Question

A shopkeeper bought two fans for

₹ 5000

. He sold one at a profit of

10 %

and the other at a loss of

10 %

. If the SP of both the fans are equal, find the cost price of each fan.

Accepted Answer

Let the cost price of the first fan be $₹ x$ .

So, the cost price of the second fan is $10 %$ .

According to question,

Given that he sold one at a profit of $10 %$

We know that, profit $% = \frac{profit}{CP} \times 100$

$\Rightarrow 10 = \frac{profit}{x} \times 100$

Therefore, Profit $= \frac{x}{10}$

Also, $SP = CP + profit$

So, Selling Price of first fan $= x + \frac{x}{10} = \frac{11 x}{10}$

It is given that he sold the other at loss of $10 %$

So, using loss $% = \frac{loss}{CP} \times 100$ , we get

$10 = \frac{Loss}{5000 - x} \times 100$

$\Rightarrow$ Loss $= \frac{5000 - x}{10}$

So, Selling Price of second fan $= (5000 - x) - \frac{5000 - x}{10}$

Also, it is given that, both SP are same

$\Rightarrow \frac{11 x}{10} = (5000 - x) - \frac{5000 - x}{10}$

$\Rightarrow \frac{11 x}{10} = \frac{50000 - 10 x - 5000 + x}{10}$

$\Rightarrow 11 x = 45000 - 9 x$

$\Rightarrow 20 x = 45000$

$\Rightarrow x = 2250$

Therefore, Cost Price of first fan is $₹ 2250$ .

Cost Price of second fan is $5000 - x = 5000 - 2250 = ₹ 2750$ .

S.N. Chhibber Solutions for Chapter: Profit, Loss and Discount, Exercise 1: Exercise

S.N. Chhibber Mathematics Solutions for Exercise - S.N. Chhibber Solutions for Chapter: Profit, Loss and Discount, Exercise 1: Exercise

Questions from S.N. Chhibber Solutions for Chapter: Profit, Loss and Discount, Exercise 1: Exercise with Hints & Solutions

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