Mark-up, Discount and a Delivery Cost
A shop buys a machine for Rs 12,000. It marks the price up by 25% on cost. During a promotion it advertises 10% off the marked price. A 5% sales tax is added to the discounted price and is remitted to the government; it is not shop revenue. The shop also pays a fixed Rs 500 delivery charge for each machine sold. The manager wants to know the customer's final payment, the profit per machine, and what discount would yield a target profit of Rs 2,000 per machine.
1. Compute the customer's final payment and the shop's profit per machine.
Read the worked answer
Marked price = 12,000 × 1.25 = Rs 15,000. Discounted price = 15,000 × 0.90 = Rs 13,500. Sales tax = 13,500 × 0.05 = Rs 675, so the customer pays 13,500 + 675 = Rs 14,175.
The tax is remitted, so the shop keeps Rs 13,500. Its costs are the purchase price plus delivery: 12,000 + 500 = Rs 12,500.
Profit = 13,500 − 12,500 = Rs 1,000 per machine.
A common trap is to count the Rs 675 tax as revenue; that would wrongly inflate profit to Rs 1,675.
2. What single discount rate on the marked price would give a profit of Rs 2,000 per machine, with the same tax treatment and delivery cost?
Read the worked answer
Work backwards from the required profit.
Required revenue before tax = purchase cost + delivery + target profit = 12,000 + 500 + 2,000 = Rs 14,500.
The marked price is Rs 15,000. The discount must therefore be 15,000 − 14,500 = Rs 500.
Discount rate = 500 ÷ 15,000 = 1/30 ≈ 3.33%.
Check: 15,000 × (1 − 1/30) = 14,500. Subtract 12,500 of costs to get Rs 2,000 profit. The 5% tax is added afterwards and passed on, so it does not enter the profit calculation.
3. The manager says: 'My mark-up is 25% and my discount is 10%, so I still make 15% profit on cost.' Identify two errors in this statement and give the actual profit percentage on cost.
Read the worked answer
First error: the percentages have different bases. The 25% mark-up is on the Rs 12,000 cost, while the 10% discount is on the Rs 15,000 marked price. Subtracting 10 from 25 treats them as if they shared a base.
Second error: the Rs 500 delivery cost is ignored.
The actual arithmetic: the mark-up adds Rs 3,000; the discount removes Rs 1,500; the gross margin is Rs 1,500, which is 12.5% of cost. Subtracting delivery of Rs 500 leaves Rs 1,000, which is 1,000 ÷ 12,000 ≈ 8.33% of cost. The claimed 15% is therefore far too high.