Percentage for RRB Group D

"Per cent" means "out of 100". 35% is simply 35/100. That one idea powers a large share of the arithmetic in the RRB Group D maths section: profit and loss is percentage on the cost price, discount is percentage on the marked price, interest is percentage per year, and population growth is percentage change repeated.

So if percentage feels shaky, fix it before anything else. The good news is that there are only a few question types, and each has a clear method.

Percentages as fractions

Most quick percentage work is really fraction work. These pairs let you do many questions in your head:

So 62.5% of 480 is 5/8 of 480 = 300. No long multiplication needed.

The three basic questions

A fast way to find odd percentages: build them from 10% and 1%. 12% of 450 = 10% (45) + 2% (9) = 54.

Percentage change

• Change % = change ÷ original × 100.
• The base is always the original (old) value, never the new one.

"More than" and "less than"

If A is 25% more than B, B is not 25% less than A. Take B = 100, so A = 125. B is 25 less than A, and 25 out of 125 is 20%.

The rule: if A is r% more than B, then B is r ÷ (100 + r) × 100 per cent less than A. If A is r% less than B, then B is r ÷ (100 − r) × 100 per cent more than A.

The same idea handles price and consumption. If a price rises by r%, a family must cut consumption by r ÷ (100 + r) × 100 per cent to keep spending the same.

Successive changes

Two changes of a% and b% (use a minus sign for a decrease):

• Net change = a + b + (a × b ÷ 100)

Or start with 100 and apply each change in turn. The "start with 100" method never fails and is easy to check.

Worked examples

Example 1: A salary rises from ₹15,000 to ₹18,000. Find the percentage rise.

• Rise = 3,000. Base = the old salary, 15,000.
• 3,000 ÷ 15,000 × 100 = 20%.

Example 2: The price of sugar rises by 25%. By what percentage must a family reduce consumption so that spending stays the same?

• 25 ÷ 125 × 100 = 20%.
• Check: 1.25 × 0.80 = 1. Spending is unchanged.

Example 3: A student needs 35% to pass. The student scores 180 marks and fails by 30 marks. Find the maximum marks.

• Pass mark = 180 + 30 = 210.
• 210 is 35% of the maximum: 210 × 100 ÷ 35 = 600.

Example 4: In an election between two candidates, the winner gets 60% of the votes and wins by 400 votes. All votes are valid. Find the total number of votes.

• The loser gets 40%. The gap is 60% − 40% = 20%.
• 20% of the total = 400, so the total = 2,000.

Example 5: A village has 8,000 people. The population grows 5% a year. What will it be after 2 years?

• 8,000 × 1.05 = 8,400; 8,400 × 1.05 = 8,820.

Common mistakes

• Using the new value as the base for percentage change.
• Assuming a 20% rise and a 20% fall cancel out. They give a 4% fall.
• Saying B is 25% less than A when A is 25% more than B.
• Adding percentages of different amounts, such as 10% of one price and 10% of another.
• For growth over two years, adding 5% + 5% = 10% instead of applying it twice.

Practice set

1. Find 25% of 640.
2. 60 is what percentage of 240?
3. A price falls by 20% and then rises by 20%. What is the net change?
4. 40% of a number is 120. Find the number.
5. A town of 10,000 people grows 10% a year. What is the population after 2 years?
6. A's salary is 20% less than B's. By what percentage is B's salary more than A's?
7. In a two-candidate election with all votes valid, the winner gets 55% and wins by 1,500 votes. How many votes were cast?
8. One candidate scores 30% and fails by 20 marks. Another scores 40% and gets 20 marks more than the pass mark. Find the maximum marks.

Answers:

1. 160. 25% = 1/4; 640 ÷ 4.
2. 25%. 60 ÷ 240 × 100.
3. 4% decrease. 100 → 80 → 96.
4. 300. 120 × 100 ÷ 40.
5. 12,100. 10,000 → 11,000 → 12,100.
6. 25%. Take B = 100, A = 80. B is 20 more than A; 20 ÷ 80 × 100 = 25%.
7. 15,000. Gap = 55% − 45% = 10%; 10% = 1,500.
8. 400. The gap between 30% and 40% is 10%, and it equals 20 + 20 = 40 marks, so 100% = 400. (Pass mark is 140.)

What to do next

• Learn the percentage–fraction table both ways.
• Do 20 "x% of y" questions using only the fraction table, without writing long multiplication.
• Practise five successive-change questions with the "start at 100" method.
• Revise decimals and fractions, then apply all this in profit and loss.