Profit, loss and discount for SBI PO

Profit and loss questions in SBI PO-style papers rarely stop at one step. They combine a mark-up with a discount, two items sold at the same price, or a dishonest weight with a price change. They appear as word problems in the prelims, inside caselets and DI sets in the mains, and as one side of a quantity comparison.

The good news is that one habit solves most of them: take the cost price as 100. Percentages then become plain numbers, and every step is a multiplication. This guide explains the core formulas and why they work, then goes through the patterns you will meet, with a practice set.

The core ideas

Why the bases differ. Profit is always measured on cost, because that is what the seller risked. Discount is always measured on the marked price, because that is the price the buyer sees. Mixing the bases is the most common error in this chapter.

Why CP = 100 works. Profit percentages don't depend on the actual cost. If a 25% mark-up and 12% discount give 10% profit on an item costing ₹100, they give 10% on one costing ₹3,700 too. Starting at 100 just makes the arithmetic clean.

Pattern 1: mark-up and discount

Goods are marked 25% above cost and sold at a 12% discount. What is the profit percentage?

• CP 100, MP 125, SP = 125 × 0.88 = 110.
• 10% profit.

Working backwards. A seller wants a 20% profit after giving a 25% discount. How far above cost should the goods be marked?

• SP must be 120. SP = MP × 0.75, so MP = 120 ÷ 0.75 = 160.
• Mark 60% above cost.

Pattern 2: successive discounts

Discounts of 20% and then 10% are not a 30% discount.

• MP 100, after 20%: 80, after 10%: 72.
• Single equivalent discount = 28%.
• The rule a + b − ab/100 gives 20 + 10 − 2 = 28. The second discount works on a smaller price, so it removes less.

Pattern 3: same selling price, equal profit and loss

Two items are each sold for ₹990, one at a 10% profit and the other at a 10% loss.

• CP₁ = 990 ÷ 1.1 = 900. CP₂ = 990 ÷ 0.9 = 1,100.
• Total CP 2,000; total SP 1,980.
• Loss of ₹20, or 1%.

When the selling prices are equal and the profit and loss percentages are both x, there is always a loss of x²/100 percent. Here, 10²/100 = 1%. The reason: the item sold at a loss cost more, so the same percentage costs more rupees on it.

Pattern 4: false weights

A shopkeeper uses a 900 g weight in place of 1 kg and sells at the cost price.

• The shopkeeper gives 900 g but charges for 1,000 g. Gain = 100 g on 900 g actually given.
• Profit = 100 ÷ 900 × 100 = 11.11%.

The base is what the shopkeeper actually gave, 900 g, because that is their real cost.

Cheating on both sides. A trader takes 10% extra when buying (1,100 g for the price of 1,000 g) and gives 10% less when selling (900 g for the price of 1,000 g).

• For the price of 1,000 g, the trader gets 1,100 g and sells 900 g at a time.
• Profit = 1,100 ÷ 900 − 1 = 2/9 ≈ 22.22%.

Pattern 5: free-item offers

"Buy 4, get 1 free." What is the effective discount?

• The customer pays for 4 and receives 5.
• Discount = 1 ÷ 5 × 100 = 20%. The base is the number of items received.

Pattern 6: cost of some equals selling price of others

The selling price of 12 items equals the cost price of 15. What is the profit percentage?

• Take CP of one item as 1. SP of 12 = 15, so the profit on 12 items is 3.
• Profit = 3 ÷ 12 × 100 = 25%.
• General rule: if SP of a items = CP of b items, profit % = (b − a) ÷ a × 100. If b < a, it is a loss.

Pattern 7: profit on selling price

A trader earns a profit equal to 20% of the selling price. What is the profit as a percentage of cost?

• SP 100, profit 20, so CP 80.
• Profit on cost = 20 ÷ 80 × 100 = 25%.

Quick reference

Practice set

1. Goods are marked 40% above cost and sold at a 15% discount. What is the profit percentage?
2. The cost price of 20 items equals the selling price of 16. What is the profit percentage?
3. "Buy 3, get 1 free." What is the effective discount?
4. Two items are each sold for ₹1,200, one at a 20% profit and one at a 20% loss. What is the overall result?
5. What single discount equals successive discounts of 25% and 20%?
6. A seller wants a 26% profit after a 10% discount. How far above cost should the goods be marked?
7. An article sold for ₹1,380 gives a 15% profit. What is its cost price?

Answers:

1. 19%. 100 → 140 → 140 × 0.85 = 119.
2. 25%. Profit on 16 items = CP of 4 items; 4 ÷ 16 × 100.
3. 25%. Pays for 3, receives 4; 1 ÷ 4 × 100.
4. 4% loss (₹100). CPs are 1,000 and 1,500; total CP 2,500, total SP 2,400. Check: 20²/100 = 4.
5. 40%. 25 + 20 − 500/100 = 40. Or 100 → 75 → 60.
6. 40%. SP must be 126; MP = 126 ÷ 0.9 = 140.
7. ₹1,200. 1,380 ÷ 1.15.

What to do next

• Solve every question in this chapter with CP = 100 for a week, even when the actual price is given.
• Learn the quick-reference table, but make sure you can derive each line.
• Try profit questions inside a caselet and as statements in data sufficiency.
• Move on to simple and compound interest, which uses the same multiplying-factor idea.