The value of a dimond varies dirctly with square of itd weight. A dimond broke into 3 pieces whose weight are in ratio 32:24:9 the loss cause due to brokrage was 25.44lakhs.find initial value of dimond.
Answers
Answered by
3
Price varies directly with square of weight.
Weight of the broken pieces are in the ratio 32:24:9
Let the weights of the pieces = 32x, 24x and 9x
Let price of diamond of weight 32x = (32x)² = 1024x²
price of diamond of weight 24x = (24x)² = 576x²
price of diamond of weight 9x = (9x)² = 81x²
Total price of broken pieces = 1024x² + 576x² + 81x² = 1681x²
Weight of the diamond before breaking = 32x + 24x + 9x = 65x
price of diamond of weight 65x = (65x)² = 4225x²
Loss = 4225x² - 1681x² = 2544x²
given that loss = 25.44 lakh
So 2544x² = 25.44 lakh
⇒ x² = (25.44/2544) lakh = 0.01 lakh
Initial value of diamond = 4225x² = 4225×0.01 lakh = 42.25 lakh
Weight of the broken pieces are in the ratio 32:24:9
Let the weights of the pieces = 32x, 24x and 9x
Let price of diamond of weight 32x = (32x)² = 1024x²
price of diamond of weight 24x = (24x)² = 576x²
price of diamond of weight 9x = (9x)² = 81x²
Total price of broken pieces = 1024x² + 576x² + 81x² = 1681x²
Weight of the diamond before breaking = 32x + 24x + 9x = 65x
price of diamond of weight 65x = (65x)² = 4225x²
Loss = 4225x² - 1681x² = 2544x²
given that loss = 25.44 lakh
So 2544x² = 25.44 lakh
⇒ x² = (25.44/2544) lakh = 0.01 lakh
Initial value of diamond = 4225x² = 4225×0.01 lakh = 42.25 lakh
Similar questions