The cost of diamond varies directly as the square of its weight. Once this diamond broke into 4 pieces with weights in the ratio 5 : 2 : 3 : 1. When the pieces were sold the merchant got 41000 less. Find the original price of the diamond?
The cost of diamond varies directly as the square of its weight. Once this diamond broke into 4 pieces with weights in the ratio 5 : 2 : 3 : 1. When the pieces were sold the merchant got 41000 less. Find the original price of the diamond? Correct Answer Rs. 60500
Given:
New ratio is 5 ∶ 2 ∶ 1 ∶ 3.
The price of diamond before broken is Rs. 41000.
Concept used:
Using the concept simple ratio.
Calculation:
Let the weight of each piece of diamond be 5x, 2x, x and 3x.
Total weight of diamond = 5x + 2x + x + 3x = 11x
Cost of the diamond = (11x)2 = 121x2
Cost of first piece = (5x)2 = 25x2
Cost of second piece = (2x)2 = 4x2
Cost of third piece = (x)2 = x2
Cost of fourth piece = (3x)2 = 9x2
Total cost of diamond after weight = 25x2 + 4x2 + x2 + 9x2
⇒ New cost = 39x2
According to the question,
121x2 – 39x2 = 41000
⇒ 82x2 = 41000
⇒ x2 = 500
So, the original price of the diamond = 121x2 = 121 × 500 = Rs. 60500
∴ The original price of the diamond is Rs. 60500.
