The weight of Mr. Gupta and Mrs. Gupta are in the ratio 7 : 8 and their total weight is 120 kg. After taking a dieting course Mr. Gupta reduces by 6 kg and the ratio between their weights change to 5 : 6, so Mrs. Gupta has reduced by = ?

Answer: Option B

	Mr.	:	Mrs.
Before	7x	:	8x
After	5y	:	6y

Before 7x + 8x = 120
⇒ 15x = 120
⇒ x = 8
∴ Mr. Gupta = 7 × 8 = 56
Mrs. Gupta = 8 × 8 = 64
∴ After losing 6kg by Mr. Gupta the ratio becomes 5 : 6
⇒ Let Mrs. Gupta loss x kg
$$\begin{array}{rl}& \therefore \frac{56-6}{64-x}\times \frac{5}{6}\\ & \left(\text{Cross multiplication}\right)\end{array}$$
⇒ 300 = 320 - 5x
⇒ 5x = 20
∴ x = 4 kg