Profit Loss discount question query

[shaji]

A merchant marks her goods up by 'x%' above the cost price and then offers a discount of 'd%' on the marked price. She makes a net loss on account of offering the discount. Which of the following can be inferred from this?
d > x
d < x
d > = x
d < = x
None of these

The correct answer in my opinion is d>=x. The correct answer is shown as None of these.

Please clarify . Sahji

[ksb]

The given answer is correct.

It is easy if you use numbers to understand this question.

Let the cost be 100.

Let the mark up x be say, 40. Therefore, marked price is 140.

Let d be 40. Therefore, discount offered = 40% of 140 = 56. Hence, loss. i.e., d = x
Let d be 50. Therefore, discount offered = 50% of 140 = 70. Hence, loss. i.e., d > x
Let d be 30. Therefore, discount offered = 30% of 140 = 42. Hence, loss i.e., d < x.

Therefore, if we know that the merchant made a loss, we cannot conclusively state that d >= x. On the contrary, if we had known that d > = x, then we can conclusively state that there will be a loss.

Hope this clarifies.

KSB

[shaji]

Thanks indeed. The hidden fallacy lies in the nature of the function relating d and x.

There will be a loss if d>x/(1+x).

Shaji.