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

	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
$$\eqalign{ & \therefore \frac{{56 - 6}}{{64 - x}} \times \frac{5}{6} \cr & \left( {{\text{Cross multiplication}}} \right) \cr} $$
⇒ 300 = 320 - 5x
⇒ 5x = 20
∴ x = 4 kg