Calculation Shortcuts: Squares, Multiplication Tricks and Fractions Formula Guide for SSC

Speed matters in the SSC exam: Tier 1 gives only about 36 seconds per question (100 questions in 60 minutes). Calculation shortcuts cut the time for squares, multiplication, division and percentages. This formula guide collects the most useful tricks, each with a solved example, a table of fractions and percentages, practice questions and FAQs.

Squares

Multiplication Tricks

Division and Percentage Tricks

• Dividing by 5: multiply by 2 and divide by 10. For example, 360 ÷ 5 = 720/10 = 72.
• Dividing by 25: multiply by 4 and divide by 100. For example, 350 ÷ 25 = 1400/100 = 14.
• Dividing by 0.5 is the same as multiplying by 2.
• x% of y = y% of x. For example, 8% of 50 = 50% of 8 = 4.
• 10% of a number: shift the decimal one place left; 5% is half of 10%; 15% = 10% + 5%.
• Successive changes of a% and b%: net change = a + b + ab/100.

Fraction and Percentage Table

Squares, Cubes and Algebraic Shortcuts

• a² − b² = (a + b)(a − b).
• (a + b)² − (a − b)² = 4ab, and (a + b)² + (a − b)² = 2(a² + b²).
• (a + b)³ = a³ + b³ + 3ab(a + b).
• Sum of the first n natural numbers = n(n + 1)/2; of the first n odd numbers = n².
• Learn squares up to 30 and cubes up to 15 by heart.

Checking Answers with the Digital Root

• The digital root of a number is the single digit left after adding its digits repeatedly (and 9 counts as 9).
• For multiplication, the digital root of the product equals the digital root of the product of the digital roots.
• Example: 123 × 45 = 5535. The digital root of 123 is 6 and of 45 is 9; 6 × 9 = 54, whose root is 9. The root of 5535 is also 9 (5 + 5 + 3 + 5 = 18 → 9), so the result passes the check.
• This check catches most calculation errors but does not prove the answer is right.

Approximation Tips

• Round numbers to the nearest convenient value (for example, 49.8 ≈ 50) when the options are far apart.
• For roots, use the nearest perfect square: √50 is slightly more than 7.
• Use the fraction-percentage table instead of long division.
• Estimate the answer first, then eliminate the options.

Quick Tips

• Practise one trick a day until it becomes automatic.
• Use the digital root to double-check big multiplications.
• Learn squares up to 30; they appear in many questions.
• Do not use a trick unless you are sure of its condition (for example, units adding up to 10).

Quick Revision Points

• n5² = n(n + 1) followed by 25.
• × 25 = ÷ 4 × 100; × 125 = ÷ 8 × 1000.
• a² − b² = (a + b)(a − b).
• Successive change = a + b + ab/100.
• 1/7 = 14.28%; 1/8 = 12.5%; 1/9 = 11.11%.

Practice Questions With Answers

1. Find 65².
   Answer: 4225
2. Find 35 × 11.
   Answer: 385
3. Find 48 × 25.
   Answer: 1200
4. Find 52 × 48 using a² − b².
   Answer: 2496
5. Find 99 × 8.
   Answer: 792
6. Find 97 × 98.
   Answer: 9506
7. What is 12.5% as a fraction?
   Answer: 1/8
8. Find 240 ÷ 5.
   Answer: 48
9. What is 1/6 as a percentage?
   Answer: 16.67%
10. Find 18% of 50 using 50% of 18.
    Answer: 9

How to Practise This Chapter

Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Calculation Shortcuts notes page.

Frequently Asked Questions

Why learn calculation shortcuts?

They save time in SSC papers where speed decides the score.

How do I square a number ending in 5?

Multiply the first part by one more than itself and write 25 at the end.

What is the trick for multiplying by 11?

Write the first digit, add each pair of neighbouring digits, then write the last digit.

How do I multiply by 25 quickly?

Divide the number by 4 and multiply by 100.

What is the near-100 method?

Subtract the deficits crosswise and multiply the deficits to get the last two digits.

What is the digital root check?

A quick check of multiplication using the single-digit sums of the numbers.

How do I find x% of y quickly?

You can use y% of x, which is often easier to calculate.

Which fractions should I memorise?

Fractions up to 1/16 with their percentage values.

Do shortcuts always work?

Each shortcut has a condition; check it before using the trick.

How many squares should I learn?

At least squares up to 30 and cubes up to 15.

Can shortcuts help in the CGL Tier 2?

Yes, they help in the quantitative section, where speed is important.

How can I practise them?

Solve a set of 10 shortcut questions daily with a timer.