SSC CGL Percentage Notes and Free Practice

Free SSC CGL percentage notes with six worked examples: reverse percentages, successive changes, percentage points and expenditure. Try 15 original practice questions.

Practice and revisionDetailed answer reviewMobile-friendly flow

Percentage notes with worked examples

Identify the base, combine changes and reverse a percentage calculation. These original lessons and questions are practice material, not an official SSC paper.

Try 15 percentage questions

Untimed, no login required. +2 correct, −0.5 wrong, 0 unattempted. Review every solution after submission.

Identify the base before calculating

Percentage = part ÷ whole × 100. For an increase or decrease, divide the change by the original value. To reverse a percentage change, divide the final amount by its multiplier; do not apply the same percentage to the final amount.

Worked example

A club has 420 members, of whom 63 joined this month. What percentage are new members?

Show solution

Use current membership as the whole: 63/420 × 100 = 15%. If the question instead asked membership growth, the original membership would be 357, giving a different denominator.

Common mistake: Underline 'of', 'original' and 'remaining' to identify which quantity represents 100%.

Successive changes and reverse percentages

An increase of r% multiplies a value by 1 + r/100; a decrease multiplies by 1 − r/100. Multiply the factors for successive changes. Equal percentage increases and decreases do not cancel because the second change has a different base. Recover the original amount by dividing by the complete multiplier.

Worked example

An item marked Rs. 2000 receives discounts of 10% and then 15%. Find the price and equivalent single discount.

Show solution

The retained fraction is 0.90 × 0.85 = 0.765. Price = 2000 × 0.765 = Rs. 1530. The overall discount is 1 − 0.765 = 0.235, or 23.5%. Adding the discounts to obtain 25% is incorrect.

Common mistake: Keep intermediate values exact and round only when requested.

Reverse comparisons and percentage points

If A is r% more than B, B is the base. To find how much less B is than A, use A as the new base. A percentage-point change is the arithmetic difference between two percentage rates. Relative percentage change divides this difference by the original rate.

Worked example

A completion rate rises from 20% to 25%. Find the percentage-point rise and relative percentage increase.

Show solution

The rise is 25 − 20 = 5 percentage points. Relative to the original rate, the increase is 5/20 × 100 = 25%. Label these two different comparisons carefully.

Common mistake: A 5-percentage-point rise is not automatically a 5% increase.

Price changes when expenditure is fixed

Expenditure = price × quantity. With spending unchanged, quantity varies inversely with price. Divide quantity by the price multiplier. For a price rise of r%, quantity falls by 100r/(100 + r)%. For a price fall of r%, with r < 100, affordable quantity rises by 100r/(100 − r)%.

Worked example

Rice becomes 60% more expensive per kilogram. By what percentage must quantity fall to keep spending unchanged?

Show solution

Suppose the old price is Rs. 10 per kg and quantity is 100 kg, costing Rs. 1000. The new price is Rs. 16 per kg, allowing 1000/16 = 62.5 kg. Quantity falls by 37.5%.

Common mistake: Price and quantity do not change by equal percentages when spending is fixed.

Combine groups using counts

For differently sized groups, convert each percentage into a count, add the counts and divide by the combined group size. Averaging rates directly works only when their bases are equal. In a two-candidate election with all votes valid, the winning margin is the difference between vote shares multiplied by valid votes.

Worked example

Of 40 learners in one group, 60% pass. Of 60 learners in another, 80% pass. Find the overall pass percentage.

Show solution

The groups contribute 40 × 0.60 = 24 and 60 × 0.80 = 48 passes. Together, 72 out of 100 pass: 72%. The simple average, 70%, incorrectly weights the groups equally.

Common mistake: Registered voters, votes cast and valid votes are different possible bases.

Find the quantity that stays unchanged

When only water is lost in drying, dry material stays constant. Set total mass × dry fraction equal before and after drying. For savings, first calculate income minus expenditure, then compare old and new savings; savings and income have different bases.

Worked example

A 60 kg batch contains 75% water. Only water evaporates until the remaining batch contains 40% water. Find the new mass.

Show solution

Dry material is initially 25% of 60 = 15 kg. Afterwards it is 60% of the remaining mass M. Thus 0.60M = 15, so M = 25 kg. The lost 35 kg is water; dry mass remains 15 kg.

Common mistake: A fall in water percentage is not the same as the percentage fall in total mass.

Put the method into practice

Write the base beside each percentage. After reviewing a mistake, decide whether it came from the base, the multiplier or arithmetic. Rework the question without looking at the solution.

Percentage concept check Number-system basics Profit, loss and discount practice

Practice Test 1