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Question

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A. $ 600 $

B. $ 480 $

C. $ 500 $

D. $ 450 $

Answer

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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).