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A man sells an article at a profit of 25 %. If he had bought it at 20 % less and sold it for Rs. 36.75 less, he would have gained $30 % .$ Find the cost price of the article.

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Rs.182

Rs.246

Rs.175

Rs.189

answer is C.

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Detailed Solution

Given that he would have gained 30% if he had bought at 20% less and sold for Rs 36.75 less and his gain = 25%.
Let the CP of the article be Rs.x.
Original selling price,

SP = x + 25 x 100 ⇒ SP = 5 x 4

If he purchased it at 20% less,

CP = x − 20100 x ⇒ 4 x 5

He sold the article at Rs.36.75 less.
So, the selling price

=Rs . 5 x 4 − 36 .75

.
Given that he would have gained 30% selling at the price.
Therefore,

G a i n % = S P − C P C P (100) S P − C P = 5 x 4 − 36.75 − 4 x 5 ⇒ 5 x 4 − 4 x 5 − 36.75 ⇒ 9 x 20 − 36.75

Now,

Gain % = SP − CP CP (100) ⇒ 30 = 9 x 20 − 36.75 4 x 5 (100) ⇒ 30 = 9 x − 735 16 x (100) ⇒ 225 x − 18375 4 x = 30 ⇒ 225 x − 18375 = 120 x ⇒ 105 x = 18375 ⇒ x = 175

Thus, the cost price of the article is Rs.175.
Therefore, option (3) is correct.

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