Question

A merchant buys a \[50\] liter cask of wine for \[Rs.6250\]and sells it at \[Rs.130\]per liter. His loss or gain percent is:

Answer 1

Hint: As we know that Cost Price (C.P) means the amount which is paid by the seller to acquire that product and Selling Price (S.P) is the money that is finally received by the seller after selling that same product to any customer.
We need to use a unitary method in this case. In unitary method if we know price of a particular product, we can find price of number of products by multiplication, also we can price of single product if we are given with price of number of products with division.
If S.P \[ > \] C.P then there will be profit.
If C.P \[ > \] S.P then there will be loss.

Complete step by step solution:
Given,
Cost of \[50l\]cask of Wine \[ = Rs.6250\]
Selling price of \[1l\] wine \[ = Rs.130\]
Cost price of \[50l\]wine \[ = Rs.6250\]
Cost price of \[1l\]wine \[ = Rs.\dfrac{{6250}}{{50}} = Rs.125\]
We were given the Cost Price of \[50l\] wine. Hence by unitary method we got the Cost Price of \[1l\] wine i.e. \[Rs.125\]by division.
We have,
Cost price of \[1l\] wine \[ = Rs.125\] …… (i)
Selling price of \[1l\] wine \[ = Rs.130\] …… (ii)
As, Selling Price \[ > \] Cost Price
We have, Profit \[ = Selling\\Price - \,\operatorname{Cos} tPrice\]
     Using, value from (i) and (ii)
     Profit \[ = \,Rs.130 - Rs.125\]
Hence, Profit \[ = \,Rs.5\]
The gain percent \[ = \,\]\[\dfrac{{Gain(Profit)}}{{C.P}} \times 100\]
Put Profit \[ = 5\] and C.P \[ = 125\]
Gain \[\% = \dfrac{1}{{25}} \times 100 = 4\% \]
Therefore, the merchant gad \[4\% \] profit.


Note: Profit \[\% \] can also be calculated by simply using the formula given below:
\[C.P = \dfrac{{100}}{{100 + P\% }} \times S.P\]
Never Confuse C.P with S.P where C.P means the cost price whereas the S.P means selling price.