Question

A man bought a certain number of pens and sold them at a gain of x%. Had he sold at a loss of x%, he would
have lost Rs.x when compared to the selling price for a gain of x%. Which of the following statements is true?​

Answer 1

Given :-

• A man bought a certain number of pens and sold them at a gain of x%.
• Had he sold at a loss of x%, he would have lost Rs.x when compared to the selling price for a gain of x%.

Solution :-

Let us Assume that, Total money man spend on buy pens is Rs.100 .

Case 1) when he sold them at a gain of x%.

Than,

→ CP = Rs.100

→ Gain = x %

→ SP = CP * (100 + Gain%) / 100

→ SP = 100 * (100 + x)/100

→ SP = Rs.(100 + x).

Case 2) . when he sold them at a loss of x%.

Than,

→ CP = Rs.100

→ Loss = x %

→ SP = CP * (100 - Loss%) / 100

→ SP = 100 * (100 - x)/100

→ SP = Rs.(100 - x).

Now, we have given that, he would have lost Rs.x when compared to the selling price for a gain of x%.

So,

→ SP of gain - SP of Loss = Rs.x

→ (100 + x) - (100 - x) = x

→ 100 - 100 + x + x = x

→ 2x = x

which is Not Possible.

Hence, we can conclude that, from given data , their is no value of x which satisfy the given condition.