Profit, Loss & Discount · Topic 4 of 8

🔗 Successive Selling

1 exam question type, fully solved

One item is resold down a chain (A → B → C), each seller taking their own profit or loss. The prices multiply, they never add.

Chain the multipliers

Each sale multiplies the running price by its own factor: for a profit, for a loss.

• Final price = original CP × the product of all the factors.

• To find a final price, multiply forwards from A; to find the original CP, divide the final price by the product.

Use fractions like and so factors cancel: 20% then 25% profit is just × (a flat 50% rise).

Read carefully which seller's price is asked — sometimes you only step back one link.

🔗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.

A→B at 20% profit, B→C at 25% profit: overall factor = × = .

Q1A sells to B at 20% profit, B to C at 25% profit. If A paid ₹100, C pays:

Q2After a 10% profit and then a 10% loss in a chain, the net factor on the original CP is:

Q3X sells to Y at 25% profit; Y pays ₹500. X's cost was:

📚

Real exam questions — Successive Selling

1 question types · 4 solved examples from real SSC papers

Resale chains multiply: each sale scales the price by its own factor. Multiply forwards, divide backwards.

How to solve this type

Each sale multiplies the running price by its own factor:

\dfrac{100+p}{100}

for a

p\%

profit, or

\dfrac{100-l}{100}

for an

l\%

loss. The final price equals the original CP times the product of every one of these multipliers. To find a final price, work forwards from A, multiplying step by step; to find the original CP, divide the final price by that same product. Using fractions like

\dfrac{6}{5}

\dfrac{11}{10}

instead of decimals lets factors cancel and keeps it fast. Never just add the percentages — each rate sits on the previous seller's price, not on the original cost.

Anil sells a car to Bina at 20% profit; Bina sells it to Karan at 25% profit. Karan pays ₹2,25,000. What was Anil's original cost price?

A₹1,25,000B₹1,50,000C₹1,75,000D₹2,00,000

Akash sells to Navin at 10% profit; Navin sells to Vinay at 20% profit; Vinay sells to Vishal at 5% loss. Vishal pays ₹62,700. What is Akash's cost price?

A₹48,000B₹48,500C₹50,000D₹52,500

Raju sells to Ravi at 10% gain; Ravi sells to Ramu at 10% loss. Ramu pays ₹1,485. Find the price Raju charged Ravi (Raju's selling price).

A₹1,200B₹1,500C₹1,650D₹1,800

A jewel passes through three hands and its price rises 80% overall. The first seller makes 20% profit and the second 25% profit. What is the third seller's profit%?

A5%B10%C15%D20%