Two numbers, A and B, are such that the sum of 10% of A and 8% of B is $\frac{3}{5}$ th of the sum of 12% of A and 16% of B. The ratio A : B is:

4 ∶ 7

a% of b = $\frac{a}{100}$ x b

10% of A + 8% of B = $\frac{3}{5}$(12% of A + 16% of B)

⇒ [($\frac{10A}{100}$) +($\frac{8B}{100}$)] = ($\frac{3}{5}$)[($\frac{12A}{100}$) +($\frac{16B}{100}$)]

⇒(10A + 8B) = ($\frac{3}{5}$)(12A + 16B)

⇒ 5 x (10A + 8B) = 3 x (12A + 16B)

⇒ 50A + 40B = 36A + 48B 

⇒ 14A = 8B 

⇒ $\frac{A}{B}$ = $\frac{8}{14}$

⇒ A  :  B = 8 : 14 = 4 : 7