SSC GD 2021 PYQ — Question 51

The correct answer is option 1 i.e. 50%

An average of 39% of A and 42% of B is three-fifths of the difference of A and B i.e 

(39% of A + 42% of B)/2 = 3/5(A - B)

($\dfrac{39 × A}{100}$ + $\dfrac{42 × B}{100}$)/2 = $\dfrac{3}{5} (A - B)$

$\dfrac{39A + 42B}{200}$ = $\dfrac{3}{5} (A - B)$

⇒ 39A + 42B = 120A - 120B

⇒ 81A = 162B

⇒ A = 2B

⇒ B = $\dfrac{A}{2}$

SO B is 50% of A.