural fit.
Q52. The collector proudly displayed the first _____________ of the rare comic book in a glass case.
(a) depth
(b) edition
(c) emphasis
(d) ability
(e) moment
Answer: (b)
Solution: In the world of collectibles and publishing, an “edition” refers to a specific version or release of a book. A “first edition” is the most valuable and logical thing for a collector to display.
Directions (53-57): Rearrange the following sentences in the proper sequence to form a meaningful paragraph; then answer the questions given below them.
(a) Trust in institutions and interpersonal trust are positively correlated with economic prosperity, as they reduce transaction costs and encourage investment.
(b) The survey also highlighted that countries with higher trust levels tend to have better governance, which further contributes to their economic success.
(c) A recent survey explored the relationship between trust and prosperity, revealing a strong link between the two.
(d) Consequently, nations that foster trust within their societies often experience greater economic growth and stability.
(e) According to the survey, trust not only enhances social cohesion but also plays a crucial role in facilitating economic transactions.
Q53. Which of the following should be the FIRST sentence after rearrangement?
(a) D
(b) A
(c) E
(d) C
(e) B
Answer: (d)
Solution:
The Correct Sequence: C – E – A – B – D
Sentence (C) – The Introduction: This is the best starting sentence because it introduces the primary subject (a recent survey) and the two main variables being discussed: trust and prosperity.
Sentence (E) – Survey Detail 1: This follows (C) directly because it begins with “According to the survey…” It expands on the findings by stating trust affects both social cohesion and economic transactions.
Sentence (A) – Specific Mechanism: This sentence provides the “why” behind sentence (E). It explains that trust reduces transaction costs and encourages investment, which leads to the prosperity mentioned in the intro.
Sentence (B) – Survey Detail 2: The word “also” indicates an additional point. It connects higher trust levels to “better governance,” adding another layer to why these countries are successful.
Sentence (D) – The Conclusion: Starting with “Consequently,” this sentence serves as a summary of the entire paragraph, linking the presence of trust back to the final outcome of economic growth and stability.
Thus, correct answer is option (d)
Q54. Which of the following should be the FOURTH sentence after rearrangement?
(a) A
(b) D
(c) B
(d) E
(e) C
Answer: (c)
Solution:
The Correct Sequence: C – E – A – B – D
Sentence (C) – The Introduction: This is the best starting sentence because it introduces the primary subject (a recent survey) and the two main variables being discussed: trust and prosperity.
Sentence (E) – Survey Detail 1: This follows (C) directly because it begins with “According to the survey…” It expands on the findings by stating trust affects both social cohesion and economic transactions.
Sentence (A) – Specific Mechanism: This sentence provides the “why” behind sentence (E). It explains that trust reduces transaction costs and encourages investment, which leads to the prosperity mentioned in the intro.
Sentence (B) – Survey Detail 2: The word “also” indicates an additional point. It connects higher trust levels to “better governance,” adding another layer to why these countries are successful.
Sentence (D) – The Conclusion: Starting with “Consequently,” this sentence serves as a summary of the entire paragraph, linking the presence of trust back to the final outcome of economic growth and stability.
Thus, correct answer is option (c).
Q55. Which of the following should be the SECOND sentence after rearrangement?
(a) C
(b) E
(c) D
(d) A
(e) B
Answer: (b)
Solution:
The Correct Sequence: C – E – A – B – D
Sentence (C) – The Introduction: This is the best starting sentence because it introduces the primary subject (a recent survey) and the two main variables being discussed: trust and prosperity.
Sentence (E) – Survey Detail 1: This follows (C) directly because it begins with “According to the survey…” It expands on the findings by stating trust affects both social cohesion and economic transactions.
Sentence (A) – Specific Mechanism: This sentence provides the “why” behind sentence (E). It explains that trust reduces transaction costs and encourages investment, which leads to the prosperity mentioned in the intro.
Sentence (B) – Survey Detail 2: The word “also” indicates an additional point. It connects higher trust levels to “better governance,” adding another layer to why these countries are successful.
Sentence (D) – The Conclusion: Starting with “Consequently,” this sentence serves as a summary of the entire paragraph, linking the presence of trust back to the final outcome of economic growth and stability.
Thus, correct answer is option (b).
Q56. Which of the following should be the THIRD sentence after rearrangement?
(a) B
(b) E
(c) D
(d) C
(e) A
Answer: (e)
Solution:
The Correct Sequence: C – E – A – B – D
Sentence (C) – The Introduction: This is the best starting sentence because it introduces the primary subject (a recent survey) and the two main variables being discussed: trust and prosperity.
Sentence (E) – Survey Detail 1: This follows (C) directly because it begins with “According to the survey…” It expands on the findings by stating trust affects both social cohesion and economic transactions.
