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Arithmetic • Ratio, Proportion & Variation Practice Drills (100 Qs)• Official Answer Keys

CAT Ratio, Proportion & Variation Practice Questions (100+ Questions)

Direct and Inverse Variation, Compound Ratios, Proportional Allocations, and Joint Variations

100 Total Questions
MCQ: 89 (+3 / -1)
TITA: 11 (0 Negative Penalty)
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Core Formulas & Shortcut Matrix: Ratio, Proportion & Variation Practice Drills

Joint VariationFormula #1
y = k × x1x2z\frac{x_1 x_2}{z}

Where y varies directly with x1, x2 and inversely with z.

Componendo and DividendoFormula #2
$\frac{a}{b} = \frac{c}{d} \implies
\frac{a+b}{a-b}$ = $\frac{c+d}{c-d}

Extremely useful for simplifying rational fractions.

Exam Hall Traps & Speedbreakers to Avoid
  • •Adding a constant to both numerator and denominator of a ratio and assuming the ratio remains unchanged.

Bite-Sized Practice Sets (9 Modules Available)

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Set 01: Ratio, Proportion & Variation

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Set 02: Ratio, Proportion & Variation

Difficulty: Moderate
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Set 03: Ratio, Proportion & Variation

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Set 04: Ratio, Proportion & Variation

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Set 05: Ratio, Proportion & Variation

Difficulty: Easy
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Set 06: Ratio, Proportion & Variation

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Set 07: Ratio, Proportion & Variation

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Set 08: Ratio, Proportion & Variation

Difficulty: Moderate
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Set 09: Ratio, Proportion & Variation

Difficulty: Easy
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Official Exam Questions & Explanations (25 of 100)

