If 2 times Mary's present age is 27 years more than 5 times Dia's present age, and 7 times Dia's present age is 9 years less than Mary's present age, then what is the difference (in years) between the ages of Mary and Dia?

Correct option is B

Given:

Two times Marry present age = 5 times Dia age + 27 

7 times Dia present age = Marry present age - 9 

2M = 27 + 5D

7D = M - 9

Find the difference between ages of Mary (M) and Dia (D)

Solution: 

Let Marry present age be M and Dia present age be D 

So, 

2M = 27 + 5D .........(1)

7D = M - 9 ............(2) 

From second equation:

M = 7D + 9

Substitute into first:

2(7D + 9) = 27 + 5D

14D + 18 = 27 + 5D

14D - 5D = 27 - 18

9D = 9

D = 1

Now,

M = 7D + 9 = 7(1) + 9 = 16

Difference = M - D = 16 - 1 = 15 years