Sentence (A) – Specific Mechanism: This sentence provides the “why” behind sentence (E). It explains that trust reduces transaction costs and encourages investment, which leads to the prosperity mentioned in the intro.
Sentence (B) – Survey Detail 2: The word “also” indicates an additional point. It connects higher trust levels to “better governance,” adding another layer to why these countries are successful.
Sentence (D) – The Conclusion: Starting with “Consequently,” this sentence serves as a summary of the entire paragraph, linking the presence of trust back to the final outcome of economic growth and stability.
Thus, correct answer is option (e)
Q57. Which of the following should be the FIFTH sentence after rearrangement?
(a) C
(b) A
(c) E
(d) B
(e) D
Answer: (e)
Solution:
The Correct Sequence: C – E – A – B – D
Sentence (C) – The Introduction: This is the best starting sentence because it introduces the primary subject (a recent survey) and the two main variables being discussed: trust and prosperity.
Sentence (E) – Survey Detail 1: This follows (C) directly because it begins with “According to the survey…” It expands on the findings by stating trust affects both social cohesion and economic transactions.
Sentence (A) – Specific Mechanism: This sentence provides the “why” behind sentence (E). It explains that trust reduces transaction costs and encourages investment, which leads to the prosperity mentioned in the intro.
Sentence (B) – Survey Detail 2: The word “also” indicates an additional point. It connects higher trust levels to “better governance,” adding another layer to why these countries are successful.
Sentence (D) – The Conclusion: Starting with “Consequently,” this sentence serves as a summary of the entire paragraph, linking the presence of trust back to the final outcome of economic growth and stability.
Thus, correct answer is option (e).
Q58. A word has been used in the sentences given below. Identify the statement(s) where the word has been used in a contextually and grammatically correct manner.
KNEE
(I) She is so powerful that even her toughest opponents were forced to bend their knees in submission.
(II) While playing basketball, she injured her knee when she landed awkwardly after a jump.
(III) To make the perfect loaf of bread, you need to knee the dough until it becomes smooth and elastic.
(a) Only (III)
(b) Both (I) and (II)
(c) Both (II) and (III)
(d) Only (I)
(e) All of these
Answer: (b)
Solution:
The word Knee has two main meanings:
- Noun: The joint in the middle of your leg.
- Metaphor: An expression for submission (e.g., “to bend the knee”).
Sentence Breakdown
Sentence (I): “She is so powerful that even her toughest opponents were forced to bend their knees in submission.” $\Rightarrow$ CORRECT.
- This is a common phrase meaning to surrender or show respect. It correctly uses “knee” as the body part involved in kneeling.
Sentence (II): “While playing basketball, she injured her knee when she landed awkwardly after a jump.” $\Rightarrow$ CORRECT.
- This is the literal use of the word. It correctly refers to the physical joint of the leg that can be injured during sports.
Thus, correct answer is option (b) Both (I) and (II)
Directions (59-61): In each of the questions given below, a sentence is given with four words highlighted. These four words may or may not be in their correct position. The sentence is then followed by options with the correct combination of words that should replace each other in order to make the sentence grammatically and contextually correct. Find the correct combination of the words that replace each other.
Q59. The paper pulled (a) into (b) the inner part of the copy machine and had to be jammed (c) out (d) by the printer technician.
(a) A-B
(b) C-D
(c) A-C
(d) B-D
(e) No interchange required
Answer: (c)
Solution:
- Paper does not “pull” itself into a machine; it gets jammed (C).
- A technician does not “jam” paper out; they pull (A) it out to fix the machine.
Correction: Interchange A and C.
Correct Sentence: “The paper jammed (A) into the inner part of the copy machine and had to be pulled (C) out by the printer technician”.
Thus, correct answer is option (c) A-C.
Q60. Mrs. Griffin has enough (a) about going (b) her own school but is worried that she wouldn’t have thought (c) students to keep it opening (d) .
(a) A-B
(b) C-D
(c) A-B & C-D
(d) A-C & B-D
(e) No interchange required
Answer: (d)
Solution:
- You don’t “have enough” about a plan; you have a thought (C) about it.
- You don’t “go” a school in this context; you opening (B) (start) a school.
- You need enough (A) students (sufficiency) to keep the school going (D) (running).
Correction: Interchange A-C and B-D.
Correct Sentence: “Mrs. Griffin has thought (A) about opening (B) her own school but is worried that she wouldn’t have enough (C) students to keep it going (D)“.
Thus, correct answer is option (d) A-C & B-D.
Q61. It was unfortunate that our team’s halftime (a) were raised (b) so high during spirits (c) , because we were subsequently crushed (d) .
