Question

A man bought a certain quantity of rice at the rate of Rs. 650 per quintal. 20% of the rice was spoiled. At what rate should he sell the remaining rice to gain 20% on the outlay?\[\]
A. Rs.775 \[\]
B. Rs. 850\[\]
C. Rs.890\[\]
D. Rs.975\[\]

Answer 1

Hint: We convert quintal to kilograms (kg) and we find the amount of rice that was non-spoiled as${{A}_{n}}$. We find the cost price per kg as $\dfrac{{{A}_{n}}}{650}$ and then the selling price per kg at 20% profit. Then we multiply 100 to get the selling price for the quintal.\[\]

Complete step by step answer:
We know that percentage profit $P$ of any merchandise is given with cost price CP on selling price SP by,
\[P=\dfrac{SP-CP}{SP}\times 100\]
We know from the weight measurement that 1 quintal is equal to 100kg. The cost price CP for the man is given in the question as 650 rupees per quintal or 100 kg. It is also given that 20% of the rice was spoiled. So the amount of rice that was spoiled per quintal is
\[{{A}_{s}}=\dfrac{20}{100}\times 100=100\]
The rest of the rice per quintal is the non-spoiled rice that man can sell. The amount of non-spoiled rice is the difference between total rice and spoiled rice which is,
\[{{A}_{n}}=100-20-80\]
So the man can sell 80 kg rice for which he has the same cost 650 rupees before the spoiling. The cost price of rice per kg in rupees is,
\[C{{P}_{1}}=\dfrac{650}{{{A}_{n}}}=\dfrac{650}{80}\]
He has to sell at 20% profit as given in the question. So the amount of profit he has to make is rupees per kg is
\[{{P}_{1}}=\dfrac{20}{100}\times \dfrac{650}{80}=0.2\times \dfrac{650}{80}\]
So the selling price of rice per kg in rupees at 20% profit is
\[S{{P}_{1}}=\dfrac{650}{80}+0.2\times \dfrac{650}{80}=1.2\times \dfrac{650}{80}=9.75\]
Hence the selling price of the rice per quintal that is 100kg at 20% profit is,
\[S{{P}_{100}}=S{{P}_{1}}\times 100=9.75\times 100=975\]
So the correct option is D.\[\]

Note:
We can also solve the problem by taking the whole quintal of rice as a mixture of spoiled and unspoiled rice. If the man would have made a loss instead of profit, the percentage loss is given on the selling price is $L=\dfrac{CP-SP}{SP}\times 100$.