Three times the present age of Sujatha is 5 years more than two times the present age Vanita. After 3 years: three times the age of Vanita will be 4 years less than four times the age of Sujatha. The age of Vanita is k years more than that of Sujatha. What is the value of k?

Correct option is B

Given:

Three times of present age of Sujatha is 5 years more than 2 times the present age of Vanita

After 3 years, 3 times age of Vanita will be 4 years less than 4 times the age of Sujatha

Solution:

Let the present age of Sujatha be x and present age of Vanita be y

Then 3x = 2y + 5    ….(1)

After 3 years age of Sujatha will be x+3 and Vanita will be y +3

3(y+3) = 4(x+3) - 4    

3y+ 9 = 4x + 12 - 4

4x - 3y = 1    ….(2)

Multiplying eq(1) by 4 and eq(2) by 3    

12x -8y = 20

12x - 9y = 3

Solving eq(1) and eq(2) we get

y = 17

The age of Vanita is 17 years

x = 13years

The age of Sujatha is 13 years

The age of Vanita is 4 more than age of Sujatha hence the value of k = 4