Question

Three numbers are in the ratio 1/2 : 2/3 : 3/4. The difference between the largest and the smallest number is 21. The sum of all the numbers is _______.
1. 210
2. 150
3. 161
4. 195

Answer 1

Correct Answer - Option 3 : 161

Given:

Three numbers are in the ratio 1/2 : 2/3 : 3/4. 

Largest number - Smallest number = 21

Calculation:

Given ratio = 1/2 : 2/3 : 3/4

⇒ 12 × 1/2 : 12 × 2/3 : 12 × 3/4

⇒ 6 : 8 : 9

Now, let the ratio be x 

1st Number = 6x, 2nd Number = 8x & 3rd Number = 9x 

Now, Again according to the question

9x - 6x = 21

⇒ 3x = 21

⇒ x = 7

Now, Sum of three numbers = 6x + 8x + 9x

⇒ Sum of three numbers = 23x

⇒ Sum of three numbers = 23 × 7 = 161

∴ The sum of three numbers is 161.