The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1 : 2 : 3 : 4. When the pieces were sold, the merchant got Rs. 70,000 less.
Find the original price of the diamond.  Select:
A) Rs. 1.4 lakh	B) Rs. 2 lakh	C) Rs. 1.4 lakh	D) Rs. 1 lakh	E) None of these
Explanation :   If we assume weight of diamond 10x. Well I came up with 10x because the ratio   Given 1 : 2 : 3 : 4 adds upto 10.   So, individual weights of diamonds will be x, 2x, 3x and 4x   Original price = k(10x)2   Price for pieces = k(x2 + 4x2 + 9x2 + 16x2) = k30x2   Thus change in price we see is 100kx2 - 30kx2 = 70kx2 which is given as 70,000.   Thus the original price 100kx2 will be 1,00,000.   Answer : Rs. 1 lakh
<result>D</result>
The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1 : 2 : 3 : 4. When the pieces were sold, the merchant got Rs. 70,000 less.
Find the original price of the diamond.