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 = ?
A. 2 kg
B. 4 kg
C. 3 kg
D. 5 kg
Answer: Option B
Solution(By Examveda Team)
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
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