SSC CGL Maths · Percentage, Profit and Loss

Profit and Loss

Profit or loss is the gap between the selling price and the cost price, and its percentage is always taken on the cost price unless the question says otherwise.

All Percentage, Profit and Loss notes

Why this matters

61 questions in the bank, 38 EASY and 23 MODERATE. Most are one division: a cost price from a selling price, or a profit percentage. The MODERATE ones are the 24 that sell several items or lots at different rates, where the overall profit has to be built from totals rather than averaged.

Concept 1 of 4: Cost price, selling price and profit percentage

A trader buys at the cost price (CP) and sells at the selling price (SP). A profit of 20% means the SP is the CP plus a fifth of the CP: the cost price is the base, the 100, of every profit and loss percentage.

Definition

Profit $= SP - CP$ ; loss $= CP - SP$ .
Profit % $= \frac{\text{profit}}{CP} \times 100$ , and loss % the same way.
$SP = CP\left(1 + \frac{p}{100}\right)$ and $CP = \frac{SP}{1 + p/100}$ . For a loss, use $1 - \frac{l}{100}$ .
Fraction route: a 25% profit makes $SP = \frac{5}{4}CP$ ; a 20% loss makes $SP = \frac{4}{5}CP$ .
If the profit is $\frac{1}{n}$ of the selling price, then $CP = \frac{n - 1}{n}SP$ and the profit is $\frac{1}{n - 1}$ of the cost.
Transport, repairs and other expenses are added to the cost price before you work out the profit.

Profit percentage and the two prices

\text{profit}\% = \frac{SP - CP}{CP} \times 100 \qquad SP = CP\left(1 + \frac{p}{100}\right) \qquad CP = \frac{SP}{1 + \frac{p}{100}}

Worked example

A cycle bought for ₹4,800 is sold for ₹5,400. Find the profit percentage.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 15 Sep 2025, Shift 1 · Q60Easy

Example 1 · Percentage, Profit and Loss · Profit and Loss

The ratio of the profit to the cost price of a product is 2: 7. What is the ratio of its selling price to its profit?

Taking the profit on the selling price

Profit percentage uses the cost price as its base. A profit of one-sixth of the selling price is one-fifth of the cost, so it is 20%, not

16\frac{2}{3}\%

Leaving out the overheads

Transport or repair money is part of what the trader paid. Add it to the cost price first, or the profit comes out too large.

Drill 24 more on cost price, selling price and profit percentage

Concept 2 of 4: Two selling prices of the same article

When a question gives two different selling prices for the same article, its cost price is the same in both. So the gap between the two selling prices is the gap between the two percentages, taken of that one cost price.

Definition

$SP_2 - SP_1 = \frac{p_2 - p_1}{100} \times CP$ , with a loss written as a negative profit. From a 5% loss to a 5% gain is a swing of 10%.
If the profit at one price equals the loss at another (in rupees or in per cent), the cost price is halfway between them: $CP = \frac{SP_1 + SP_2}{2}$ .
For 'if the selling price doubles, the profit becomes k times', write the profits as $S - C$ and $2S - C$ and set $2S - C = k(S - C)$ .
Fast route: the options are cost prices. Put one in and see whether both selling prices fit.

Swing between two selling prices

SP_2 - SP_1 = \frac{p_2 - p_1}{100} \times CP \qquad CP = \frac{SP_1 + SP_2}{2} \text{ (equal profit and loss)}

Worked example

A fan sold at a loss of 8% would have given a profit of 12% if it had been sold for ₹240 more. Find its cost price.

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 12 Sep 2025, Shift 3 · Q64Easy

Example 2 · Percentage, Profit and Loss · Profit and Loss

The profit made on an item sold for ₹2200 is equal to the loss incurred when it is sold for ₹1800. What will be the profit or loss percentage if the item is sold for ₹2050?

Subtracting a loss from a profit

From a 16% loss to a 20% gain the price moves by 36% of the cost, not 4%. A loss sits on the other side of zero.

Drill 7 more on two selling prices of the same article

Concept 3 of 4: An article sold through several hands

When A sells to B and B sells to C, B's cost price is A's selling price. Each sale multiplies the price by its own factor, exactly like successive percentage changes.

