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A man sells an article at a gain of $20 %$ . If he had bought it for $20 %$ less and sold it for Rs. $264$ less, he would have still gain $20 %$ . The cost price of the article is:

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Rs.

1100

Rs.

2400

Rs.

2600

Rs.

2650

answer is A.

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Detailed Solution

Given that a man sells an article at a gain of

20 %

. Also, if he had bought it for

20 %

less and sold it for

Rs . 264

less, he would have still gain

20 %

.
Let C.P. be

x

.
We know,

S . P . = C . P + \frac{Gain %}{100} \times C . P .

Hence,

\Rightarrow S . P = x + \frac{20}{100} x

\Rightarrow S . P = x + 0.2 x

\Rightarrow S . P = 1.2 x

If he had bought it for

20 %

less, then new C.P. will be,

C . P = x - 20 %

x

\Rightarrow C . P = x - \frac{20}{100} x

\Rightarrow C . P = x - 0.2 x

\Rightarrow C . P = 0.8 x

And the new S.P.

= 1.2 x - 264

Gain

= 20 %

We know,
Gain %

= \frac{S . P . - C . P .}{C . P .} \times 100

\Rightarrow 20 % = \frac{(1.2 x - 264) - 0.8 x}{0.8 x} \times 100

\Rightarrow \frac{20}{100} = \frac{(1.2 x - 264) - 0.8 x}{0.8 x}

\Rightarrow \frac{0.4 x - 264}{0.8 x} = \frac{20}{100}

\Rightarrow 40 x - 26400 = 16 x

\Rightarrow 40 x - 16 x = 26400

\Rightarrow 24 x = 26400

\Rightarrow x = 1100

Thus, the C.P. of the article is Rs.

1100

.
Therefore, the correct option is 1.

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