X sells a laptop to Y at a loss of 35% and Y sells that laptop to Z at a…
2025
X sells a laptop to Y at a loss of 35% and Y sells that laptop to Z at a profit of 36%. If Z bought the laptop for ₹4,862, then what was the price (in ₹) of the laptop for X?
- A.
5761
- B.
5510
- C.
5638
- D.
5500
Attempted by 15 students.
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Correct answer: D
When an item passes through a chain of sales, each seller's selling price becomes the next buyer's cost price. A loss of L% at a stage multiplies that stage's cost by (1 − L/100); a profit of P% multiplies it by (1 + P/100). The final price after a chain of such stages equals the original price times the product of all the stage multipliers.
Let X's price (X's cost) = ₹P.
X sells to Y at a loss of 35%, so Y's cost = P × (1 − 35/100) = 0.65P.
Y sells to Z at a profit of 36%, so Z's price = 0.65P × (1 + 36/100) = 0.65P × 1.36 = 0.884P.
Z bought the laptop for ₹4,862, so 0.884P = 4,862.
P = 4,862 ÷ 0.884 = ₹5,500.
Cross-check: ₹5,500 × 0.65 = ₹3,575 (Y's cost); ₹3,575 × 1.36 = ₹4,862, which matches the price Z paid — confirming X's price was ₹5,500.