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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: b
Explanation:
  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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