Profit, Loss & Discount · Topic 8 of 8

🧩 Tricky / Multi-step

4 exam question types, fully solved

The hardest questions just chain the earlier ideas together. The only way to slip is to attach a percentage to the wrong base — so pin each one down.

Anchor every percentage to its base

• Profit/loss → on CP. Discount → on MP. In a resale chain, one seller's SP becomes the next buyer's CP — work one link at a time.

• Perishables: the good fraction alone must cover the whole cost, so markup = − 1.

• Mixtures: add the full cost of every batch, add the target profit, then divide by the total quantity.

• Cost-price shift: if MP and discount stay fixed, the SP is locked — recompute profit% on the NEW cost.

🔗Chain Multipliersuccessive % changes multiply, never add

starting value (₹)

step 1%× 6/5→ ₹1,200

step 2%× 5/4→ ₹1,500

6/5 × 5/4 = × 3/2

one overall multiplier = +50% net

₹1,000 × 6/5 → ₹1,200 × 5/4 → ₹1,500 Shortcut: ₹1,000 × 3/2 = ₹1,500 in one move — the % changes never simply add.

Marked 30% up, 12% discount: profit% = 30 − 12 − = %.

Q1Marked 30% above CP, 12% discount. Profit% is:

Q220% of stock spoils; the rest must give 20% overall profit. Markup on good items:

Q3Two parts: 1/3 sold at 30% loss; what gain on the rest breaks even?

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Real exam questions — Tricky / Multi-step

4 question types · 12 solved examples from real SSC papers

Multi-step, mixtures and cost-price shifts — pin each % to its own base and take one link at a time.

How to solve this type

Anchor every percentage to its own base: profit and loss are on cost price, discount on marked price. For resale chains, one seller's SP becomes the next buyer's CP, so work one link at a time. Assume a convenient cost (₹100 per unit) and count cost only for the items actually paid for. When selling prices are given as a ratio, convert each SP back to its CP before you compare.

A sells a TV to B at a 19% loss for ₹4,860. B then sells it to C at a price that would have given A a 17% profit. Find B's gain.

A₹2,160B₹1,160C₹3,160D₹4,160

Shyam buys 16 pens and gets 4 pens free. He marks each pen 20% above its cost price and sells all 20 at the marked price. Find his profit%.

A36%B48%C50%D37.5%

The selling price of a first shirt is twice that of a second. The first is sold at 8% profit and the second at 3% loss. Find the overall profit% (to 2 decimal places).

A3.86%B4.07%C4.60%D4.86%