(a) A-C
(b) C-B
(c) A-B
(d) B-D
(e) No interchange required
Answer: (a)
Solution:
- “Halftime” is a time period and cannot be “raised high”.
- Spirits (C) refers to the team’s morale, which can be raised (B).
- The high morale happened during the halftime (A) break.
Correction: Interchange A and C.
Correct Sentence: “It was unfortunate that our team’s spirits (A) were raised (B) so high during halftime (C), because we were subsequently crushed (D)“.
Thus, correct answer is option (a) A-C.
Directions (62-65): In the following questions, a sentence is provided with a highlighted phrase that may be incorrect. If the highlighted phrase is incorrect, choose the option that best replaces the phrase to make the sentence both grammatically and contextually correct.
Q62. Despite renewable energy’s potential, the global economy remains heavily reliant in fossil fuels, complicating the shift to sustainability.
(a) remain heavily reliant in
(b) remained heavily reliant in
(c) remaining heavily reliant on
(d) remains heavily reliant on
(e) No correction required
Answer: (d)
Solution:
- The word reliant is an adjective that describes dependency.
- In English grammar, “reliant” must always be followed by the preposition “on”.
- Using “in” is contextually and grammatically incorrect here.
Correction: The phrase should be “remains heavily reliant on.”
Thus, correct answer is option (d)
Q63. Digital platforms have intensified ideological divisions, leading at concerns about social media’s impact on public discourse and dialogue.
(a) who lead to concerns about
(b) leading to concerns about
(c) lead to concerns about
(d) leading to concerns on
(e) No correction required
Answer: (b)
Solution:
- The phrase “leading to” is used to show a cause-and-effect relationship.
- The intensified divisions (cause) are resulting in concerns (effect).
- The preposition “at” does not fit here and fails to convey the intended meaning.
Correction: The phrase should be “leading to concerns about.”
Thus, correct answer is option (b)
Q64. Cognitive biases often distorting our perception of reality, leading to decisions that contradict rational thinking.
(a) often distort our perception of reality
(b) often distorted our perception of reality
(c) often distorts our perception of reality
(d) often distort our perception in reality
(e) No correction required
Answer: (a)
Solution:
- Subject: “Cognitive biases” is a plural noun.
- Verb: A plural subject requires a plural verb form. “Distort” is the correct plural verb.
- The present participle “distorting” is incorrect because it is not part of a continuous tense or a proper relative clause in this context.
Correction: The phrase should be “often distort our perception of reality.”
Thus, correct answer is option (a)
Q65. Before I had sat in the car, the driver opened the door for me.
(a) Before I have sat
(b) Before I sat in the car
(c) Once I had been sitting
(d) Before I am sitting
(e) No replacement required
Answer: (b)
Solution:
- The sentence describes a clear sequence of events in the past.
- When the sequence is already made clear by the word “Before,” the past perfect (“had sat”) is unnecessary and bulky.
- The simple past tense (“sat”) accurately and simply reflects the sequence of actions.
Correction: The phrase should be “Before I sat in the car.”
Thus, correct answer is option (b)
Directions (66-70): The graph shows the total number of orders received by five restaurants (A, B, C , D & E). Read the line graph and answer the following questions.
Q66. Find the average number ordered received by A, B and D.
(a) 76
(b) 72
(c) 24
(d) 66
(e) 42
Answer: (a)
Solution:
Based on the line graph “Number of orders received”:
- Restaurant A: 72 orders
- Restaurant B: 60 orders
- Restaurant C: 80 orders
- Restaurant D: 96 orders
- Restaurant E: 88 orders
Formula: $\text{Average} = \frac{\text{Sum of values}}{\text{Total number of items}}$
Calculation: $\frac{72 + 60 + 96}{3} = \frac{228}{3} = 76$
Thus, correct answer is option (a) 76
Q67. The orders received by D, 25% are veg orders and rest are non- veg orders, then find the nonveg orders received by D.
(a) 80
(b) 72
(c) 84
(d) 76
(e) 92
Answer: (b)
Solution:
Total orders for D: 96
Veg orders (25%): $25\% \text{ of } 96 = 24$
Non-veg orders: $96 – 24 = 72$
Thus, correct answer is option (b) 72
Q68. Restaurant X received 33.37% more orders than that of A and Restaurant Y received 12.5% more orders than E. find the total orders received by X and Y.
(a) 195
(b) 190
(c) 194
(d) 196
(e) 192
Answer: (a)
Solution:
Restaurant X: $33.33\% \text{ (or } \frac{1}{3}\text{) more than A}$.
- Calculation: $72 + (\frac{1}{3} \times 72) = 72 + 24 = 96$.
