How do you solve profit and loss questions with marked price and discount?

A shopkeeper in Sarojini Nagar buys a kurta for Rs.800. That is the cost price (CP). He writes Rs.1,000 on the tag. That is the marked price (MP). You bargain and he gives 10% off, so you pay Rs.900. That is the selling price (SP).

He made Rs.100 on a Rs.800 purchase, so his profit is 100 / 800 = 12.5%. Two rules solve most questions:

• Profit and loss percent are on CP.
• Discount percent is on MP.

Question: A shopkeeper marks an item 25% above cost and allows a 10% discount. If the cost price is Rs.800, find the profit percent.

1. MP = 800 x 125 / 100 = Rs.1,000.
2. Discount = 10% of 1,000 = Rs.100, so SP = Rs.900.
3. Profit = 900 - 800 = Rs.100.
4. Profit % = 100 / 800 x 100 = 12.5%.

Shortcut with multipliers: 1.25 x 0.90 = 1.125, so SP is 112.5% of CP, a 12.5% profit. You do not even need the Rs.800.

const cp = 800;
const mp = cp * 125 / 100;   // marked 25% above cost
const sp = mp * 90 / 100;    // 10% discount
console.log(sp); // Output: 900
console.log((sp - cp) / cp * 100); // Output: 12.5

• Profit = SP - CP. Loss = CP - SP.
• Profit % = Profit / CP x 100. Loss % = Loss / CP x 100.
• SP = CP x (100 + profit%) / 100, or CP x (100 - loss%) / 100.
• SP = MP x (100 - discount%) / 100.
• To find CP from SP: CP = SP x 100 / (100 + profit%).
• Faulty weights: a dealer who claims to sell at cost but gives 900 g for 1 kg gains 100 / 900 x 100 = 11.11%. Gain % = error / (true weight - error) x 100.

These questions appear in TCS NQT, Infosys, Wipro, AMCAT and bank exams. The same thinking helps when you see "MRP Rs.1,999, now Rs.1,399" on Myntra or Flipkart: that is a discount of 600 / 1,999, about 30%. It also helps you check whether "buy 2 get 1 free" is really better than a flat 30% off (it is a 33.3% discount on three items).

• Taking profit percent on the selling price instead of the cost price.
• Taking discount percent on the cost price instead of the marked price.
• Adding successive discounts: 20% plus 10% off is 28% off, not 30%.
• Assuming that selling two items at the same price, one at x% profit and one at x% loss, means no profit or loss. It is always a loss of x squared / 100 percent.

• An article sold for Rs.1,200 gives a 20% profit. At what price should it be sold for a 30% profit?
• Two phones are each sold for Rs.990, one at 10% profit and the other at 10% loss. What is the overall result?
• The cost price of 15 pens equals the selling price of 12 pens. Find the profit percent.