Question

. A shopkeeper makes a profit of Q% by selling an
object for 24. Had the cost price and selling price
been interchanged, it would have led to a loss of
62.50%. With the latter cost price, what should be
the new selling price to get a profit of Q%?
(a) 34.40
(b) 32.50
(c) 25.60
(d) 38.4​

Answer 1

Answer:

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Math Competition Problems: A shopkeeper makes a profit of Q% by selling an object for Rs. 24. Had the cost price and selling price been interchanged, it would have led to a loss of 62.5Q%. With the latter cost price, what should be the new selling price to get a profit of Q?

Step-by-step explanation:

Let x be the cost price; then

(24-x)*100/x = Q; also

(24-x)*100/24 = 62.5*Q/100

(24-x)*100/24 = .625*(24-x)*100/x

=>x = 24*.625 = 15

=>Q=60%

Therefore, the new selling price = 24*1.6 = Rs.38.40

alternatively,

We can use convenient number. let Q be 20.

This implies c.p. is 20 and s.p. is 24. When you interchange, the loss is 100/6%.

If loss is 100/6% then c.p. is 20; actually we have to find for 62.5*Q%, which is equal to 12.5% or 100/8%.

If loss is 100/8% , then c.p. is 15. This implies Q is 60%.

Therefore, the required s.p. is 24*1.6=Rs.38.40

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