Restaurant Y: $12.5\% \text{ (or } \frac{1}{8}\text{) more than E}$.
- Calculation: $88 + (\frac{1}{8} \times 88) = 88 + 11 = 99$.
Total (X + Y): $96 + 99 = 195$
Thus, correct answer is option (a) 195
Q69. Find the orders received by A and E together are what percent more/less than that of B and C together.
(a) 15%
(b) 66.66%
(c) 33.33%
(d) 20%
(e) 14.28%
Answer: (e)
Solution:
Orders A + E: $72 + 88 = 160$
Orders B + C: $60 + 80 = 140$
Comparison: A and E together are more than B and C.
Percentage more: $\frac{160 – 140}{140} \times 100 = \frac{20}{140} \times 100 = 14.28\%$
Thus, correct answer is option (e) 14.28%
Q70. Find the ratio of orders received by E to orders received B and D together.
(a) 22:39
(b) 39:22
(c) 19:14
(d) 19:16
(e) 12:13
Answer: (a)
Solution:
Restaurant E: 88
Restaurants B + D: $60 + 96 = 156$
Ratio: $88 : 156$. Dividing both by 4 gives $22 : 39$.
Thus, correct answer is option (a) 22:39
Q71. In April 2019, a man has Rs 17500 and it is increased by 20% every year in the starting of April.
If man spends 60% of total amount in April 2021, then find total amount (in Rs.) man has at the end of April 2021?
(a) 15120
(b) 10060
(c) 9080
(d) 10080
(e) 12080
Answer: (d)
Solution:
Total Amount (April 2021): The amount increases for 2 years (2019 to 2021).
$$17,500 \times \frac{6}{5} \times \frac{6}{5} = 25,200 \text{ Rs.}$$
Remaining Amount: If he spends 60%, he has 40% (or $\frac{2}{5}$) left.
$$25,200 \times \frac{2}{5} = 10,080 \text{ Rs.}$$
Thus, correct answer is option (d) 10,080.
Q72. The ratio of length to breadth of a rectangle is 4 : 3 and area of the rectangle is 300 cm square.
If the breadth of rectangle decreased by 20% and the length is increased by 10%, then find the new perimeter (in cm) of the rectangle?
(a) 68
(b) 70
(c) 60
(d) 84
(e) 48
Answer: (a)
Solution:
Initial Sides: Let $L = 4x$ and $B = 3x$.
$$4x \times 3x = 300 \rightarrow 12x^2 = 300 \rightarrow x^2 = 25 \rightarrow x = 5$$
Original $L = 20\text{ cm}$, $B = 15\text{ cm}$.
New Sides: New $B = 15 \times \frac{4}{5} = 12\text{ cm}$. New $L = 20 \times \frac{11}{10} = 22\text{ cm}$.
New Perimeter: $2 \times (22 + 12) = 68\text{ cm}$.
Thus, correct answer is option (a) 68
Q73. A and B started a business with some amount. After 9 months, A left the business. At the end of a year, the profit share of A and B is in the ratio of 9 : 16. Find the ratio of investment of A and B respectively?
(a) 1 : 3
(b) 3 : 4
(c) 2 : 3
(d) 4 : 3
(e) 3 : 5
Answer: (b)
Solution:
Formula: $\text{Profit} = \text{Investment} \times \text{Time}$.
Let investments be $x$ and $y$.
$$\frac{x \times 9}{y \times 12} = \frac{9}{16} \rightarrow \frac{9x}{12y} = \frac{9}{16} \rightarrow \frac{x}{y} = \frac{12}{16} = \frac{3}{4}$$
Thus, correct answer is option (b) 3:4.
Q74. A, B and C together can do a work in 4 days, while B and C together can do the same work in 20/3 days. Find in how many days A alone can do 60% of the work?
(a) 20
(b) 18
(c) 8
(d) 6
(e) 24
Answer: (d)
Solution:
Total Work (LCM of 4 and 20/3): 20 units.
Efficiency of A+B+C: $20 \div 4 = 5\text{ units/day}$.
Efficiency of B+C: $20 \div (20/3) = 3\text{ units/day}$.
Efficiency of A: $5 – 3 = 2\text{ units/day}$.
Time for 60% Work: $60\% \text{ of } 20 = 12\text{ units}$. Time $= 12 \div 2 = 6\text{ days}$.
Thus, correct answer is option (d) 6
Q75. The speed of a train is 72 km/hr and it crosses a pole in 16 seconds. If speed of the train is increased by 12 meters/second, then find the time taken by the train to cross the same pole (in seconds)?
(a) 20
(b) 12
(c) 15
(d) 5
(e) 10
Answer: (e)
Solution:
Convert Speed: $72\text{ km/hr} = 72 \times \frac{5}{18} = 20\text{ m/s}$.
