SSC Selection Post 2020 PYQ — Question 63

The correct answer is option 1 i.e. 11 : 15.

 

A = x , B = y

4 years ago, their ages were:

A = x - 4 , B = y - 4

$\frac{x - 4}{y - 4} = \frac{9}{13} \Rightarrow 13(x - 4) = 9(y - 4) \Rightarrow 13x - 52 = 9y - 36$

$\Rightarrow 13x - 9y = 16$ Equation 1

8 years hence, their ages will be:

A = x + 8 ,  B = y + 8

$\frac{x + 8}{y + 8} = \frac{3}{4} \Rightarrow 4(x + 8) = 3(y + 8) \Rightarrow 4x + 32 = 3y + 24$

$\Rightarrow 4x - 3y = -8$ Equation 2

$3(4x - 3y) = 3(-8) \Rightarrow 12x - 9y = -24$ Equation 3

Now subtract Equation 3  from Equation 1:

$(13x - 9y) - (12x - 9y) = 16 - (-24) \Rightarrow x = 40$

x = 40 into Equation 1:

$13(40) - 9y = 16 \Rightarrow 520 - 9y = 16 \Rightarrow 9y = 504$

$\Rightarrow y = 56$

A’s age =  40 + 4 = 44

B’s age = 56 + 4 = 60

Ratio = $\frac{44}{60} = \frac{11}{15}$