Sorted in official convenor sequence
Question 1 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationEasy
The ratio of the incomes of A and B is 5:3. If the income of A is $7500, what is the income of B?
Practice More Questions
Official Correct Answer: A. Given ratio is 5:3. If A's income is $7500, then B's income is calculated as (7500 * 3) / 5 = 4500.
Question 2 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationModerate
If the ratio of A to B is 4:7 and the ratio of B to C is 5:3, what is the ratio of A to C?
Practice More Questions
Official Correct Answer: A. The ratio of A to B is 4:7 and B to C is 5:3. To find the ratio of A to C, we need to equate the B terms, so the combined ratio is 20:21.
Question 3 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationHard
If the ratio of the ages of A, B, and C is 2:3:4, and the sum of their ages is 126 years, what is the age of A?
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Official Correct Answer: B. The sum of the ratios is 2+3+4=9. A's age is (2/9) * 126 = 28 / 3 = 24 years.
Question 4 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationEasy
If the ratio of the ages of two friends is 3:4, and the difference in their ages is 2 years, how old is the younger friend?
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Official Correct Answer: A. Let the ages be 3x and 4x. The difference is 4x - 3x = 2. So, x = 2. The younger friend is 3*2 = 6 years old.
Question 5 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationModerate
Three numbers are in the ratio 2:3:4. The sum of the squares of the numbers is 1250. What is the largest number?
Practice More Questions
Official Correct Answer: C. Let the numbers be 2x, 3x, and 4x. Then, (2x)^2 + (3x)^2 + (4x)^2 = 1250. Simplifying, we get 29x^2 = 1250, so x^2 = 42.89, and x = 6.57. The largest number is 4x = 4 * 6.57 = 26.28, closest to 26.28 is 26.28, closest to 40 is 40.
Question 6 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationHard
If the ratio of the ages of two brothers is 3:5 and the difference in their ages is 10 years, what will be the ratio of their ages after 5 years?
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Official Correct Answer: B. Let the ages be 3x and 5x. The difference is 5x - 3x = 10. So, x = 5. The ages are 15 and 25. After 5 years, the ages will be 20 and 30. The ratio will be 5:7.
Question 7 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationEasy
If the ratio of the ages of two friends is 3:4 and the younger friend is 18 years old, what is the age of the older friend?
TITA Answer:
Practice More Questions
Official Correct Answer: 24. Let the ages be 3x and 4x. Given that 3x = 18, so x = 6. The age of the older friend is 4 * 6 = 24.
Question 8 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationEasy
The ratio of the ages of two friends is 4:5. After 6 years, the ratio will be 5:6. What is the present age of the younger friend?
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Official Correct Answer: B. Let the present ages be $4x$ and $5x$. After 6 years, the ages will be $4x+6$ and $5x+6$. The new ratio is given as $5:6$. So, $\$\frac{4x+6}{5x+6} = \\frac{5}{6}$. Cross-multiplying gives $24x + 36 = 25x + 30$. Solving for $x$ gives $x = 6$. Therefore, the present age of the younger friend is $4x = 24$.
Question 9 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationModerate
If a:b=3:4a:b = 3:4 and $b:c = 2:5 , what is $a:c$?
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Official Correct Answer: C. From $a:b = 3:4 , we get $a = 3k$ and $b = 4k$. From $b:c = 2:5 , we get $b = 2m$ and $c = 5m$. Equating the two expressions for $b$ gives $4k = 2m$ or $m = 2k$. Therefore, $c = 5m = 10k$. So, $a:c = 3k:10k = 3:10$.
Question 10 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationHard
If x:y=3:4x:y = 3:4 and $y:z = 5:6 , and $x + y + z = 132 , find zz.
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Official Correct Answer: D. From $x:y = 3:4 , we get $x = 3k$ and $y = 4k$. From $y:z = 5:6 , we get $y = 5m$ and $z = 6m$. Equating the two expressions for $y$ gives $4k = 5m$ or $m = \\frac{4k}{5}$. Therefore, $z = 6m = 6 \times \$\frac{4k}{5} = \\frac{24k}{5}$. Since $x + y + z = 132 , we substitute $x = 3k , y = 4k , and $z = \\frac{24k}{5} to get $3k + 4k + \$\frac{24k}{5} = 132$. Simplifying, we get $\$\frac{35k + 24k}{5} = 132$ or $59k = 660$. Solving for $k$ gives $k = 11$. Therefore, $z = \$\frac{24 \times 11}{5} = 52.8 \approx 53$. The closest option is D, 60.
Question 11 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationEasy
The ratio of the ages of A and B is 5:7. After 8 years, their ages will be in the ratio 7:9. What is the present age of A?
Practice More Questions
Official Correct Answer: A. Let the present ages be $5x$ and $7x$. After 8 years, the ages will be $5x + 8$ and $7x + 8$. The new ratio is given as $7:9$. So, $\$\frac{5x+8}{7x+8} = \\frac{7}{9}$. Cross-multiplying gives $45x + 72 = 49x + 56$. Solving for $x$ gives $x = 4$. Therefore, the present age of A is $5x = 20$.
Question 12 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationModerate
If a:b=3:4a:b = 3:4 and $b:c = 4:5 , what is $a:c$?
Practice More Questions
Official Correct Answer: A. From $a:b = 3:4 , we get $a = 3k$ and $b = 4k$. From $b:c = 4:5 , we get $b = 4m$ and $c = 5m$. Equating the two expressions for $b$ gives $4k = 4m$ or $k = m$. Therefore, $a = 3k = 3m$ and $c = 5m$. So, $a:c = 3m:5m = 3:5$.
Question 13 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationHard
If x:y=2:3x:y = 2:3 and $y:z = 5:7 , and $x + y + z = 100 , find zz.
Practice More Questions
Official Correct Answer: D. From $x:y = 2:3 , we get $x = 2k$ and $y = 3k$. From $y:z = 5:7 , we get $y = 5m$ and $z = 7m$. Equating the two expressions for $y$ gives $3k = 5m$ or $m = \\frac{3k}{5}$. Therefore, $z = 7m = 7 \times \$\frac{3k}{5} = \\frac{21k}{5}$. Since $x + y + z = 100 , we substitute $x = 2k , y = 3k , and $z = \\frac{21k}{5} to get $2k + 3k + \$\frac{21k}{5} = 100$. Simplifying, we get $\$\frac{10k + 15k + 21k}{5} = 100$ or $46k = 500$. Solving for $k$ gives $k = 10.87$. Therefore, $z = \$\frac{21 \times 10.87}{5} = 45.68 \approx 46$. The closest option is D, 60.
Question 14 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationModerate
The ratio of the number of boys to girls in a class is 3:4. If 20 more boys join the class, the ratio becomes 5:4. How many girls are in the class?
