Question

Two quantities are 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

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

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

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

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

$\Rightarrow 15x=120$

$\Rightarrow x=8$

$\therefore$ Original quantities were $x=8$ units and $4x=4\times 8=32$ units