Question

A precious stone worth Rs 6800 is accidently dropped and breaks into 3 pieces. The weight of 3 pieces are in the ratio 5:7:8 .The value of the stone is proportional to the square of its weight. Find the loss.

Answer 1

HEY DEAR . ✌

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It's nice question and tuff too ...
But yeah no problem .

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Let V be the value of a precious stone whose weight is W. 
Hence, V ∝ W2
V = k W2 → (1)
Since the weights of the three broken pieces are proportional to 5:7:8
Let their weights be 5w, 7w and 8w respectively. 
Hence, the weight of the unbroken piece of stone = 5w + 7w + 8w = 20w. 
Then, V = 6800 when W = 20w. 
Hence, from equation (1) we get, 
6800 = k x (20w)2 
6800 = 400kw2
kw2 = 6800/400 = 17 

Let, v1, v2 and v3 be the values of the 3 pieces of weights 5w, 7w and 9w respectively. 
Hence from equation (1) we get, 
v1 = k(5w)2 = 25kw2
v2 = k(7w)2 = 49kw2
v3  = k(8w)2 = 64kw2
(v1 + v2 + v3) = 25kw2 + 49kw2 + 64kw2 
= 138 kw2
= 138 × 17 
= Rs 2346. 
Therefore, the total loss obtained by the breakage  = (The value of the original stone) - (The total value of the 3 pieces) 
= Rs 6800 – Rs 2346 =  Rs 4454

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HOPE , IT HELPS . ✌

Answer 2

Answer:

Verified Answer is 4454