Profit and Loss Questions for AFCAT

Core Definitions

Cost Price (CP) is what you pay to buy or produce an item. Selling Price (SP) is what you charge the customer. If SP is more than CP, you earn Profit. If SP is less than CP, you suffer Loss. Overhead expenses like transport or rent are always added to CP before calculating profit or loss.

• Profit = SP - CP (when SP > CP)
• Loss = CP - SP (when CP > SP)
• Profit% and Loss% are always calculated on CP, not SP
• Marked Price (MP) is the listed price before any discount
• Discount is always calculated on MP, not CP
• Net SP after discount = MP x (1 - Discount%/100)

Marked Price, Discount, and Double Trouble

Many AFCAT questions combine a markup (increase on CP to get MP) and a discount (reduction on MP to get SP). The trick is that profit or loss is still measured against CP. When two successive discounts of x% and y% are given, you cannot simply add them — use the combined formula.

• MP is set above CP to allow room for discount and still make profit
• Single discount of x% on MP: SP = MP x (100-x)/100
• Two successive discounts x% and y%: effective discount = x + y - xy/100
• To find overall profit/loss, compare final SP with original CP
• If profit% = discount%, the markup percentage is higher than both

Dishonest Shopkeeper and False Weight

A classic AFCAT trap question involves a shopkeeper who claims to sell at cost price but uses a faulty weight. For example, he sells 900g but charges for 1000g. His actual gain is calculated using the error in weight. The formula below handles this directly without you needing to assign actual prices.

• Shopkeeper uses less weight but charges full price — that difference is his profit
• Profit% is based on what the customer actually receives (true value), not what is charged
• Formula uses error (short weight) over true weight, not over stated weight
• If selling above CP with false weight, combine both gains using multipliers

Equal Selling Price Trap (Two Items, Same SP)

This is one of the most frequently repeated AFCAT patterns. Two items are sold at the same price, one at x% profit and one at x% loss. Intuition says they cancel out — but they never do. There is always a net loss. The formula gives you the loss percentage directly.

• Same SP, one profit x%, one loss x% — the seller always ends up at a net loss
• Higher CP item (the loss one) always outweighs the lower CP item (the profit one)
• Net loss% depends only on x, not on the actual SP

• Calculating profit% or loss% on SP instead of CP — always anchor percentage to cost price
• Adding successive discounts directly (10% + 20% = 30%) instead of using the formula — actual effective discount is always less than the sum
• In the false weight problem, dividing error by stated weight (1000g) instead of true weight received (900g) — this gives a wrong and lower answer
• Forgetting to add overhead expenses (freight, packaging) to CP before computing profit percentage
• In the equal SP trap, assuming profit and loss cancel — they never cancel; there is always a net loss equal to x-squared over 100

• CSPM hook — Cost, Sell, Profit, Marked: CP comes first in every formula, SP is what the customer sees, Profit/Loss% ride on CP, Discount rides on MP
• Equal SP trap mnemonic: SAME PRICE, SAME LOSS RATE — if both percentages are x, net loss is x-squared over 100. Think: same rhymes with pain (loss)
• False weight trick: Gain% = Error over WHAT THEY GOT, not what you said. Customer got less, so divide by less.
• Successive discount visual: peel an onion in two rounds — each round takes a percentage of what remains, not of the original. Never add the layers.

• AFCAT typically gives 2-3 Profit and Loss questions per paper, often at moderate difficulty. Expect at least one to involve MP and discount combined with CP, testing whether you can chain two formula steps correctly.
• The equal SP trap question (one profit, one loss at same percentage) has appeared in multiple AFCAT papers. Memorise the x-squared over 100 formula and you solve it in under 20 seconds.
• Questions are mostly single-step or two-step. If your solution is going beyond 3 steps, you have likely chosen a harder method — try the direct formula instead.
• Watch for percentage chains: a 20% rise followed by a 20% fall does NOT return to original. Use multiplier method: 1.2 x 0.8 = 0.96, so there is a 4% net loss. This pattern disguises itself as profit-loss but is actually percentage change.
• Time target: spend max 75 seconds on a standard Profit and Loss question. If it involves false weights or successive discounts, allow up to 90 seconds. Do not let one tricky question eat into your Numerical section time.