Question : 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 reduced by 6 kg and the ratio between their weights changed to 5 : 6. So Mrs. Gupta has reduced by:
Option 1: 2 kg
Option 2: 4 kg
Option 3: 3 kg
Option 4: 5 kg
Correct Answer: 4 kg
Solution :
Initial ratio = 7 : 8
Initial total weight = 120 kg
Initial weight of Mr. Gupta = $\frac{7×120}{7+8}$ = 56 kg
Initial weight of Mrs. Gupta = $\frac{8×120}{7+8}$ = 64 kg
Reduced weight of Mr. Gupta = 56 – 6 = 50 kg
Final ratio = 5 : 6
Reduced weight of Mrs. Gupta = $\frac{6×50}{5}$ = 60 kg
$\therefore$ Weight reduced = 64 – 60 = 4 kg
Hence, the correct answer is 4 kg.
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