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If a man reduces the selling price of a fan from ${\text{Rs}}{\text{. }}400$ to ${\text{Rs}}{\text{.}}\;380$ his loss increases by $4\%$ . What is the cost price of the fan in rupeesA. $600$ B. $480$ C. $500$ D. $450$

Last updated date: 17th Jun 2024
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Hint: Take $x$ as cost price then find the first loss percentage the formula for first loss percentage is subtract cost price from selling price by cost price into $100$ . Then find the second loss the formula for is subtraction of cost price and the sold price by cost price into $100$ . Then subtracting the first loss from the second loss is equal to $4\%$ .

The selling price of the fan is ${\text{Rs }}400$ .
The reduced selling price is ${\text{Rs}}{\text{. 380}}$ .
The loss percentage is $4$ .
Let us assume that the cost price of a fan is ${\text{Rs}}{\text{. }}x$ .
We know the formula to find the first loss is,
${\text{first loss % = }}\dfrac{{\left( {{\text{cost price - selling price}}} \right)}}{{{\text{cost price}}}} \times 100$
On substituting the values of cost price and selling price in the above equation we obtain,
${\text{first loss % }} = \dfrac{{\left( {x - 400} \right)}}{x} \times 100\\ = \dfrac{{100x - 40000}}{x}\%$
The formula to find the second loss is,
${\text{second loss % = }}\dfrac{{\left( {{\text{cost price - loss selling price}}} \right)}}{{{\text{cost price}}}}$
On substitute the values of cost price and loss selling price in the above equation we obtain,
${\text{second loss % = }}\dfrac{{\left( {x - 380} \right)}}{x} \times 100\\ = \dfrac{{100x - 38000}}{x}\%$
Then we know the formula for loss percentage is,
${\text{second loss percentage - first loss percentage = loss percentage}}$
On putting the second loss percentage and first loss percentage and loss percentage in the above equation we obtain,
$\dfrac{{\left( {100x - 38000} \right)}}{x} - \dfrac{{\left( {100x - 40000} \right)}}{x} = 4\\ 100x - 38000 - 100x + 40000 = 4x\\ 2000 = 4x\\ x = 500$
Therefore, the cost price of a fan is ${\text{Rs}}{\text{.}}\;500$ and the correct option is (c).
So, the correct answer is “Option C”.

Note: In these types of questions, make sure to find the second loss and first loss because two selling prices are given then make sure to subtract the second loss percentage from the first loss percentage which is equal to total loss.