A wholesaler marks up a batch of 100 identical clocks by 80% on cost and offers a trade discount of 25% to retailers. A retailer purchases all the clocks and spends Rs. 48,000. What is the cost price per clock for the wholesaler?

Correct — A. The retailer pays the marked price less the trade discount, so chain the two factors on the cost.

Price per clock: 48,000 ÷ 100 = 480
Combined factor: 1.80 × 0.75 = 1.35
Cost price: 480 ÷ 1.35 = 355.555…
Rounded to paise: ₹355.56 → option (a)

Why the others are wrong

• (b)
  Rs. 426.56 — ₹426.56 × 1.35 = ₹575.86 per clock, about ₹57,586 for the batch. That is well above the ₹48,000 the retailer paid.
• (c)
  Rs. 385.56 — ₹385.56 × 1.35 = ₹520.51 per clock, about ₹52,051 for 100 clocks, not the ₹48,000 paid.
• (d)
  Rs. 435.56 — ₹435.56 × 1.35 = ₹588.01 per clock, about ₹58,801 for the batch, again more than the ₹48,000 paid.

Successive percentage changes multiply, they do not add. An 80% markup multiplies cost by 1.80, and a 25% discount then multiplies by 0.75. Together that is 1.35, a net 35% above cost, not 55%.

So the retailer's price = 1.35 × CP. Divide the known price by the combined factor to recover the cost.

Key facts

• Marked price = CP × (1 + markup⁄100).
• Price after a discount = MP × (1 − discount⁄100).
• Two successive changes of a% and b% equal a single change of a + b + ab⁄100 percent. Here 80 − 25 − 20 = 35%.
• 1.35 = 27⁄20, so CP = 480 × 20⁄27 = 9600⁄27 ≈ 355.56.

Common traps

• Netting the percentages: 80 − 25 = 55% gives 480 ÷ 1.55 ≈ ₹309.68, which is not an option.
• Dividing the batch price of ₹48,000 by 1.35 and forgetting to divide by the 100 clocks.

No directly related past PYQ was found.