Length of Train (Distance): $20\text{ m/s} \times 16\text{ s} = 320\text{ meters}$.
New Speed: $20 + 12 = 32\text{ m/s}$.
New Time: $320 \div 32 = 10\text{ seconds}$.
Thus, correct answer is option (e) 10
Q76. A man invested Rs X in scheme A at the rate of 20% p.a. for two years on compound interest annually. Also, he invested same amount in scheme B at rate of 30% p.a. for two years on simple interest. If the difference between interest received from both schemes is Rs 896, then find the value of X (in Rs.)?
(a) 6000
(b) 6400
(c) 4800
(d) 5600
(e) 3600
Answer: (d)
Solution:
Formula Used:
- Equivalent Rate for C.I. (2 years): $R + R + \frac{R^2}{100}$
- Simple Interest: $\frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100}$
Step-by-Step Calculation:
- Compound Interest (Scheme A) Rate: $20 + 20 + \frac{20 \times 20}{100} = 44\%$
- Simple Interest (Scheme B) Rate: $30\% \times 2 = 60\%$
- Find the Difference: The problem states the difference between these interests is 896.
- $X \times (\frac{60}{100} – \frac{44}{100}) = 896$
- $X \times \frac{16}{100} = 896$
- $16X = 89,600 \rightarrow X = 5,600$
Thus, correct answer is option (d) 5600
Q77. Cost price of two articles A and B is equal. Article A sold at profit of 20% and article B sold at loss of 30%, so overall loss of Rs 50 occurred. For received a profit of 40%, article B should sell at what price (in Rs)?
(a) 700
(b) 840
(c) 560
(d) 420
(e) 980
Answer: (a)
Solution:
Formula Used:
- Selling Price (Profit): $\text{Cost Price} \times \frac{100 + \text{Profit}\%}{100}$
- Loss: $\text{Cost Price} – \text{Selling Price}$
Step-by-Step Calculation:
- Assume Cost Price (CP): Let the CP of each article be Rs. 100x.
- Find Selling Prices (SP):
- $\text{SP of A} = 100x \times \frac{120}{100} = 120x$
- $\text{SP of B} = 100x \times \frac{70}{100} = 70x$
- Use Overall Loss: Total CP ($200x$) minus Total SP ($120x + 70x$) = 50.
- $200x – 190x = 50$
- $10x = 50 \rightarrow x = 5$
- Calculate Specific Price:
- $\text{CP of article B} = 100 \times 5 = 500 \text{ Rs.}$
- $\text{Target SP for 40\% profit} = 500 \times \frac{140}{100} = 700 \text{ Rs.}$
Thus, correct answer is option (a) 700
Directions (78-82): Find the missing term of the given series.
Q78. 100, 101, 103, 109, 133, ?
(a) 253
(b) 216
(c) 240
(d) 200
(e) 210
Answer: (a)
Solution:
Pattern: Each subsequent number is found by adding the factorial of increasing natural numbers.
- $100 + 1! (1) = 101$
- $101 + 2! (2) = 103$
- $103 + 3! (6) = 109$
- $109 + 4! (24) = 133$
- $133 + 5! (120) = \mathbf{253}$
Thus, correct answer is option (a) 253
Q79. 12600, 1800, 300, 60, ?, 5
(a) 15
(b) 16
(c) 40
(d) 20
(e) 30
Answer: (a)
Solution:
Pattern: Each term is multiplied by a decreasing fraction (effectively divided by decreasing integers).
- $12600 \times \frac{1}{7} = 1800$
- $1800 \times \frac{1}{6} = 300$
- $300 \times \frac{1}{5} = 60$
- $60 \times \frac{1}{4} = \mathbf{15}$
- $15 \times \frac{1}{3} = 5$
Thus, correct answer is option (a) 15
Q80. ?, 189, 176, 193, 172, 197
(a) 150
(b) 180
(c) 140
(d) 120
(e) 130
Answer: (b)
Solution:
Pattern: The differences between the numbers follow an alternating addition and subtraction pattern, where the absolute difference increases by 4 each time.
- $\mathbf{180} + 9 = 189$
- $189 – 13 = 176$
- $176 + 17 = 193$
- $193 – 21 = 172$
- $172 + 25 = 197$
Thus, correct answer is option (b) 180
Q81. 8, 224, 249, 313, 322, ?
(a) 315
(b) 330
(c) 340
(d) 320
(e) 300
Answer: (b)
Solution:
Pattern: Alternatingly add the cube and the square of decreasing integers, starting from 6.
