SSC CGL Arithmetic Shortcuts & Tricks

Fraction to Percentage

Memorize these conversions:

• 1/2 = 50%
• 1/3 = 33.33%
• 1/4 = 25%
• 1/5 = 20%
• 1/6 = 16.66%
• 1/8 = 12.5%
• 1/10 = 10%

Percentage Increase/Decrease

Quick calculation method:

• If a number increases by x%, multiply by (100+x)/100
• If a number decreases by x%, multiply by (100-x)/100
• For successive changes, use multiplication instead of addition

Base Value Technique

Assume base = 100 for easy calculations:

• Assume original value = 100
• Apply percentage changes
• Compare with final value
• Calculate actual values using proportion

Successive Profit/Loss

Single equivalent percentage:

For successive profits of a% and b%:

Net effect = a + b + (a×b)/100

Example: 20% and 30% profit = 20 + 30 + (20×30)/100 = 56%

False Weight

When dealer cheats on weight:

Profit % = [(Error)/(True Value - Error)] × 100

Example: If 1000g is sold as 800g, profit % = [(200)/(1000-200)] × 100 = 25%

Discount & MP

Marked Price relationships:

• SP = MP × (100 - Discount%)/100
• Successive discounts: Similar to successive profit
• Single discount equivalent to two discounts of a% and b% = a + b - (a×b)/100

Componendo & Dividendo

If a/b = c/d, then:

(a+b)/(a-b) = (c+d)/(c-d)

Application: Useful when ratios are given and we need to find relationship between sum and difference.

Ratio Division

Dividing quantity in given ratio:

If quantity Q is divided in ratio a:b:c

First part = a/(a+b+c) × Q

Second part = b/(a+b+c) × Q

Third part = c/(a+b+c) × Q

Partnership

Profit sharing ratio:

If A invests ₹X for T₁ months and B invests ₹Y for T₂ months

Profit ratio = (X × T₁) : (Y × T₂)

Work & Efficiency

Key formulas:

• Work = Time × Efficiency
• If A can do work in 'a' days, efficiency = 1/a
• Combined work: 1/(1/a + 1/b + 1/c)
• If A is twice as efficient as B, A:B efficiency = 2:1

Speed, Time & Distance

Important relationships:

• Speed = Distance/Time
• Average speed = Total Distance/Total Time
• If equal distances at different speeds, avg speed = 2ab/(a+b)
• Relative speed (same direction) = |a-b|
• Relative speed (opposite direction) = a+b

Average Shortcuts

Quick calculations:

• Average of consecutive numbers = (First+Last)/2
• If average increases by x when a number is replaced, the new number is larger by n×x
• Weighted average = Σ(wᵢ×xᵢ)/Σwᵢ