Definition

Final price $=$ first cost $\times \left(1 + \frac{p_1}{100}\right)\left(1 + \frac{p_2}{100}\right)\cdots$ , with a loss as $1 - \frac{l}{100}$ .
To find one dealer's share when the total is known, divide the factors: second factor $=$ total factor $\div$ first factor.
Selling at a loss and putting all the money into a second deal works the same way: multiply the two factors.

Price after two sales

\text{final} = C\left(1 + \frac{p_1}{100}\right)\left(1 + \frac{p_2}{100}\right)

Worked example

A sells a bicycle to B at a 10% profit, and B sells it to C at a 20% profit. C pays ₹3,960. What did A pay for it?

Practice this conceptself-check · 2 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 17 Sep 2024, Shift 2 · Q68Moderate

Example 3 · Percentage, Profit and Loss · Profit and Loss

An article passing through two hands is sold at a total profit of 40% of the original cost price. If the first dealer makes a profit of 30%, then the profit percentage made by the second dealer is:

Adding the dealers' profits

Profits of 20% and then 40% make a factor of

1.2 \times 1.4 = 1.68

, a total of 68%, not 60%.

Drill 3 more on an article sold through several hands

Concept 4 of 4: Overall profit on several items or lots

When several items or lots are sold at different rates, the overall profit is total profit over total cost. The separate percentages can only be averaged when every item cost the same.

Definition

Overall % $= \frac{\text{total SP} - \text{total CP}}{\text{total CP}} \times 100$ .
Equal costs: average the percentages. A gain of 8% on one and a loss of 6% on an equal-cost other is a 1% gain overall.
Equal or ratio selling prices: find each cost by dividing its SP by its factor, then add the costs.
Parts of one stock: weight each rate by its share of the cost. Five-eighths at a 20% gain and the rest at cost give $\frac{5}{8} \times 20 = 12.5\%$ .
Mixtures: cost per kg of the mix $=$ total cost $\div$ total kg.
Spoilt or thrown-away stock still counts in the cost; only the rest brings in money.

Overall profit

\text{overall}\% = \frac{\sum SP - \sum CP}{\sum CP} \times 100

Worked example

A trader buys 40 kg of sugar at ₹45 per kg and 60 kg at ₹50 per kg, mixes them and sells the mixture at ₹52 per kg. Find his profit percentage.

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 24 Sep 2025, Shift 3 · Q62Easy

Example 4 · Percentage, Profit and Loss · Profit and Loss

A shopkeeper bought 100 pens at Rs 10 each. He sold 60 pens at

20\%

profit and the rest at

10\%

loss. What is the overall profit or loss percentage?

Averaging percentages on different costs

Two articles sold at the same price, one at a 20% gain and one at a 20% loss, always give a 4% loss overall, not zero, because the loss-making one cost more.

Leaving the spoilt stock out of the cost

Broken eggs or withered flowers were paid for. Their cost stays in the total cost; only the sales shrink.

Drill 23 more on overall profit on several items or lots

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (4)

Cost price, selling price and profit percentage
Profit percentage and the two prices
$\text{profit}\% = \frac{SP - CP}{CP} \times 100 \qquad SP = CP\left(1 + \frac{p}{100}\right) \qquad CP = \frac{SP}{1 + \frac{p}{100}}$
Two selling prices of the same article
Swing between two selling prices
$SP_2 - SP_1 = \frac{p_2 - p_1}{100} \times CP \qquad CP = \frac{SP_1 + SP_2}{2} \text{ (equal profit and loss)}$
An article sold through several hands
Price after two sales
$\text{final} = C\left(1 + \frac{p_1}{100}\right)\left(1 + \frac{p_2}{100}\right)$
Overall profit on several items or lots
Overall profit
$\text{overall}\% = \frac{\sum SP - \sum CP}{\sum CP} \times 100$

Watch out for (6)

Taking the profit on the selling price
→ Cost price, selling price and profit percentage
Leaving out the overheads
→ Cost price, selling price and profit percentage
Subtracting a loss from a profit
→ Two selling prices of the same article
Adding the dealers' profits
→ An article sold through several hands
Averaging percentages on different costs
→ Overall profit on several items or lots
Leaving the spoilt stock out of the cost
→ Overall profit on several items or lots

Test yourself on Percentage, Profit and Loss

20 past SSC CGL questions from this chapter, timed at 12 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

Take the Percentage, Profit and Loss chapter test Drill all 61 questions