- $8 + 6^{3} (216) = 224$
- $224 + 5^{2} (25) = 249$
- $249 + 4^{3} (64) = 313$
- $313 + 3^{2} (9) = 322$
- $322 + 2^{3} (8) = \mathbf{330}$
Thus, correct answer is option (b) 330
Q82. 21, ?, 135, 544, 2725, 16356
(a) 105
(b) 84
(c) 100
(d) 24
(e) 44
Answer: (e)
Solution:
Pattern: Multiply by $n$ and then add $n$, where $n$ starts at 2 and increases by 1 for each step.
- $21 \times 2 + 2 = \mathbf{44}$
- $44 \times 3 + 3 = 135$
- $135 \times 4 + 4 = 544$
- $544 \times 5 + 5 = 2725$
- $2725 \times 6 + 6 = 16356$
Thus, correct answer is option (e) 44
Q83. Seven years hence, the ratio of age of A to that of B will be 2:1. If the ratio of age of A to that of B three years hence will be 5:2, then find the present age (in years) of B?
(a) 12
(b) 5
(c) 9
(d) 6
(e) 8
Answer: (b)
Solution:
Seven years from now: The ages will be $(a + 7)$ and $(b + 7)$.
$$\frac{a + 7}{b + 7} = \frac{2}{1} \implies a + 7 = 2b + 14 \implies a = 2b + 7 \quad \text{— (Eq. 1)}$$
Three years from now: The ages will be $(a + 3)$ and $(b + 3)$.
$$\frac{a + 3}{b + 3} = \frac{5}{2} \implies 2a + 6 = 5b + 15 \implies 2a – 5b = 9 \quad \text{— (Eq. 2)}$$
Substitution: Substitute $a$ from Eq. 1 into Eq. 2:
$2(2b + 7) – 5b = 9 \implies 4b + 14 – 5b = 9 \implies -b = -5 \implies \mathbf{b = 5}$
Thus, correct answer is option (b) 5
Q84. The difference of two positive numbers is 2. If 50% of bigger number is equal to 60% of smaller number, then find the bigger number?
(a) 12
(b) 10
(c) 9
(d) 14
(e) 16
Answer: (a)
Solution:
Equation 1: $x – y = 2$
Equation 2: $50\% \text{ of } x = 60\% \text{ of } y$
$0.5x = 0.6y \implies 5x = 6y \implies x = \frac{6y}{5}$
Solve: Substitute $x$ in the first equation:
$\frac{6y}{5} – y = 2 \implies \frac{y}{5} = 2 \implies y = 10$.
Since $x = y + 2$, then $\mathbf{x = 12}$.
Thus, correct answer is option (a) 12
Q85. A vessel contains 120 liters mixture of milk and water and water is 25% of milk in the vessel. If 12 liters of water added in the vessel, then find the ratio of water to milk in the resulting mixture?
(a) 5 : 8
(b) 8 : 3
(c) 3 : 8
(d) 1 : 5
(e) 2 : 3
Answer: (c)
Solution:
Initial Ratio: If milk is $100\%$, water is $25\%$. Ratio $M:W = 100:25 = 4:1$.
Find Quantities: Total parts = $4 + 1 = 5$.
- Milk $= 120 \times \frac{4}{5} = 96$ liters.
- Water $= 120 \times \frac{1}{5} = 24$ liters.
After Adding Water: New water $= 24 + 12 = 36$ liters. Milk remains $96$ liters.
New Ratio (Water : Milk): $36 : 96$. Dividing both by $12$, we get $\mathbf{3 : 8}$.
Thus, correct answer is option (c) 3 : 8
Q86. The ratio of upstream speed of a boat and speed of current is 4:1. If in downstream the boat can cover 60 km in 2.5 hours, then find out the speed of current?
(a) 6 kmph
(b) 4 kmph
(c) 5 kmph
(d) 8 kmph
(e) 3 kmph
Answer: (b)
Solution:
Definitions: Let speed of boat in still water be $u$ and speed of current be $v$.
- Upstream speed $= u – v$
- Downstream speed $= u + v$
Given Ratio: $\frac{u – v}{v} = \frac{4}{1} \implies u – v = 4v \implies u = 5v$.
Downstream Calculation: Speed $= \frac{\text{Distance}}{\text{Time}} = \frac{60}{2.5} = 24$ kmph.
So, $u + v = 24$.
Solve for $v$: Substitute $u = 5v$:
$5v + v = 24 \implies 6v = 24 \implies \mathbf{v = 4}$ kmph.
Thus, correct answer is option (b) 4 kmph
Q87. If the numerator of a fraction is increased by 150% and the denominator of the fraction is decreased by 25%, the resultant fraction is of 8. What is the original fraction.?
