Profit and loss for RRB Group D

Profit and loss is percentage used in a shop. The seller buys at one price, sells at another, and the question asks how much was gained or lost, as an amount or a percentage. Add a marked price and a discount, and you have almost every question type you will see.

The whole topic rests on two rules about the base. Get the base right and the rest is arithmetic you already know from the percentage guide.

The terms

The formulas

• Profit % = profit ÷ CP × 100
• Loss % = loss ÷ CP × 100
• Discount % = discount ÷ MP × 100
• SP = MP − discount

The multiplier method

Instead of finding the profit and adding it, multiply straight away:

• SP = CP × multiplier.
• CP = SP ÷ multiplier. This is the one people get wrong. If ₹1,080 includes a 20% profit, the cost price is 1,080 ÷ 1.2 = 900, not 1,080 − 20% of 1,080.

Mark-up and discount together

A shopkeeper marks goods above cost, then gives a discount. Take CP = 100 and apply both multipliers in turn. You get the SP, and the profit % can be read off directly.

Successive discounts

Two discounts are not simply added. Apply them one after the other, or use the single equivalent discount:

• Equivalent discount = a + b − (a × b ÷ 100)

For 10% and 5%: 10 + 5 − 0.5 = 14.5%, not 15%.

Two special cases

• Same SP, same % profit and loss: if two items are sold at the same price, one at x% profit and the other at x% loss, the overall result is always a loss of (x × x ÷ 100)%.
• False weights: a dealer who claims to sell at cost price but gives less weight gains on every sale. Profit % = error ÷ (true value − error) × 100. With a 900 g weight for 1 kg, the profit is 100 ÷ 900 × 100 = 11 1/9%.

Worked examples

Example 1: CP = ₹800, SP = ₹920. Find the profit %.

• Profit = 120. 120 ÷ 800 × 100 = 15%.

Example 2: An item is sold for ₹1,080 at a 20% profit. Find the CP.

• CP = 1,080 ÷ 1.2 = ₹900.
• Check: 20% of 900 = 180; 900 + 180 = 1,080.

Example 3: A shopkeeper marks goods 20% above cost and gives a 10% discount. Find the profit %.

• CP = 100 → MP = 120 → SP = 120 × 0.9 = 108.
• Profit = 8%.

Example 4: Marked price ₹2,000, successive discounts of 10% and 5%. Find the SP.

• 2,000 × 0.9 = 1,800; 1,800 × 0.95 = ₹1,710.
• Check with the equivalent discount: 14.5% of 2,000 = 290; 2,000 − 290 = 1,710.

Example 5: Two phones are sold for ₹990 each. One gives a 10% profit and the other a 10% loss. Find the overall result.

• CP of the first = 990 ÷ 1.1 = 900. CP of the second = 990 ÷ 0.9 = 1,100.
• Total CP = 2,000; total SP = 1,980. Loss = 20, which is 1%.
• Shortcut: 10 × 10 ÷ 100 = 1% loss.

Example 6: A trader buys 12 pens for ₹96 and sells them at ₹10 each. Find the profit %.

• CP of one pen = 96 ÷ 12 = ₹8. SP = ₹10.
• Profit = 2 ÷ 8 × 100 = 25%.

Common mistakes

• Working out profit % on the selling price.
• Adding successive discounts (10% + 5% is not 15%).
• Finding the CP by subtracting the profit % from the SP instead of dividing by the multiplier.
• Working out a discount on the cost price instead of the marked price.
• Assuming equal profit and loss percentages cancel out.

Practice set

1. CP = ₹400, SP = ₹440. Find the profit %.
2. CP = ₹250, loss 20%. Find the SP.
3. An item is sold for ₹660 at a 10% profit. Find the CP.
4. Find the single discount equal to successive discounts of 20% and 10%.
5. A trader buys oranges at 4 for ₹10 and sells them at 3 for ₹10. Find the profit %.
6. An article costs ₹500. At what price must it be marked so that the seller can give a 20% discount and still make a 20% profit?
7. Selling an item for ₹540 gives a 10% loss. At what price should it be sold for a 10% profit?
8. A dealer claims to sell at cost price but uses an 800 g weight for 1 kg. Find the profit %.

Answers:

1. 10%. Profit 40; 40 ÷ 400 × 100.
2. ₹200. 250 × 0.8.
3. ₹600. 660 ÷ 1.1.
4. 28%. 20 + 10 − (20 × 10 ÷ 100) = 28.
5. 33⅓%. Take 12 oranges: CP = ₹30, SP = ₹40; profit 10 ÷ 30 × 100.
6. ₹750. Required SP = 500 × 1.2 = 600; MP = 600 ÷ 0.8 = 750.
7. ₹660. CP = 540 ÷ 0.9 = 600; 600 × 1.1 = 660.
8. 25%. Error 200 g on a true 800 g: 200 ÷ 800 × 100.

What to do next

• Write the two base rules (profit on CP, discount on MP) on a card and read it before every practice set.
• Practise ten CP-from-SP questions using division by the multiplier.
• Solve five mark-up plus discount questions starting from CP = 100.
• Continue with simple and compound interest, which uses the same multipliers year after year.