Profit, Loss and Discount

Profit and loss is pure percentage dressed in shopkeeper language, and SBI Clerk asks two to four questions from it every year. Every sum reduces to three quantities — cost price, selling price and marked price — so once you fix what each letter stands for, the formulas fall out on their own. The trap that costs marks is never the arithmetic; it is calculating a percentage on the wrong base, so anchor everything to cost price unless told otherwise.

Cost Price, Selling Price and the Core Formulas

Cost price (CP) is what the seller pays, selling price (SP) is what the buyer pays, and the gap between them is profit or loss. Both profit% and loss% are always taken on CP, which is the base you must never confuse. Reading SP as a single multiplier of CP — SP = CP × (100 + profit%)/100 — lets you jump straight to the answer instead of finding the profit and adding it back separately. When two articles are sold at the same price, one at x% profit and the other at x% loss, there is always a net loss of x²/100 percent, never a break-even — a standard SBI Clerk one-liner that mirrors the equal rise-and-fall result and rewards the formula over the tempting 'they cancel out' guess.

Profit% = (SP − CP)/CP × 100 SP = CP × (100 + profit%)/100 CP = SP × 100/(100 + profit%)

Marked Price and Discount

Marked price (MP) is the tag price before any reduction, and discount is always a percentage of MP, not of CP — this is the second base you must keep straight. So SP = MP × (100 − discount%)/100. A shopkeeper marks goods above cost, then offers a discount, and still profits, which is exactly the layered situation the exam loves. Track two bases at once: profit on CP, discount on MP, and the sum untangles cleanly.

Solved Examples

Example 1: CP 400, SP 500 → profit% = 100/400 × 100 = 25%. Example 2: An item marked at 800 with a 20% discount sells at 800 × 80/100 = 640. Example 3: SP 660 at 10% profit means CP = 660 × 100/110 = 600, so always divide back by (100 + profit%) to recover cost.

✗ Taking discount as a percentage of cost price  |  ✓ Taking discount as a percentage of marked price

The Dishonest Dealer

A classic SBI Clerk twist is the dealer who sells at cost price but uses a false weight — giving 900 grams for a marked kilogram. Here the profit comes from the short weight, not the price, so profit% = (error / true weight) × 100 = 100/900 × 100 ≈ 11.1%. The base is the amount actually delivered, not the claimed one. Spot this wording early, apply the goods-left-over base, and a question that looks tricky becomes a one-line calculation. If the dealer also marks the price up or offers a discount on top of the false weight, combine the two gains as a successive change rather than adding them, and the overall profit still resolves in a couple of steps.