{"id":90554,"date":"2025-06-01T10:30:55","date_gmt":"2025-06-01T10:30:55","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90554"},"modified":"2025-06-01T10:30:55","modified_gmt":"2025-06-01T10:30:55","slug":"the-cost-of-gold-varies-directly-as-the-cube-of-its-weight-a-gold-pie","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-cost-of-gold-varies-directly-as-the-cube-of-its-weight-a-gold-pie\/","title":{"rendered":"The cost of gold varies directly as the cube of its weight. A gold pie"},"content":{"rendered":"

The cost of gold varies directly as the cube of its weight. A gold piece weighing 20 decigram costs \u20b91,000. If it is broken into two pieces whose weights are in the ratio 2 : 3, then what is the profit or loss incurred?<\/p>\n

[amp_mcq option1=”\u20b9280 profit” option2=”\u20b9280 loss” option3=”\u20b9720 profit” option4=”\u20b9720 loss” correct=”option4″]<\/p>\n

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This question was previously asked in<\/div>\n
UPSC CAPF – 2020<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\u20b9720 loss<\/section>\n
The cost of gold is directly proportional to the cube of its weight ($C \\propto W^3$). When the piece is broken, its total weight remains the same, but the combined cost of the pieces is calculated based on the cubed weights of the individual pieces.<\/section>\n
Let the cost be C and the weight be W. Given $C = kW^3$ for some constant k.
\nFor the original piece: $W_1 = 20$ dg, $C_1 = \u20b91000$.
\n$1000 = k \\times (20)^3 = k \\times 8000$
\n$k = \\frac{1000}{8000} = \\frac{1}{8}$.
\nThe piece is broken into two pieces with weights in the ratio 2:3. The total weight is 20 dg. The weights of the two pieces are $\\frac{2}{2+3} \\times 20 = \\frac{2}{5} \\times 20 = 8$ dg and $\\frac{3}{2+3} \\times 20 = \\frac{3}{5} \\times 20 = 12$ dg.
\nLet the costs of the two pieces be $C_2$ and $C_3$.
\n$C_2 = k \\times (8)^3 = \\frac{1}{8} \\times 512 = 64$.
\n$C_3 = k \\times (12)^3 = \\frac{1}{8} \\times 1728 = 216$.
\nThe total value of the broken pieces is $C_2 + C_3 = 64 + 216 = \u20b9280$.
\nThe original cost was \u20b91,000. The value after breaking is \u20b9280.
\nThe profit or loss is $280 – 1000 = -720$. This is a loss of \u20b9720.<\/section>\n","protected":false},"excerpt":{"rendered":"

The cost of gold varies directly as the cube of its weight. A gold piece weighing 20 decigram costs \u20b91,000. If it is broken into two pieces whose weights are in the ratio 2 : 3, then what is the profit or loss incurred? [amp_mcq option1=”\u20b9280 profit” option2=”\u20b9280 loss” option3=”\u20b9720 profit” option4=”\u20b9720 loss” correct=”option4″] This … <\/p>\n

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