The cost of gold varies directly as the cube of its weight. A gold piece weighing 20 decigram costs ₹1,000. If it is broken into two pieces whose weights are in the ratio 2 : 3, then what is the profit or loss incurred?
₹280 profit
₹280 loss
₹720 profit
₹720 loss
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CAPF – 2020
For the original piece: $W_1 = 20$ dg, $C_1 = ₹1000$.
$1000 = k \times (20)^3 = k \times 8000$
$k = \frac{1000}{8000} = \frac{1}{8}$.
The 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.
Let the costs of the two pieces be $C_2$ and $C_3$.
$C_2 = k \times (8)^3 = \frac{1}{8} \times 512 = 64$.
$C_3 = k \times (12)^3 = \frac{1}{8} \times 1728 = 216$.
The total value of the broken pieces is $C_2 + C_3 = 64 + 216 = ₹280$.
The original cost was ₹1,000. The value after breaking is ₹280.
The profit or loss is $280 – 1000 = -720$. This is a loss of ₹720.