# The cost price of piece of diamond varies with square of its weight . A diamond of rs 5184 value is cut into 3 pieces whose weight are in ratio 1:2:3. Find the loss involved in cutting

$Let\;the\;total\;weight\;of\diamonds\;be\;6\times x\\* Diamond\;is\;cut\;into\;three\parts\;with\;weight\;ratio\;1:2:3\\* weight\;of\;respective\;piece\;is\;1\times x, 2\times x, 3\times x, respectively\\*Cost\;price\;varies\;with\;the\;square\;of\;weight\\* initial\;price\;=5184\\* \Rightarrow (6\times x)^2\propto 5184\\*we\;are\;removing\;proportionality\;and\;taking\;constant\;k \;as\;multiple\\* so,\;\\*\Rightarrow k\times (6\times x)^2=5184\\*\Rightarrow k\times 36\times x^2=5184\\*\Rightarrow k\times x^2= 5184\div 36\\* \Rightarrow k\times x^2=144\\*price\;of\;individual\;piece\;is\\*\Rightarrow k\times x^2=144\\* \Rightarrow4\times k\times x^2= 576\\* \Rightarrow 9\times k\times x^2=1296\\* total\;loss\;will\;be\;equal\; to\;difference\;between\;initial\;price\;and\;final\;price\\*\Rightarrow loss=5184-(144+576+1296)\\* \Rightarrow loss=5184 - 2016=3168\\* Hence,\;the\;loss\;is\;3168$

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