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The value of a ruby varies directly as the square of its weight. One such ruby breaks and the weight of its pieces is in the ratio of 2 ∶ 3 ∶ 4. If damage due to breakdown is Rs. 26,000, what was the cost of the original ruby?

The value of a ruby varies directly as the square of its weight. One such ruby breaks and the weight of its pieces is in the ratio of 2 ∶ 3 ∶ 4. If damage due to breakdown is Rs. 26,000, what was the cost of the original ruby? Correct Answer Rs. 40500

Given:

Value of a ruby ​​varies directly as the square of its weight

After breaking one ruby weight of its pieces is in the ratio 2 : 3 : 4

Damage due to breakdown = Rs. 26,000

Concept Used:

Concept of ratio and proportion

Calculation:

Total weight of unbroken ruby = 9x

According to question,

⇒ Original price = 81x2

After adding prices of individual ruby

⇒ x2(22 + 32 + 42)

⇒ x2(4 + 9 + 16) = 29x2

Loss = Original price - broken price

Loss = (81 - 29)x2 = 52x2

⇒ 52x2 = Rs.26,000

⇒ x2 = 26000 ÷ 52

⇒ x2 = 500

Price of original ruby = 81x2

⇒ 81 × 500 = 40,500

∴ Price of original ruby = Rs. 40,500.

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