2.5 Profit, Loss & Discount

Why This Matters

Profit, loss, and discount appear in 4 to 6 RRB Group D mathematics questions per cycle, often as short word problems about shopkeepers, marked prices, or dishonest weights. The arithmetic is simple once the vocabulary is locked; the trap is always the base on which the percentage is calculated.

Core Definitions and Formulas

• Cost Price (CP): the price at which an article is bought.
• Selling Price (SP): the price at which it is sold.
• Marked Price (MP): the label price the seller quotes (also called the list price).
• Profit = SP - CP (when SP is greater than CP); Loss = CP - SP (when CP is greater than SP).
• Profit % = (Profit / CP) * 100; Loss % = (Loss / CP) * 100.
• Discount = MP - SP; Discount % = (Discount / MP) * 100.

The single rule that prevents most errors: profit/loss percentage is always on CP; discount percentage is always on MP. Mixing the two bases is the most common RRB trap.

Worked Examples — Basic Profit and Loss

Example 1. An article bought for Rs 400 is sold for Rs 500. Find the profit percentage. Profit = 100. Profit % = (100/400) * 100 = 25%. This is not 20%; 20% would be the profit as a percentage of SP, which is wrong.

Example 2. A watch is sold for Rs 720 at a loss of 10%. Find CP. SP = 90% of CP, so 0.9 * CP = 720, giving CP = 720 / 0.9 = Rs 800.

Marked Price and Discount

Shopkeepers mark an article above CP and then offer a discount. The chain is CP, then MP, then SP.

• SP = MP * (1 - d/100), where d is the discount percentage.
• If a trader wants a profit of p% after allowing a discount of d%, then MP = CP * (100 + p) / (100 - d).

Worked example. A shopkeeper marks goods 40% above cost and allows a 10% discount. Find the profit percentage. Let CP = 100. MP = 140. SP = 140 * 0.9 = 126. Profit = 26, so profit % = 26%.

Successive Discounts

When two or more discounts are given one after another, treat them like successive percentages:

Net discount % = d1 + d2 - (d1 * d2)/100

Equivalently, SP = MP * (1 - d1/100) * (1 - d2/100).

Worked example. A shopkeeper offers 20% and then 10% on the marked price of Rs 1,000. What does the customer pay? SP = 1000 * 0.8 * 0.9 = Rs 720. The equivalent single discount = 1000 - 720 = Rs 280, which is 28%, not the 30% you would get by adding.

Dishonest Dealer and Weight Tricks

This is a classic RRB favourite. A dealer claims to sell at cost price but uses a false weight. The gain comes from giving less quantity than the customer pays for.

Formula: Gain % = (True weight - False weight) / False weight * 100.

Worked example. A dealer sells rice at cost price but uses a 900 g weight for 1 kg. Find the gain percentage. Gain % = (1000 - 900) / 900 * 100 = 100/900 * 100 = 11.11%.

The trap is to put the difference over the true weight (1000), which gives 10%, but that is wrong. The dealer's gain is measured on the quantity he actually parts with, which is the false weight, and that is the base.

Quick Reference Table

A Famous RRB Result — Equal Profit and Loss at the Same SP

If two articles are sold at the same selling price, one at a profit of p% and the other at a loss of p%, the net result is always a loss of (p^2 / 100) percent.

Worked example. A man sells two watches for Rs 1,000 each, one at a profit of 20% and the other at a loss of 20%. Net effect? Net loss = (20 * 20) / 100 = 4%. The two percentages do not cancel; they always produce a loss because the two cost prices differ.

Exam Scenarios and Common Traps

• Profit % base = CP, not SP. "Bought for Rs 400, sold for Rs 500" gives a profit of 25%, not 20%.
• Discount % base = MP, not CP. A 10% discount on a Rs 140 marked price is Rs 14 off, not Rs 10 (which would be 10% of CP).
• Adding successive discounts: 20% + 10% is not 30%. Multiply the factors.
• False-weight base: the denominator is the false weight, not the true weight.
• "Sells at cost price" wording: if a dealer "sells at cost price" and still gains, it must be a false-weight problem; there is no other source of profit.
• Same SP, equal profit % and loss %: the net is always a loss of (p^2 / 100)%, a result RRB reuses.

Mastering these patterns means most shopkeeper questions collapse to a single formula applied once, saving precious seconds under the 90-minute clock.