SSC CGL Maths · Percentage, Profit and Loss

Faulty Weights and Article Counts

A seller who hands over less than he charges for gains on quantity as well as on price; both effects multiply, and 'cost of x articles equals selling price of y' is the same idea counted in pieces.

All Percentage, Profit and Loss notes

Why this matters

28 questions in the bank, 20 of them MODERATE, which makes this the hardest page of the chapter for its size. Every one is the same comparison of what the customer pays for against what the seller gives, so learn the one factor and the dishonest-dealer questions become two-line sums.

Concept 1 of 3: Faulty weight at the cost price

A grocer who charges for 1 kg but hands over 900 g keeps 100 g for free on every sale. He paid only for the 900 g he gave, so his gain is the 100 g he kept, measured against the 900 g he gave.

Definition

Gain % $= \frac{\text{true weight} - \text{false weight}}{\text{false weight}} \times 100$ . The base is what the seller gives, because that is what he paid for.
Working back: for a gain of g% at cost price, he gives $1000 \times \frac{100}{100 + g}$ grams for each kilogram.
Counting cheats work the same way: selling 11 eggs as a dozen gains 1 on 11.
In rupees, the profit is the money taken minus the cost of the goods actually handed over.

Gain from a short weight

\text{gain}\% = \frac{\text{true} - \text{false}}{\text{false}} \times 100

Worked example

A grocer claims to sell at cost price but uses a 900 g weight for 1 kg. Find his gain percentage.

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 9 Sep 2024, Shift 1 · Q51Easy

Example 1 · Percentage, Profit and Loss · Faulty Weights and Article Counts

A grocer professes to sell rice at the cost price, but uses a fake weight of

870

g for

1

kg. Find his profit percentage (correct to two decimal places).

Dividing by the true weight

50 g short on every kilogram is a gain of

\frac{50}{950} \times 100 \approx 5.26\%

, not 5%. The base is the 950 g handed over.

Drill 5 more on faulty weight at the cost price

Concept 2 of 3: Faulty weight with a profit or loss on price

Some sellers cheat twice: they charge more than cost and they give less than the weight. The price gives one factor, the weight gives another, and the real profit factor is the product of the two.

Definition

Real factor $= \left(1 + \frac{p}{100}\right) \times \frac{\text{true}}{\text{false}}$ . Subtract 1 and multiply by 100 for the real profit %.
A loss on price uses $1 - \frac{l}{100}$ ; the short weight can still turn it into a gain.
'Weights 20% less than true' means false $= 0.8 \times$ true, so the weight factor is $\frac{1}{0.8} = 1.25$ .
Rupee route: take the cost of 1 kg as 100. Compare the money taken for the 'kilogram' with the cost of the grams actually given.

Real profit with a short weight

1 + \frac{\text{gain}}{100} = \left(1 + \frac{p}{100}\right) \times \frac{\text{true}}{\text{false}}

Worked example

A trader adds a 10% profit to the cost price and also gives 900 g for every kilogram. Find his real profit percentage.

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 · Q63Moderate

Example 2 · Percentage, Profit and Loss · Faulty Weights and Article Counts

A fruit seller sells apples at a loss of

5\%

on the cost price but uses a weight that is

20\%

less than the actual weight. Find his total profit percentage.

Adding the two gains

A 10% mark-up with a weight 10% short is not a 20% gain. The factors multiply:

1.1 \times \frac{10}{9} = \frac{11}{9}

, a gain of about 22.2%.

Reading 'weight 20% less' as a 20% gain

If the weight is 20% less than true, the seller gives 0.8 of what he charges for, so the weight factor is

\frac{1}{0.8} = 1.25

, a 25% gain from the weight alone.

Drill 13 more on faulty weight with a profit or loss on price

Concept 3 of 3: Cost price of some articles equal to the selling price of others

'The cost price of 28 oranges equals the selling price of 24' says that the money from selling 24 oranges buys 28. It is a faulty-weight question counted in pieces: the seller gets the value of 28 for handing over 24.

Definition

If CP of x articles $=$ SP of y articles, the profit % is $\frac{x - y}{y} \times 100$ . If $y > x$ , it is a loss of $\frac{y - x}{y} \times 100$ .
'Selling m articles gains the selling price of n': SP of $(m - n)$ $=$ CP of m.
'Selling m articles gains the cost price of n': the profit % is $\frac{n}{m} \times 100$ .
'Buys x articles for the price of y': his cost per article is $\frac{y}{x}$ of the price, and a discount on that price works as on the Marked Price and Discount page.

Profit when two counts are equal in value

\text{profit}\% = \frac{x - y}{y} \times 100 \text{ when CP of } x = \text{SP of } y

Worked example

The cost price of 15 pens equals the selling price of 12 pens. Find the profit percentage.

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 17 Sep 2025, Shift 2 · Q58Easy

Example 3 · Percentage, Profit and Loss · Faulty Weights and Article Counts

A fruit vendor sells 15 kg of apples for ₹750, thereby gaining the cost price of 5 kg of apples. What is his profit percentage?

Dividing by the larger count

When the cost price of 28 equals the selling price of 24, the gain is 4 on the 24 sold, so

\frac{4}{24} = 16\frac{2}{3}\%

, not

\frac{4}{28}

Mixing up 'gains the SP of n' and 'gains the CP of n'

Gaining the cost price of 3 articles on 12 sold is a gain of

\frac{3}{12} = 25\%

. Gaining the selling price of 3 on 12 sold means SP of 9 equals CP of 12, a gain of

33\frac{1}{3}\%

Drill 7 more on cost price of some articles equal to the selling price of others

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 (3)

Faulty weight at the cost price
Gain from a short weight
$\text{gain}\% = \frac{\text{true} - \text{false}}{\text{false}} \times 100$
Faulty weight with a profit or loss on price
Real profit with a short weight
$1 + \frac{\text{gain}}{100} = \left(1 + \frac{p}{100}\right) \times \frac{\text{true}}{\text{false}}$
Cost price of some articles equal to the selling price of others
Profit when two counts are equal in value
$\text{profit}\% = \frac{x - y}{y} \times 100 \text{ when CP of } x = \text{SP of } y$

Watch out for (5)

Dividing by the true weight
→ Faulty weight at the cost price
Adding the two gains
→ Faulty weight with a profit or loss on price
Reading 'weight 20% less' as a 20% gain
→ Faulty weight with a profit or loss on price
Dividing by the larger count
→ Cost price of some articles equal to the selling price of others
Mixing up 'gains the SP of n' and 'gains the CP of n'
→ Cost price of some articles equal to the selling price of others

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 28 questions