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A shopkeeper allows a discount of 10% on the marked price. How much above the cost price must he mark his goods to gain 8%?

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20%

100%

80%

None of these

answer is A.

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Detailed Solution

It is given that a discount of

10 %

is given at a marked price. And the gain should be

8 %

.
Let marked price (MP) of an article be

x

.
Discount on article

= x - 10

% of

x

\Rightarrow

Discount on article

= x - \frac{10}{100} x

\Rightarrow

Discount on article

= 0.9 x

Therefore, selling price (SP) of the article

= 0.9 x

.
Now, gain %

= \frac{SP - CP}{CP}

.
Put the value of gain % and selling price in the above equation and calculate

CP

\frac{8}{100} = \frac{0.9 x - CP}{CP}

8 CP = 90 x - 100 CP

108 CP = 90 x

CP = \frac{90 x}{108}

CP = \frac{5 x}{6}

Therefore, cost price (

CP)

marked above marked price(

MP

)

= \frac{MP - CP}{CP} \times 100

Put the values of

CP

and

MP

in the above equation,

\Rightarrow \frac{x - \frac{5 x}{6}}{\frac{5 x}{6}} \times 100

= \frac{\frac{x}{6}}{\frac{5 x}{6}} \times 100

\Rightarrow \frac{x - \frac{5 x}{6}}{\frac{5 x}{6}} \times 100

20

%
So, the goods should be marked

20 %

above the cost price.
Hence, the correct option is 1.

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