Question

Two quantities were in the ratio 1 : 4. On increasing the smaller one by 6 and decreasing the Larger one by 6, The quantities are now in the ratio 7 : 13.

What were the original quantities ?

• A. 10 and 40
• B. 7 and 28
• C. 8 and 32
• D. 4 and 16

Answer 1

The correct option is C

8 and 32

Let the quantities be x and 4x respectively.

x + 6 : 4x - 6 = 7 : 13

$\Rightarrow$ $\frac{x+6}{4x-6}$ = $\frac{7}{13}$

$\Rightarrow$ 13 (x + 6) = 7 (4x - 6)

$\Rightarrow$ 13 x + 78 = 28x - 42

$\Rightarrow$ 28x - 13x = 78 + 42

$\Rightarrow$ 15 x = 120

$\Rightarrow$ x = 8

$\therefore$ Original quantities were 8 and 32.