Profit, loss and discount for RRB NTPC: methods and practice

Profit and loss is percentage applied to buying and selling. There are only four prices to track (cost, selling, marked and discount) and two rules about which one each percentage is taken on. Get those two rules right and most questions take under a minute.

Most wrong answers in this chapter do not come from hard arithmetic. They come from taking a percentage on the wrong base. The methods below are built to stop that.

The terms and their bases

Profit % = profit ÷ CP × 100. Discount % = discount ÷ MP × 100. Unless a question says otherwise, profit and loss percentages are on cost.

The multiplier method

Every percentage change is a multiplication:

So SP = CP × (1 + profit%/100), and SP = MP × (1 − discount%/100). To go backwards, divide: CP = SP ÷ 1.2 for a 20% profit.

Why it works: a 20% profit means SP is CP plus one-fifth of CP, which is 6/5 of CP. Writing it as one multiplier lets you chain several steps (mark-up, then discount, then tax) without recalculating a base each time.

Mark-up and discount together

If goods are marked m% above cost and sold at a d% discount, then SP/CP = (1 + m/100)(1 − d/100). Take CP = 100 and you have the profit percentage straight away.

Going the other way: to make p% profit after a d% discount, the marked price must be (100 + p)/(100 − d) times the cost.

Successive discounts

Discounts of a% and then b% equal a single discount of a + b − ab/100 per cent.

Why: this is the successive-change rule from percentage with both changes negative. The second discount is taken on an already reduced price, so it removes less than b% of the original.

For 20% and 10%: 20 + 10 − 2 = 28%. Check: 100 → 80 → 72.

Two traps worth knowing

Same selling price, x% profit on one, x% loss on the other. The overall result is always a loss of x²/100 per cent.
Why: the item sold at a loss had a higher cost price, so the loss is taken on a bigger base than the profit. They never cancel.

False weights. A seller who gives less than they charge for makes a profit even at "cost price". Profit % = (true weight − false weight) ÷ false weight × 100.
Why: the seller's real cost is only for what they hand over, so the base is the false weight.

Worked questions at NTPC level

Q1. A shopkeeper marks goods 25% above cost and gives a 10% discount. Find the profit percentage.

Let CP = 100. MP = 125. SP = 125 × 0.9 = 112.5.
Profit = 12.5%.

Q2. Two articles are sold for ₹1,200 each. One is sold at a 20% profit and the other at a 20% loss. Find the overall gain or loss percentage.

Rule: loss of 20²/100 = 4%.
Check with numbers: CP₁ = 1,200 ÷ 1.2 = 1,000; CP₂ = 1,200 ÷ 0.8 = 1,500. Total CP = 2,500, total SP = 2,400. Loss = 100, and 100 ÷ 2,500 = 4%.

Q3. A dishonest shopkeeper uses a 900 g weight in place of 1 kg and sells at cost price. Find the profit percentage.

The customer pays for 1,000 g but gets 900 g. Profit = 100 on a cost of 900.
Profit % = 100 ÷ 900 × 100 = 11 1/9%.

Q4. A shopkeeper sells an article at a 10% loss. Had it been sold for ₹90 more, there would have been an 8% profit. Find the cost price.

Going from −10% to +8% is a swing of 18% of CP, and that swing is ₹90.
CP = 90 ÷ 0.18 = ₹500. Check: SP at 10% loss = 450; 450 + 90 = 540 = 1.08 × 500.

Q5. A trader buys oranges at 12 for ₹10 and sells them at 10 for ₹12. Find the profit percentage.

Take a number of oranges both 12 and 10 divide: 60.
Cost of 60 = 5 × ₹10 = ₹50. Selling price of 60 = 6 × ₹12 = ₹72.
Profit = 22 on 50 = 44%.

Q6. How far above cost must an article be marked so that, after a 20% discount, the trader still makes a 20% profit?

MP/CP = (100 + 20)/(100 − 20) = 120/80 = 1.5. So mark it 50% above cost.
Check: CP 100, MP 150, SP = 150 × 0.8 = 120.

Common mistakes

• Profit % on selling price. Always divide by cost unless told otherwise.
• Adding successive discounts. 20% and 10% is 28%, not 30%.
• Assuming equal profit and loss percentages cancel when the selling prices are equal.
• Using the wrong base for false weights. Divide by the weight actually given, 900, not by 1,000.
• Confusing marked price with cost price in discount questions.

Practice set

1. CP = ₹500, SP = ₹575. Find the profit percentage.
2. An article sold for ₹720 gives a 20% profit. Find the cost price.
3. The marked price is ₹1,200 and the discount is 25%. Find the selling price.
4. Find the single discount equal to successive discounts of 10% and 10%.
5. Goods are marked 40% above cost and sold at a 20% discount. Find the profit percentage.
6. An article is sold at a 5% profit. Had it been sold for ₹60 more, the profit would have been 10%. Find the cost price.
7. By selling 33 m of cloth, a trader gains the cost price of 11 m. Find the profit percentage.
8. Two articles are sold for ₹990 each, one at a 10% profit and one at a 10% loss. Find the overall result.

Answers:

1. 15%. Profit 75; 75 ÷ 500 × 100.
2. ₹600. 720 ÷ 1.2.
3. ₹900. 1,200 × 0.75.
4. 19%. 10 + 10 − 1.
5. 12%. 1.4 × 0.8 = 1.12.
6. ₹1,200. The 5% gap is ₹60, so CP = 60 ÷ 0.05.
7. 33 1/3%. Profit is the cost of 11 m on the cost of 33 m; 11/33 = 1/3.
8. 1% loss. 10²/100 = 1. Check: CPs are ₹900 and ₹1,100, total ₹2,000; SP ₹1,980; loss ₹20.

What to do next

• For the next 20 profit and loss questions, start each one by writing CP = 100.
• Learn the four multiplier pairs you meet most (1.2 and 0.8, 1.25 and 0.75) as fractions too: 6/5, 4/5, 5/4, 3/4.
• Revise successive change in percentage, then move on to simple interest.