Question

A merchant buys 50 litre cask of wine for Rs. 6250 and sells it for Rs 130 per litre. His loss/ gain% is
[a] $3\dfrac{11}{50}\%$ loss
[b] 4% profit
[c] 25% profit
[d] 5% profit

Answer 1

Hint: Find the total amount for which he sells 50 litres of wine. Hence find the amount gained or lost by the merchant. Hence find the corresponding gain%age. Gain%age/loss%age is defined as the amount gained/lost per 100 units of cost price. Alternatively, you can find the gain %age/loss%age using the formula $gain/loss\%=\dfrac{gain/loss}{C.P}\times 100$. Hence find the gain/loss %age.

Complete step-by-step answer:
The amount for which the cask of wine was purchased = Rs. 6250
Hence, we have C.P = Rs. 6250
Now, we have the merchant sells 1 litre for Rs. 130
Hence the amount for which 50 litres of wine is sold is equal to $130\times 50=6500$
Hence, we have S.P = Rs. 6500
Since S.P>C.P, the merchant has earned a profit from this transaction.
Now, we know that profit = S.P – C.P
Hence, we have Profit = 6500 – 6250 = Rs. 250
Hence the amount gained on Rs 6250 of C. P = Rs. 250
Hence the amount gained on Re 1 of C.P = $\dfrac{250}{6250}=\dfrac{1}{25}$
Hence, the amount gained on Rs. 100 of C.P $=\dfrac{1}{25}\times 100=4$
Hence the gain%age = 4%.
Hence option [b] is correct.

Note: We can also calculate gain%age on 1 litre of wine.
Cost of 1 litre of wine $=\dfrac{6250}{50}=125$
Hence, we have amount gained on 1 litre = 130 – 125 = Rs. 5
We know that $gain\%=\dfrac{gain}{C.P}\times 100$
Hence, we have
$gain\%=\dfrac{5}{125}\times 100=4$, which is the same as obtained above
Hence option [b] is correct.