Percentage Tricks (Competitive Exams) – Shortcuts + Solved Examples

TRICK 1 — Break % into easy parts (10%, 5%, 1%, etc.)

Fast Parts

Instead of direct multiplication, split the percentage into easy pieces like 10%, 5%, 1% and add them. Example: 18% = 10% + 5% + 3%.

Useful: 10% = number ÷ 10, 5% = 10% ÷ 2, 1% = number ÷ 100

Solved (5)

1) 18% of 250

10% = 25, 5% = 12.5, 3% = 7.5 ⇒ Total = 45

2) 15% of 360

10% = 36, 5% = 18 ⇒ Total = 54

3) 12% of 400

10% = 40, 2% = 8 ⇒ Total = 48

4) 25% of 240

25% = 1/4 ⇒ 240 ÷ 4 = 60

5) 5% of 600

10% = 60 ⇒ 5% = 30 ⇒ 30

TRICK 2 — Swap rule: x% of y = y% of x

Swap

Swap the percentage and the number to make calculation easier. Example: 16% of 75 = 75% of 16.

x% of y = (x/100)×y = (y/100)×x = y% of x

Solved (5)

1) 16% of 75

= 75% of 16 = (3/4)×16 = 12

2) 8% of 125

= 125% of 8 = 1.25×8 = 10

3) 30% of 40

= 40% of 30 = 0.4×30 = 12

4) 22% of 50

= 50% of 22 = 11

5) 6% of 150

= 150% of 6 = 1.5×6 = 9

TRICK 3 — Successive % change (two-step change in one line)

Successive

If value changes by a% then by b%, use signs (+ for increase, − for decrease).

Net % change = a + b + (a×b)/100

Solved (5)

1) +10% then +20%

Net = 10 + 20 + (10×20)/100 = 30 + 2 = 32% increase

2) −15% then −10%

Net = −15 + (−10) + (150/100) = −25 + 1.5 = −23.5% (decrease)

3) +20% then −20%

Net = 20 − 20 + (−400/100) = −4% (decrease)

4) +5% then +10%

Net = 5 + 10 + (50/100) = 15 + 0.5 = 15.5% increase

5) +30% then −15%

Net = 30 − 15 + (−450/100) = 15 − 4.5 = 10.5% increase

TRICK 4 — Reverse percentage (find original value quickly)

Reverse

If a value becomes Final after x% increase/decrease, find the original directly.

After x% increase: Original = Final ÷ (1 + x/100)
After x% decrease: Original = Final ÷ (1 − x/100)

Solved (5)

1) Final 240 after 20% increase

Original = 240 ÷ 1.2 = 200

2) Final 360 after 10% decrease

Original = 360 ÷ 0.9 = 400

3) Final 150 after 25% increase

Original = 150 ÷ 1.25 = 120

4) Final 80 after 20% decrease

Original = 80 ÷ 0.8 = 100

5) Final 132 after 10% increase

Original = 132 ÷ 1.1 = 120

TRICK 5 — Return-to-original shortcut (undo % change)

Back to 100%

Very common in exams: “After a change, what % is needed to come back to the original value?”

If increased by x%, required decrease to return = x/(100+x) × 100
If decreased by x%, required increase to return = x/(100−x) × 100

Solved (5)

1) Price ↑ 20%, drop needed to return?

= 20/120×100 = 16.67%

2) Price ↑ 50%, drop needed to return?

= 50/150×100 = 33.33%

3) Price ↓ 20%, rise needed to return?

= 20/80×100 = 25%

4) Salary ↑ 15%, drop needed to return?

= 15/115×100 = 13.04%

5) Salary ↓ 10%, rise needed to return?

= 10/90×100 = 11.11%

10 Practice Questions (no solutions here)

Practice

What is 17% of 450?
Find 6% of 350 (use 5% + 1%).
Find 18% of 125 (use swap rule).
A value increases by 15% and then by 20%. Find the net % change.
A value decreases by 12% and then increases by 8%. Find the net % change.
After a 25% increase, the final value is 250. Find the original value.
After a 20% decrease, the final value is 320. Find the original value.
A price increases by 30%. What % decrease is needed to return to the original price?
A salary decreases by 15%. What % increase is needed to return to the original salary?
Find 22% of 360 (use parts/swap).

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