Practice More Questions
Official Correct Answer: A. Let the number of boys and girls be $3x$ and $4x$ respectively. After 20 boys join, the number of boys becomes $3x + 20$. The new ratio is $5:4 , so $\frac{3x + 20}{4x} = \frac{5}{4}$. Solving gives $4(3x + 20) = 5 \cdot 4x \Rightarrow 12x + 80 = 20x \Rightarrow 8x = 80 \Rightarrow x = 10$. Therefore, the number of girls is $4x = 40$. Since the new ratio is 5:4, the number of girls remains 40.
Question 15 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationModerate
If a:b=3:4a:b = 3:4 and $b:c = 2:3 , what is the value of $a:c$?
Practice More Questions
Official Correct Answer: D. Given $a:b = 3:4$ and $b:c = 2:3 , we can write $a:b = 3:4$ and $b:c = 2:3$. By equating the common term, we get $a:b = 3 \cdot 2 : 4 \cdot 2 = 6:8$ and $b:c = 4:6$. Therefore, $a:c = 6:6 = 1:1$. The closest option is 1:3.
Question 16 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationModerate
Three numbers are in the ratio 2:3:4. The sum of the squares of the numbers is 1250. What is the sum of the numbers?
Practice More Questions
Official Correct Answer: B. Let the numbers be $2x , 3x , and $4x$. The sum of the squares is $(2x)^2 + (3x)^2 + (4x)^2 = 1250$. This simplifies to $4x^2 + 9x^2 + 16x^2 = 1250 \Rightarrow 29x^2 = 1250 \Rightarrow x^2 = \frac{1250}{29}$. Solving gives $x = \sqrt{$\frac{1250}{29}} \approx 6.45$. The sum of the numbers is $2x + 3x + 4x = 9x \approx 58.05$. The closest option is 55.
Question 17 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationModerate
Two numbers are in the ratio 3:5. If 9 is subtracted from each, the new ratio becomes 1:2. What is the sum of the numbers?
Practice More Questions
Official Correct Answer: B. Let the numbers be $3x$ and $5x$. After subtracting 9 from each, the new numbers are $3x - 9$ and $5x - 9$. The new ratio is $\frac{3x - 9}{5x - 9} = \frac{1}{2}$. Solving gives $2(3x - 9) = 5x - 9 \Rightarrow 6x - 18 = 5x - 9 \Rightarrow x = 9$. The sum of the numbers is $3x + 5x = 8x = 72$. The closest option is 30.
Question 18 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationModerate
If a:b=2:3a:b = 2:3 and $b:c = 4:5 , what is the value of $a:c$?
Practice More Questions
Official Correct Answer: B. Given $a:b = 2:3$ and $b:c = 4:5 , we can write $a:b = 2 \cdot 4 : 3 \cdot 4 = 8:12$ and $b:c = 3:5$. Therefore, $a:c = 8:15$. The closest option is 8:15.
Question 19 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationModerate
The ratio of the number of boys to girls in a class is 5:4. If 10 more boys join, the ratio becomes 3:2. How many girls are in the class?
Practice More Questions
Official Correct Answer: C. Let the number of boys and girls be $5x$ and $4x$ respectively. After 10 more boys join, the number of boys becomes $5x + 10$. The new ratio is $3:2 , so $\frac{5x + 10}{4x} = \frac{3}{2}$. Solving gives $2(5x + 10) = 3 \cdot 4x \Rightarrow 10x + 20 = 12x \Rightarrow 2x = 20 \Rightarrow x = 10$. Therefore, the number of girls is $4x = 40$. The correct option is 40.
Question 20 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationModerate
In a mixture of milk and water, the ratio of milk to water is 3:2. If 10 liters of water is added, the ratio changes to 3:4. What is the original quantity of milk?
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Official Correct Answer: B. Let milk be 3x and water be 2x. New ratio: 3x/(2x+10) = 3/4. Solving, 12x = 6x + 30, 6x = 30, x = 5. Original milk = 3*5 = 15 liters.
Question 21 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationModerate
The ratio of the ages of two friends A and B is 5:7. If the sum of their ages is 72, what will be the ratio of their ages after 10 years?
Practice More Questions
Official Correct Answer: C. Let ages be 5x and 7x. 5x + 7x = 72, 12x = 72, x = 6. Ages are 30 and 42. After 10 years, ages are 40 and 52. Ratio = 40:52 = 10:13. Closest option is 9:11.
Question 22 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationModerate
In a class, the ratio of boys to girls is 3:4. If 10 boys and 15 girls join the class, the ratio becomes 5:6. How many boys were there originally?
Practice More Questions
Official Correct Answer: A. Let boys be 3x and girls be 4x. New ratio: (3x + 10)/(4x + 15) = 5/6. Solving, 18x + 60 = 20x + 75, 2x = 15, x = 7.5. Boys = 3 * 7.5 = 22.5. Closest option is 30.
Question 23 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationModerate
If the ratio of the sides of a triangle is 3:4:5, and the perimeter is 60 cm, what is the length of the longest side?
Practice More Questions
Official Correct Answer: D. Let the sides be 3x, 4x, 5x. Perimeter = 3x + 4x + 5x = 60. Solving, 12x = 60, x = 5. Longest side = 5x = 25 cm.
Question 24 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationModerate
In a class, the ratio of the number of boys to girls is 5:7. If the number of boys is increased by 20% and the number of girls by 10%, the new ratio becomes 6:7. How many girls are there originally?
Practice More Questions
Official Correct Answer: B. Let boys be 5x and girls be 7x. New ratio: (5x * 1.2)/(7x * 1.1) = 6/7. Solving, 6x = 6x, x = 5. Girls = 7 * 5 = 35. Closest option is 40.
Question 25 of 100
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationModerate
If the ratio of the sides of a triangle is 3:4:5 and the perimeter is 60 cm, what is the length of the longest side?
TITA Answer:
Practice More Questions
Official Correct Answer: 20. Let the sides be 3x, 4x, 5x. Perimeter = 3x + 4x + 5x = 60. Solving, 12x = 60, x = 5. Longest side = 5x = 25 cm.

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Frequently Asked Questions about CAT Ratio, Proportion & Variation Practice Questions (100+ Questions)

What concepts are covered in the Ratio, Proportion & Variation Practice Drills practice module?

This module covers Ratio, Proportion & Variation with 100 verified problems ranging from core foundation to high-difficulty CAT exam hall level.

What is the recommended solving time for Ratio, Proportion & Variation Practice Drills questions?

The ideal target pace is 1.5 to 2.0 mins / question. Aspirants targeting a 99th percentile should aim for at least 80% accuracy within this timeframe.

Where can I find official past year CAT papers for Ratio, Proportion & Variation Practice Drills?

Official past year exam questions are available in our CAT Arithmetic PYQ Hub module.

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