Question

A shopkeeper sold 100 kg sugar for Rs\[{\mathbf{3870}}\]. He lost Rs \[{\mathbf{180}}\] in this transaction and found the cost price of 1kg of sugar.

Answer 1

Hint: Cost price is defined as the price at which products have been bought by a merchant or retailer. Selling price can be defined as price at which a good or service is sold by seller to the buyer, loss can be defined as when cost price (CP) is more than selling price we obtain loss or we can say that when we bought it at more rate and sold it at lesser rate, we obtain loss.
Here in this question SP of 100 Kg sugar is given and loss of Rs 180 is given in the whole transaction. We can use the formula \[CP{\text{ }}-{\text{ }}SP{\text{ }} = {\text{ }}Loss\]or\[CP = {\text{ }}Loss + {\text{ }}SP\].

Complete step-by -step solution:
Given:
SP of \[100{\text{ }}Kg\] sugar\[ = \] Rs\[3870\]…….(1)
Loss on the whole transaction = Rs \[180\]…….(2)
We know, \[{\text{Loss }} = {\text{ Costprice - }}Selling{\text{ }}Price\] only if C.P > S.P.
\[Cost{\text{ }}price{\text{ }} = {\text{ }}Loss + Selling{\text{ }}Price\]
On substituting the values from equations (1) and (2), we get:
Cost price \[ = {\text{ }}180 + 3870\] \[ = \] Rs \[4050\]
Cost price of \[100Kg\] sugar= Rs \[4050\]
Cost price of \[1Kg\] sugar = \[\dfrac{{4050}}{{100}}\]= Rs \[40.50\]

Note: We must never get confused in recognizing the profit or loss in the question.
If S.P> C.P then there will be profit in the whole transaction.
If C.P>S. P then there will be a loss in the whole transaction.
We can find the cost price or selling price of an object if profit or loss is given.