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A shopkeeper allows $23 %$ commission in his advertised price and still makes a profit of $10 %$ . If he gains Rs. 56 on one item, find his advertised price.

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Rs.715

Rs.830

Rs.800

Rs.368

answer is B.

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Detailed Solution

Given,

p r o f i t = 10 %

, gain is Rs. 56 and 23% commission.
Let the cost price (CP) of the item be Rs. x.
Selling price (SP) is,

SP = 100 + profit % 100 CP ⇒ 100 + 10 100 x ⇒ 110100 (x) ⇒ 1.1 x

Therefore,

Profit = 1.1 x − x ⇒ 0.1 x

So,

0.1 x = 56 ⇒ x = 560

Thus, the advertising price is,

⇒ 1.1 x 1 − 0.23

⇒ 560 1.1 0.77 ⇒ 800

Hence, the advertised price is Rs.800.
Therefore, option (2) is correct.

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