SSC CGL मात्रात्मक योग्यता महारत

Learning outcomes

By the end of this lesson, you should be able to:

• convert fractions, decimals, and percentages without a calculator;
• distinguish percentage-point change from percentage change;
• solve "more than", "less than", and reverse-percentage questions;
• combine successive percentage changes correctly;
• choose a fast base value and check whether an answer is reasonable.

1. What a percentage represents

A percentage is a ratio measured out of 100. The statement 18% of 250 means:

[ \frac{18}{100} \times 250 = 45 ]

In SSC CGL, the arithmetic is rarely difficult by itself. The real skill is translating the language of the question into the correct base quantity.

High-value conversions

Memorise these because they remove several calculation steps:

Fraction	Percentage	Fraction	Percentage
1/2	50%	1/8	12.5%
1/3	33⅓%	1/9	11⅑%
1/4	25%	1/10	10%
1/5	20%	1/16	6.25%
1/6	16⅔%	3/8	37.5%
1/20	5%	5/8	62.5%

A useful mental rule is: x% of y equals y% of x. For example, 24% of 75 is easier as 75% of 24, which is 18.

2. Percentage increase and decrease

If an original value is (V) and it changes by (r%):

• increase: new value = (V(1 + r/100))
• decrease: new value = (V(1 - r/100))

Worked example: direct increase

A salary of ₹32,000 increases by 12.5%. Since 12.5% = 1/8:

[ 32,000 + 32,000/8 = 32,000 + 4,000 = ₹36,000 ]

Worked example: reverse percentage

After a 20% discount, a jacket costs ₹1,440. The sale price is 80% of the marked price.

[ \text{Marked price} = 1,440 \times \frac{100}{80} = ₹1,800 ]

Do not add 20% of ₹1,440. The discount was calculated on the unknown marked price, not on the sale price.

3. “More than” and “less than” are not symmetric

If A is 25% more than B, choose B = 100. Then A = 125. To find how much B is less than A, compare the difference with A:

[ \frac{25}{125} \times 100 = 20% ]

Therefore, A is 25% more than B, but B is 20% less than A.

General shortcuts:

• If A is (x%) more than B, B is (100x/(100+x)%) less than A.
• If A is (x%) less than B, B is (100x/(100-x)%) more than A.

4. Successive percentage change

Never add successive percentage changes unless you also account for the changing base.

For changes of (a%) and (b%), the net percentage change is:

[ a + b + \frac{ab}{100} ]

Use negative signs for decreases.

Worked example: increase followed by decrease

A number rises by 20% and then falls by 10%.

[ 20 + (-10) + \frac{20(-10)}{100} = 8% ]

The net result is an 8% increase. With a base of 100: 100 → 120 → 108.

Same increase and decrease

A 15% increase followed by a 15% decrease is not zero:

[ 15 - 15 - \frac{15\times15}{100} = -2.25% ]

The final value is 2.25% below the original.

5. Expenditure, price, and consumption

Expenditure = price × quantity.

If price rises by 25% and expenditure must remain unchanged, choose old price = 100 and new price = 125. Quantity must be multiplied by 100/125 = 4/5, so consumption must fall by 20%.

Shortcut: if price increases by (x%), required consumption reduction is:

[ \frac{100x}{100+x}% ]

If price decreases by (x%), affordable consumption increase is:

[ \frac{100x}{100-x}% ]

6. SSC CGL traps to avoid

1. Wrong base: “A is 30% of B” and “A is 30% less than B” are different statements.
2. Percentage points: A rate moving from 40% to 50% rises by 10 percentage points, but by 25% relative to 40%.
3. Reversing a discount: A 20% fall requires a 25% rise to return to the original value.
4. Adding successive changes: +10% and +20% produce +32%, not +30%.
5. Ignoring units: Compare quantities only after converting rupees, paise, kilograms, or grams consistently.

7. Timed practice method

For each question:

1. underline the quantity that acts as the base;
2. convert familiar percentages to fractions;
3. use a base of 100 when only relative values matter;
4. estimate the direction and rough size before calculating;
5. reject options that contradict the estimate.

Target 45–60 seconds for a standard one-step percentage question and 75–90 seconds for a multi-step word problem.

Check your understanding

1. 37.5% of 640 = 240.
2. A value increases from 480 to 600. Increase = 120/480 × 100 = 25%.
3. A is 40% more than B. B is less than A by 40/140 × 100 = 28 4/7%.
4. A price falls 20% and then rises 20%. Net change = 4% decrease.
5. After a 15% discount, a product costs ₹1,700. Marked price = 1700 × 100/85 = ₹2,000.

Revision recap

• Percentage always depends on a base.
• Convert common percentages into fractions before multiplying.
• For reverse questions, divide by the remaining percentage.
• Successive changes operate on different bases.
• Use a base of 100 to expose comparison questions quickly.