Question

A manufacturer makes 750 articles at a cost of 60 paise per article. He fixes the selling price such that if only 600 articles are sold, he would make a profit of 40% on his outlay. However, he sold 630 articles at this price. Find his actual profit per cent as a percentage of the total outlay assuming that the unsold articles are useless. Explain the steps.

Answer 1

Answer on Question #43141-Math-Other

A manufacturer makes 750 articles at a cost of 60 paise per article. He fixes the selling price such that if only 600 articles are sold, he would make a profit of 40% on his outlay. However, he sold 630 articles at this price. Find his actual profit per cent as a percentage of the total outlay assuming that the unsold articles are useless.

Solution

C.P. of 750 articles at the rate of 60 paise per article is

$$Rs \left(750 \cdot \frac{60}{100}\right) = Rs\ 450.$$

Required profit is 40% of his outlay assuming that only 600 articles are sold.

S.P. of 600 articles is

$$\frac{100 + 40}{100} \cdot Rs\ 450 = Rs\ 630.$$

S.P. of 1 article is $Rs\frac{630}{600}$.

He actually sells 630 articles.

S.P. of 630 articles is $630 \cdot Rs\frac{630}{600} = Rs\ 661.50$.

Actual profit is $Rs\ 661.50 - Rs\ 450 = Rs\ 211.50$.

$$\text{Actual profit}\% = \frac{\text{Profit}}{C.P.} \cdot 100\% = \frac{211.50}{450} \cdot 100\% = 47\%.$$

Answer: $47\%$.

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