Choosing Between Successive Discounts and a Flat Discount
A bookshop marks a competitive-exam guide at ₹850. The distributor offers two purchase schemes. Scheme A gives successive discounts of 20% and 10% on the marked price, but adds a handling charge of ₹12 per book. Scheme B gives a single 28% discount with no handling charge. The shop expects to sell 40 copies at the marked price during a coaching camp. The owner bought older stock at ₹560 per copy and wants the new purchase to earn at least 12% profit on that cost. Transport is free only for orders above 30 copies; below that, ₹8 per book applies. The owner wrongly says that '20% and then 10% is the same as 30% off' and is about to choose Scheme A because the first discount looks bigger.
1. Show whether successive discounts of 20% and 10% equal a single 30% discount. Find the equivalent single discount and the rupee difference on a marked price of ₹850.
Read the worked answer
After 20% off, price = 0.80 × 850 = ₹680. After another 10% off, price = 0.90 × 680 = ₹612. The multiplier is 0.80 × 0.90 = 0.72, so the equivalent single discount is 28%, not 30%. A 30% discount would give 0.70 × 850 = ₹595. The difference is 612 − 595 = ₹17 per book. Successive discounts are smaller because the second discount is calculated on the already-reduced price, not on ₹850.
2. Compute the purchase cost per book under each scheme. If the book is sold at ₹850, find the profit percentage on the ₹560 cost under each scheme.
Read the worked answer
Scheme A: discounted price = ₹612; add handling = 612 + 12 = ₹624. Profit = 850 − 624 = ₹226. Profit % = 226 ÷ 560 × 100 = 40.36%. Scheme B: purchase cost = 0.72 × 850 = ₹612. Profit = 850 − 612 = ₹238. Profit % = 238 ÷ 560 × 100 = 42.50%. Both schemes clear the 12% target easily, but Scheme B gives the higher profit per book.
3. For 40 copies, calculate total profit under each scheme and recommend a choice. Check the transport condition and the 12% profit target.
Read the worked answer
Scheme A cost = 40 × 624 = ₹24,960. Scheme B cost = 40 × 612 = ₹24,480. Revenue at marked price = 40 × 850 = ₹34,000. Profit A = 34,000 − 24,960 = ₹9,040. Profit B = 34,000 − 24,480 = ₹9,520. Scheme B gives ₹480 more total profit. Transport is free because 40 > 30, so no ₹8-per-book charge applies. The 12% target is 0.12 × 560 = ₹67.20 per book; actual profits are ₹226 and ₹238 per book, so both pass. Choose Scheme B.