A dealer marked the price of an item 40% above the cost price. He then gave…

Concept

A markup and a discount are percentages of different bases: the markup is taken on the cost price, while each discount is taken on the price standing just before it. So the chain is multiplicative — SP = CP × (1 + markup) × (1 − d1) × (1 − d2) — and the loss is simply CP − SP. Since every percentage factor is known, one unknown cost price can be recovered from the given loss amount.

Applying it here

1. Let the cost price be ₹x. A markup of 40% above cost gives the marked price MP = 1.40x.

2. The first discount of 20% leaves 80% of the marked price: 1.40x × 0.80 = 1.12x.

3. The second discount of 25% is taken on that reduced price and leaves 75% of it: 1.12x × 0.75 = 0.84x. So SP = 0.84x.

4. Loss = CP − SP = x − 0.84x = 0.16x.

5. The loss is given as ₹720, so 0.16x = 720, which gives x = 720 ÷ 0.16 = ₹4,500 as the cost price.

6. Therefore the selling price is SP = 0.84 × 4,500 = ₹3,780.

Cross-check

Rebuild the whole chain from a cost price of ₹4,500 and confirm that the loss comes back to ₹720:

Note the trap: discounts of 20% and 25% are not a single 45% discount. Their combined effect is 1 − (0.80 × 0.75) = 0.40, i.e. 40% off. Even so, a 40% markup followed by 40% off ends in a loss, because the 40% is taken off the larger marked price while the 40% was added to the smaller cost price.