Question

4 travellers A, B, C and D are going on a trip by bus and their average age is ‘x’ years. After some time, D gets down from the bus. Now the ratio between the average age of remaining 3 travellers and the previous average age is 11 : 12. If the age of D is 9 years more than the previous average age, then find the ratio between the age of D and the average age of remaining 3 travellers?
1. 15 : 11
2. 16 : 13
3. 15 : 13
4. 16 : 11

Answer 1

Correct Answer - Option 1 : 15 : 11

Let the ages of A, B, C, and D are ‘a’, ‘b’, ‘c’ and ‘d’ respectively.

Given, the average age of 4 travellers A, B, C and D

(a + b + c + d)/4 = x

a + b + c + d = 4x      ---- (1)

So, the average age of 3 travellers A, B and C

(a + b + c)/3 = 11x/12

a + b + c = 11x/4     ---- (2)

Also given,

d – x = 9      ---- (3)

From equations (1) and (2) :

(11x/4) + d = 4x

11x + 4d = 16x

5x = 4d

5(d – 9) = 4d

d = 45 and x = 36

The average age of remaining 3 travellers = 36 × 11/12 = 33

Required ratio = 45 : 33 = 15 : 11