Discounts and Averages at Meera's Sweet Shop
Meera runs a sweet shop near the bus stand in Bhagalpur. A wholesaler's list price for a gift pack of laddus is ₹500. Meera gets a trade discount of 20 per cent on the list price, and a further cash discount of 5 per cent if she pays within ten days, which she always does. Transport from the wholesaler's godown to her shop costs ₹15 per pack. She sells the pack at ₹480. Her sales for one week were: Monday 6 packs, Tuesday 4, Wednesday 10, Thursday 4, Friday 2, Saturday 12, Sunday 4. Her friend advises her to raise the marked price so that she can offer a 10 per cent discount to college students and still earn 25 per cent on cost. Meera is unsure whether her average sale of six packs a day is a fair basis for planning; she buys stock twice a week and does not want unsold packs, which stay fresh only for four days.
1. Compute Meera's cost per pack and her profit percentage on cost and on selling price at ₹480. Show which discount is deducted where and why.
Read the worked answer
Step-by-step cost build-up:
- Trade discount is deducted from the list price and is never recorded separately in the books: ₹500 − 20% of ₹500 (₹100) = ₹400.
- Cash discount is allowed for prompt payment: 5% of ₹400 = ₹20, so the net payment is ₹380.
- Carriage inward is part of the cost of purchase, so add transport: ₹380 + ₹15 = ₹395 per pack.
Profit at a selling price of ₹480:
- Profit = ₹480 − ₹395 = ₹85 per pack.
- Profit on cost = 85 ÷ 395 × 100 = 21.52%.
- Profit on selling price = 85 ÷ 480 × 100 = 17.71%.
Why it matters: the same ₹85 is 21.52% or 17.71% depending on the base. Trade convention quotes margin on cost, so Meera should say 21.52% - if she quoted 17.71% to the wholesaler on the assumption that it was a margin on sales, she would understate her own mark-up. Note also that the ₹20 cash discount is income for Meera as buyer, but it does not reduce the ₹480 at which she sells.
2. Calculate the mean, median and mode of daily sales, and advise Meera which measure she should use for stock planning.
Read the worked answer
Arranging the data (packs per day): 6, 4, 10, 4, 2, 12, 4
Sorted: 2, 4, 4, 4, 6, 10, 12
- Mean = (6 + 4 + 10 + 4 + 2 + 12 + 4) ÷ 7 = 42 ÷ 7 = 6 packs.
- Median = the 4th value in the sorted list = 4 packs.
- Mode = the most frequent value, 4 appearing three times = 4 packs.
Interpretation: the mean is pulled upward by Saturday's 12 packs and by Wednesday's 10, so it is 50 per cent higher than what a normal day looks like. The distribution is skewed to the right. Mean is 6, median and mode are both 4, which tells Meera that four packs is the typical day and that two days - Wednesday and Saturday - carry most of the extra demand.
Advice: for perishable stock she should plan on the median, not the mean. Buying 6 a day would leave roughly 14 packs unsold over a week at a cost of ₹395 each. A safer plan is about 4 packs for Monday, Tuesday, Thursday, Friday and Sunday and 10–12 for Wednesday and Saturday, roughly 30–32 packs a week instead of 42. She should also record the range (2 to 12) so that she never stocks the everyday level on a Saturday.
3. Find the marked price Meera needs so that, after a 10 per cent student discount, she still earns 25 per cent on cost. Then comment on the result.
Read the worked answer
Step 1 - target selling price for 25% on cost: Cost = ₹395, so required profit = 25% of 395 = ₹98.75, and the required net selling price = 395 × 1.25 = ₹493.75.
Step 2 - marked price that leaves ₹493.75 after a 10% discount: If M is the marked price, M × 0.90 = 493.75, so M = 493.75 ÷ 0.90 = ₹548.61 (about ₹549).
Step 3 - check what happens if she marks only ₹493.75 and then discounts: Selling price = 493.75 × 0.90 = ₹444.38; profit = 444.38 − 395 = ₹49.38, which is 49.38 ÷ 395 × 100 = 12.5% on cost, or 11.11% on sales.
Comment: a 10 per cent discount on price does not cut profit by 10 per cent; it cuts the intended 25 per cent margin exactly in half, because the whole discount comes out of profit, not out of cost. Meera has three honest options: mark at about ₹549 (which may look expensive beside competitors selling at ₹480), offer a smaller discount such as 3–4 per cent, or reduce the cost by negotiating a higher trade discount. She should never advertise 25 per cent and then quietly accept 12.5 per cent.