# GRE® Quant Practice | Ratios Q1

#### GRE Sample Questions | Ratios Percents Profits Questionbank

The GRE maths sample question given below is a problem solving question in Ratio, Percent, Fractions. This GRE sample question is an easy word problem testing the concept of combining two ratios into one ratio.

Question 1: If the ratio of the ages of two friends A and B is 3 : 5 and that of B and C is 3 : 5 and the sum of the ages of all 3 friends is 147, how old is B ?

1. 15 years
2. 75 years
3. 49 years
4. 45 years
5. 27 years

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### Explanatory Answer | GRE Quant Sample Question 1

#### Given Data

Ratio of ages of two friends A and B = 3 : 5
Ratio of ages of two friends B and C = 3 : 5
Sum of the ages of A, B and C = A + B + C = 147 ... (i)

#### Step 1: Express the ratios such that value of B is the same in both ratios

How to equate the value of B in both the ratios?
Rewrite the two ratios such that the value of B in both ratios is the LCM of the values of B in the two ratios.

Multiply the first ratio by 3 → A : B = 9 : 15
Multiply the second ratio by 5 → B : C = 15 : 25

#### Step 2: Compute A : B : C

Now that the value of B is the same in the two ratios, A : B : C = 9 : 15 : 25

#### Step 3: Compute Age of B

So, if A is 9x years old, B will be 15x and C will be 25x old. Sum of their ages is 147.
So, 9x + 15x + 25x = 147
49x = 147 or x = 3
B's age = 15x = 15 × 3 = 45
Age of B = 45 years

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