Question

The ratio of weight of three friends, namely, Aashiqui, Aarohi and Aamrohi is 4 : 9 : 7. Their total weight is 100 kilograms. How much weight would Aamrohi would have put on if the ratio after her weight gain is 4 : 7 : 9 and their collective weight becomes 140 kilograms?

• A. 28 kilograms
• B. 63 kilograms
• C. 49 kilograms
• D. 21 kilograms
• E. 35 kilograms

Hint:

When ratios change, find the value of one part for each scenario separately.

Answer 1

The Correct Option is A

Step 1: Initial Weights:
Ratio Aashiqui : Aarohi : Aamrohi = 4 : 9 : 7, total = 20 parts = 100 kg.
1 part = \(100/20 = 5\) kg.
Initial weights:
Aashiqui = \(4 \times 5 = 20\) kg
Aarohi = \(9 \times 5 = 45\) kg
Aamrohi = \(7 \times 5 = 35\) kg

Step 2: Final Weights After Aamrohi's Gain:
New ratio = 4 : 7 : 9, total = 20 parts = 140 kg.
1 part = \(140/20 = 7\) kg.
Final weights:
Aashiqui = \(4 \times 7 = 28\) kg
Aarohi = \(7 \times 7 = 49\) kg
Aamrohi = \(9 \times 7 = 63\) kg

Step 3: Weight Gained by Aamrohi:
Gain = \(63 - 35 = 28\) kg.