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If a person reduces his selling price of an article by Rs. 40, then the suggested profit of $33 \frac{1}{3} %$ convert into a loss of 20 %. Find the cost price.

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Rs.100

Rs.150

Rs.75

Rs.200

answer is C.

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Detailed Solution

Let cost price be X
According to given condition

33 \frac{1}{3} % x - 40 = 20 % x

33 \frac{1}{3} % = \frac{(33 * 3) + 1}{3} % = \frac{100}{3} % = \frac{\frac{100}{3}}{100} = \frac{1}{3}

20 % = \frac{20}{100} = \frac{1}{5}

we can convert this fraction by using the formula for profit

1 + \frac{1}{3} = \frac{4}{3}

and for loss

1 - \frac{1}{5} = \frac{4}{5}

\frac{4}{3} x - 40 = \frac{4}{5} x

\frac{4}{3} x - \frac{4}{5} x = 40

\frac{20 x - 12 x}{15} = 40

\frac{8 x}{15} = 40

8 x = 40 * 15

x = \frac{600}{8} = 75

Cost price is Rs.75

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