Question

What quantity must be added to each term of the ratio 7:13 so as to make it equal to 9:11

• A. 21
• B. 20
• C. 19
• D. 18

Answer 1

The correct option is B

20

Let x be the quantity to be added to each term in the ratio 7:13.

The resultant ratio is equal to 9:11.

So we have,

$\frac{7+x}{13+x}=\frac{9}{11}$

ie. 11(7+x) = 9(13+x)

77 + 11x = 117 + 9x

11x - 9x = 117 - 77

2x = 40

x = 20

So the quantity that should be added to the initial ratio is 20.

Verification: LHS = $\frac{7+20}{13+20}=\frac{27}{33}=\frac{9}{11}$ = RHS