(a) 2/7
(b) 4/15
(c) 2/9
(d) 4/17
(e) 5/18
Answer: (b)
Solution:
Resultant Value: $11 \frac{1}{9}\% = \frac{100}{9}\% = \frac{1}{9}$ in fraction form.
Resultant $= \frac{1}{9} \times 8 = \frac{8}{9}$.
Apply Changes: Let original fraction be $\frac{x}{y}$.
- New Numerator $= x + 1.5x = 2.5x$
- New Denominator $= y – 0.25y = 0.75y$
Equation: $\frac{2.5x}{0.75y} = \frac{8}{9}$
$\frac{250x}{75y} = \frac{8}{9} \implies \frac{10x}{3y} = \frac{8}{9}$
$\frac{x}{y} = \frac{8}{9} \times \frac{3}{10} = \frac{4}{3} \times \frac{1}{5} = \mathbf{\frac{4}{15}}$
Thus, correct answer is option (b) 4/15
Directions (88 -100): What will come in the place of question mark (?) in the place of question mark.
Q88. $\mathbf{frac{\sqrt{48}\times\sqrt{24}}{\sqrt{35}} = ?}$
(a) 4
(b) 12
(c) 8
(d) 6
(e) 10
Answer: (d)
Solution:
Step 1: Round the numbers to the nearest perfect squares.
- $\sqrt{48} \approx \sqrt{49} = 7$
- $\sqrt{24} \approx \sqrt{25} = 5$
- $\sqrt{35} \approx \sqrt{36} = 6$
Step 2: Solve the simplified expression: $\frac{7 \times 5}{6} = \frac{35}{6} = 5.83$.
Step 3: Round $5.83$ to the nearest whole number, which is 6.
Thus, correct answer is option (d) 6
Q89. $\mathbf{\frac{85\times108\times72}{17\times18\times12} + \frac{55}{11} = \frac{370}{?}}$
(a) 0.5
(b) 1
(c) 3
(d) 2
(e) 4
Answer: (d)
Solution:
Step 1: Simplify the first fraction: $\frac{85}{17} \times \frac{108}{18} \times \frac{72}{12} = 5 \times 6 \times 6 = 180$.
Step 2: Simplify the second fraction: $\frac{55}{11} = 5$.
Step 3: Add the values: $180 + 5 = 185$.
Step 4: Set up the final equation: $185 = \frac{370}{?}$.
Step 5: $? = \frac{370}{185} = \mathbf{2}$.
Thus, correct answer is option (d) 2
Q90. $\mathbf{? + 15\frac{3}{4} – 3\frac{1}{3} \times 3\frac{3}{4} = 5}$
(a) 1.5
(b) 2.25
(c) 1.75
(d) 2
(e) 2.75
Answer: (c)
Solution:
Step 1: Convert mixed fractions to improper fractions: $15\frac{3}{4} = \frac{63}{4}$ and $3\frac{1}{3} = \frac{10}{3}$ and $3\frac{3}{4} = \frac{15}{4}$.
Step 2: Perform multiplication first: $\frac{10}{3} \times \frac{15}{4} = \frac{50}{4} = \frac{25}{2}$.
Step 3: Rewrite the equation: $? + \frac{63}{4} – \frac{25}{2} = 5$.
Step 4: $? = 5 – \frac{63}{4} + \frac{50}{4} = 5 – \frac{13}{4}$.
Step 5: $? = \frac{20 – 13}{4} = \frac{7}{4} = \mathbf{1.75}$.
Thus, correct answer is option (c) 1.75
Q91. $\mathbf{\frac{?}{\sqrt{25}} = \frac{15\times4 – 40}{2}}$
(a) 20
(b) 45
(c) 25
(d) 50
(e) 60
Answer: (d)
Solution:
Step 1: Simplify the right side: $\frac{60 – 40}{2} = \frac{20}{2} = 10$.
Step 2: Substitute $\sqrt{25} = 5$: $\frac{?}{5} = 10$.
Step 3: $? = 10 \times 5 = \mathbf{50}$.
Thus, correct answer is option (d) 50
Q92. $\mathbf{\frac{510}{?} = \sqrt{324} + \sqrt{256}}$
(a) 20
(b) 5
(c) 10
(d) 15
(e) 25
Answer: (d)
Solution:
Step 1: Find the square roots: $\sqrt{324} = 18$ and $\sqrt{256} = 16$.
Step 2: Add the roots: $18 + 16 = 34$.
Step 3: Solve for $?$: $\frac{510}{?} = 34 \implies ? = \frac{510}{34} = \mathbf{15}$.
Thus, correct answer is option (d) 15
Q93. 45% of 800 + 60 – 270 = ?
