₹360 is divided between A and B in the ratio 4 : 5. What is B's share?

₹200. There are 4 + 5 = 9 parts, each worth 360 9 = 40. B receives 5 40 = ₹200.

If a : b = 3 : 4 and b : c = 8 : 9, what is a : c?

2 : 3. Make b the same in both ratios: a : b = 6 : 8 and b : c = 8 : 9, so a : c = 6 : 9 = 2 : 3.

Two numbers are in the ratio 5 : 7. If 12 is added to each, the ratio becomes 3 : 4. What is the smaller number?

60. Let the numbers be 5x and 7x. Then 5x + 127x + 12 = 34, so 20x + 48 = 21x + 36 and x = 12. The smaller number is 5 12 = 60.

The ratio of two numbers is 3 : 5 and their sum is 96. By how much does the larger number exceed the smaller?

24. With 8 parts summing to 96, each part is 12. The numbers are 36 and 60, so the larger exceeds the smaller by 60 - 36 = 24.

₹782 is divided among three people in the ratio 12 : 23 : 34. What is the first person's share?

₹204. Clear the fractions by multiplying each part by 12: the ratio becomes 6 : 8 : 9 (23 parts). Each part is 782 23 = 34, so the first share is 6 34 = ₹204.

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Quantitative Aptitude · Averages, Ratios & Percentages

Ratio and Proportion — Questions & Answers

Ratio questions split a total into parts, combine chained ratios, or scale one quantity with another. Introduce a common multiplier $k$ so each share becomes a real number.

5 solved questions
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Key formulas included

Key formulas

If $a:b:c$ , the shares of total $T$ are $\dfrac{a}{a+b+c}T$ , and so on
Combine $a:b$ and $b:c$ by scaling to a common $b$ , giving $a:b:c$
In a proportion $a:b = c:d$ , the product of the means equals the product of the extremes: $bc = ad$

5 solved Ratio and Proportion questions

Try each question first — tap an option to check your answer, or open Learn step by step for a guided walkthrough.

01
₹360 is divided between A and B in the ratio 4 : 5. What is B's share?
3 steps · reveal one at a time
1. Step 1: Calculate Total Parts
  The amount is divided between A and B in the ratio $4:5$ . To find out how many 'shares' or parts there are in total, we need to add the ratio numbers together. This gives us the total number of equal parts.
2. Step 2: Determine Part Value
  The total amount to be divided is ₹360. We found there are $4 + 5 = 9$ total parts. Now, divide the total amount by the total number of parts to find the value of one single part. This tells us how much money each part represents.
3. Step 3: The answer
  So the answer is (C) ₹200. B's share is 5 parts of the total. Since each part is worth ₹40, B receives $5 \times 40 = \text{\text{Rs}\,}200$ .
02
If $a : b = 3 : 4$ and $b : c = 8 : 9$ , what is $a : c$ ?
5 steps · reveal one at a time
1. Step 1: Understand the Ratios
  We are given two ratios: $a : b = 3 : 4$ and $b : c = 8 : 9$ . Our goal is to find the ratio $a : c$ .
2. Step 2: Align Common Term
  To find a direct ratio between $a$ and $c$ , we need to standardize the common term, $b$ . This means making the value of $b$ the same in both given ratios.
3. Step 3: Adjust First Ratio
  In $a : b = 3 : 4$ , $b$ is $4$ . In $b : c = 8 : 9$ , $b$ is $8$ . To make $b$ equal to $8$ in the first ratio, we multiply both parts by $2$ . This gives $a : b = (3 \times 2) : (4 \times 2) = 6 : 8$ .
4. Step 4: Combine and Simplify
  Now we have $a : b = 6 : 8$ and $b : c = 8 : 9$ . Since the value of $b$ is now $8$ in both, we can see that $a : c = 6 : 9$ . This ratio can be simplified by dividing both parts by their greatest common divisor, $3$ . So, $6 : 9 = (6 \div 3) : (9 \div 3) = 2 : 3$ .
5. Step 5: The answer
  So the answer is (A) 2 : 3. This is the simplified ratio of $a$ to $c$ after making the common term $b$ consistent.
03
Two numbers are in the ratio 5 : 7. If 12 is added to each, the ratio becomes 3 : 4. What is the smaller number?
4 steps · reveal one at a time
1. Step 1: Represent the numbers
  Let the two numbers be $5x$ and $7x$ . This uses a common multiplier $x$ to represent their actual values, maintaining their initial ratio of $5 : 7$ .
2. Step 2: Formulate the equation
  When 12 is added to each number, the new ratio becomes $3 : 4$ . We can write this as an equation: $\frac{5x + 12}{7x + 12} = \frac{3}{4}$ .
3. Step 3: Solve for the multiplier
  Cross-multiply to solve for $x$ : $4(5x + 12) = 3(7x + 12)$ . This simplifies to $20x + 48 = 21x + 36$ . Subtracting $20x$ and $36$ from both sides gives $x = 12$ .
4. Step 4: The answer
  The smaller number is $5x$ . Substitute $x = 12$ into $5x$ to get $5 \times 12 = 60$ . So the answer is (C) 60, which is the smaller of the two numbers.
04
The ratio of two numbers is 3 : 5 and their sum is 96. By how much does the larger number exceed the smaller?
5 steps · reveal one at a time
1. Step 1: Understand the Ratio
  We are given two numbers in the ratio of $3 : 5$ . This means the first number can be represented as $3x$ and the second as $5x$ . Their sum is given as 96.
2. Step 2: Calculate Total Parts
  The ratio $3 : 5$ tells us there are $3 + 5 = 8$ equal parts in total. Since the sum of the two numbers is 96, these 8 parts together equal 96.
3. Step 3: Value of One Part
  To find the value of one part, we divide the total sum by the total number of parts. So, each part is worth $96 \div 8 = 12$ .
4. Step 4: Find the Numbers
  Now we can find the actual numbers. The smaller number is $3 \times 12 = 36$ . The larger number is $5 \times 12 = 60$ . We have our two numbers.
5. Step 5: The answer
  So the answer is (A) 24. The question asks by how much the larger number exceeds the smaller, which is $60 - 36 = 24$ .
05
₹782 is divided among three people in the ratio $\dfrac{1}{2} : \dfrac{2}{3} : \dfrac{3}{4}$ . What is the first person's share?
4 steps · reveal one at a time
1. Step 1: Simplify the Ratio
  The given ratio is $\frac{1}{2} : \frac{2}{3} : \frac{3}{4}$ . To make it easier to work with, we need to remove the fractions. Find the least common multiple (LCM) of the denominators (2, 3, 4), which is 12.
2. Step 2: Convert to Whole Numbers
  Multiply each part of the ratio by the LCM, 12. This gives us $(12 \times \frac{1}{2}) : (12 \times \frac{2}{3}) : (12 \times \frac{3}{4})$ , which simplifies to $6 : 8 : 9$ . This is the ratio of shares.
3. Step 3: Calculate Share Value
  The total number of parts in the simplified ratio is $6 + 8 + 9 = 23$ parts. The total amount is ₹782. So, each part is worth $782 \div 23 = 34$ rupees.
4. Step 4: The answer
  So the answer is (B) ₹204. The first person's share corresponds to 6 parts in the ratio. Therefore, the first person's share is $6 \times 34 = \text{\text{Rs}\,}204$ .

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