Question

The value of a stone is directly proportional to the square of its weight. The stone drops and breaks into 3 pieces with weights in ratio 1 ∶ 3 ∶ 7, thus the value of stone decreased by Rs.31 lakhs. What is the actual value of the stone? 
1. 60,00,000
2. 60,50,000
3. 61,50,000
4. 62,00,000

Answer 1

Correct Answer - Option 2 : 60,50,000

Given:

Weight of broken pieces = 1 ∶ 3 ∶ 7

Decrease in price = Rs.31 lakhs

Calculation:

Initial weight = 1 + 3 + 7 = 11

∵ The value of a stone is directly proportional to the square of its weight,

Initial cost = (11)² = 121 units

Cost after breaking = (1)² + (3)² + (7)² = 1 + 9 + 49 = 59 units

So, the decrease in cost after breaking = 121 – 59 = 62 units

⇒ 62 units = Rs.31,00,000

⇒ 1 unit = 31,00,000/62 = Rs.50,000

⇒ 121 unit = 50,000 × 121 = Rs.60,50,000 

∴ The actual price of stone is Rs.60,50,000