(a) 90
(b) 60
(c) 120
(d) 180
(e) 150
Answer: (e)
Solution:
Step 1: Calculate the percentage: $\frac{45}{100} \times 800 = 360$.
Step 2: Solve the rest: $360 + 60 – 270 = 420 – 270 = \mathbf{150}$.
Thus, correct answer is option (e) 150
Q94. $ \mathbf{ \frac{9}{17} \times 867 + 112\%}$ of $ \mathbf{400 – 39 = ?}$
(a) 846
(b) 868
(c) 818
(d) 826
(e) 834
Answer: (b)
Solution:
Step 1: Divide 867 by 17: $867 \div 17 = 51$.
Step 2: Multiply: $9 \times 51 = 459$.
Step 3: Calculate percentage: $1.12 \times 400 = 448$.
Step 4: Combine values: $459 + 448 – 39 = 907 – 39 = \mathbf{868}$.
Thus, correct answer is option (b) 868
Q95. $\mathbf{\frac{4}{5}}$ of $\mathbf{\frac{3}{8}}$ of $\mathbf{\frac{15}{27} \times ? = 60\%}$ of $\mathbf{270}$
(a) 898
(b) 972
(c) 540
(d) 1056
(e) 752
Answer: (b)
Solution:
Step 1: Simplify the fraction series: $\frac{4}{5} \times \frac{3}{8} \times \frac{15}{27} = \frac{1}{6}$.
Step 2: Calculate RHS: $0.6 \times 270 = 162$.
Step 3: Solve for $?$: $\frac{1}{6} \times ? = 162 \implies ? = 162 \times 6 = \mathbf{972}$.
Thus, correct answer is option (b) 972
Q96. 4 of $ \mathbf{143 \div 26 \times 12 – 200 = ?}$
(a) 58
(b) 64
(c) 72
(d) 80
(e) 74
Answer: (b)
Solution:
Step 1: Handle “of” first: $4 \times 143 = 572$.
Step 2: Divide: $572 \div 26 = 22$.
Step 3: Multiply: $22 \times 12 = 264$.
Step 4: Subtract: $264 – 200 = \mathbf{64}$.
Thus, correct answer is option (b) 64
Q97. $\mathbf{30\%}$ of $\mathbf{? = 38 + \frac{147}{3}}$
(a) 281
(b) 300
(c) 290
(d) 315
(e) None of these
Answer: (c)
Solution:
Step 1: Simplify the fraction: $\frac{147}{3} = 49$.
Step 2: Add values: $38 + 49 = 87$.
Step 3: Solve for $?$: $\frac{30}{100} \times ? = 87 \implies ? = \frac{87 \times 100}{30} = 29 \times 10 = \mathbf{290}$.
Thus, correct answer is option (c) 290
Q98. $\mathbf{\frac{272}{4} – 18 \times 6 + \sqrt[3]{1331} = ?}$
(a) -36
(b) 36
(c) -29
(d) 29
(e) None of these
Answer: (c)
Solution:
Step 1: Divide: $272 \div 4 = 68$.
Step 2: Multiply: $18 \times 6 = 108$.
Step 3: Cube root: $\sqrt[3]{1331} = 11$.
Step 4: Solve: $68 – 108 + 11 = -40 + 11 = \mathbf{-29}$.
Thus, correct answer is option (c) -29
Q99. $\mathbf{1512 \div 36 + 44 \times 32 = ?}$
(a) 1450
(b) 1350
(c) 1150
(d) 1460
(e) None of these
Answer: (a)
Solution:
Step 1: Divide: $1512 \div 36 = 42$.
Step 2: Multiply: $44 \times 32 = 1408$.
Step 3: Add: $42 + 1408 = \mathbf{1450}$.
Thus, correct answer is option (a) 1450
Q100. $\mathbf{5\frac{5}{8} \times 2\frac{2}{3} – 9\frac{1}{5} + 5\frac{1}{2} = ?}$
(a) $11\frac{3}{10}$
(b) $9\frac{7}{10}$
(c) $8\frac{3}{10}$
(d) $10\frac{7}{10}$
(e) $12\frac{3}{10}$
Answer: (a)
Solution:
Step 1: Convert to improper: $\frac{45}{8} \times \frac{8}{3} – \frac{46}{5} + \frac{11}{2}$.
Step 2: Multiply: $\frac{45}{8} \times \frac{8}{3} = 15$.
Step 3: Combine: $15 – \frac{46}{5} + \frac{11}{2} = 15 – 9.2 + 5.5 = \mathbf{11.3}$.
Step 4: Convert to mixed: $11.3 = \mathbf{11\frac{3}{10}}$.
Thus, correct answer is option (a) $11\frac{3}{10}$