Question

A shopkeeper sells an article at 10% discount on the marked price which is 20% above the cost price. Find the profit he makes if he sells an article for Rs 10.80.

Answer 1

Answer on Question #43145-Math-Other

A shopkeeper sells an article at 10% discount on the marked price which is 20% above the cost price. Find the profit he makes if he sells an article for Rs 10.80.

Solution

Selling price (S.P.) is S.P. = Rs 10.80.

Marked price is

$$M. P. = \frac{100 \cdot \text{S.P.}}{100 - \text{discount}} = \frac{100 \cdot \text{S.P.}}{100 - 10} = \frac{\text{S.P.}}{0.9}$$

The marked price is 20% above the cost price:

$$M. P. = C. P. \frac{100 + 20}{100} \rightarrow C. P. = \frac{M. P.}{1.2}$$

The profit is

$$\text{Profit} = \text{S.P.} - \text{C.P.} = \text{S.P.} - \frac{\text{S.P.}}{0.9 \cdot 1.2} = \text{S.P.} \left(1 - \frac{1}{0.9 \cdot 1.2}\right) = \text{Rs } 10.80 \left(1 - \frac{1}{0.9 \cdot 1.2}\right) = \text{Rs } 0.80.$$

Answer: Rs 0.80.

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