Percentage Questions for RRB GROUP D

What is Percentage?

Percentage simply means per hundred. When you say 40%, you mean 40 out of every 100. It is a way to express a fraction or ratio out of 100. Think of a 100-rupee note — any percentage is just how many rupees you are talking about from that 100.

• Percent symbol % means divide by 100
• To convert fraction to percent: multiply by 100
• To convert percent to fraction: divide by 100
• To convert decimal to percent: multiply by 100 (0.35 = 35%)
• To convert percent to decimal: divide by 100 (75% = 0.75)

Percentage Increase and Decrease

This is the most tested pattern in RRB Group D. A value goes up or down and you need to find the percentage change. Always remember: the change is compared to the ORIGINAL value (base), not the new value. Many aspirants make the mistake of dividing by the new value instead of the original.

• Percentage increase = (Increase / Original) x 100
• Percentage decrease = (Decrease / Original) x 100
• If price increases by R%, new price = Original x (1 + R/100)
• If price decreases by R%, new price = Original x (1 - R/100)
• Always use the ORIGINAL (old) value in the denominator

Finding Original Value (Reverse Percentage)

Sometimes the question gives you the final value after a percentage change and asks for the original. This is called reverse percentage. Think of it as working backwards. If a number after 20% increase became 600, the original is not 600 minus 20% of 600 — that is a common trap. You must use the multiplier method.

• After R% increase, final = original x (100+R)/100, so original = final x 100/(100+R)
• After R% decrease, final = original x (100-R)/100, so original = final x 100/(100-R)
• Never apply the given percentage directly to the final value to reverse it
• This concept also appears in Profit-Loss and Discount questions

Successive Percentage Change

When two or more percentage changes are applied one after another, you cannot simply add them. For example, 10% increase followed by 10% decrease does NOT give you the original value — you actually get a net loss of 1%. This is a favourite trick question in RRB exams.

• Two successive changes of a% and b% give net change = a + b + (ab/100) percent
• If both are increases, both a and b are positive
• If one is decrease, treat that as negative
• 10% up then 10% down = 10 + (-10) + (10x(-10)/100) = -1% net (a loss of 1%)
• This shortcut saves time over calculating step by step

Fraction to Percent Shortcuts (Must Memorise)

In RRB Group D, calculation speed matters. Memorising common fraction-to-percent equivalents lets you skip long division and solve in seconds. These are the most exam-relevant conversions that appear again and again.

• 1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%
• 1/6 = 16.67%, 1/7 = 14.28%, 1/8 = 12.5%, 1/9 = 11.11%, 1/10 = 10%
• 2/3 = 66.67%, 3/4 = 75%, 2/5 = 40%, 3/5 = 60%, 4/5 = 80%
• These help instantly convert wordy percentage problems into fractions for faster mental math

• Using the new (final) value as the base instead of the original value when calculating percentage change — always divide by the OLD value
• In reverse percentage, subtracting the percentage from the final value directly — for example if after 20% increase final is 600, wrong answer is 600 - 20% of 600 = 480 instead of correct 500
• In successive percentage changes, simply adding the two percentages — 20% then 20% is NOT 40% total, it is 44%
• Confusing percentage point change with percentage change — if pass rate goes from 40% to 60%, it rose by 20 percentage points but by 50% in relative terms
• Not converting percent to decimal or fraction properly before multiplying — writing 20% as 20 instead of 0.20 leads to answers 100 times too large

• BASE RULE: In percentage change, BASE is always the OLD/ORIGINAL value. Think B for Base = Before.
• Successive change formula trick: remember it as a + b + ab/100 — the extra term ab/100 is the bonus or penalty. Positive = bonus gain, negative = extra loss.
• Reverse % trick: After increase of R%, original = Final x 100/(100+R). Think of it as undoing the multiplier — you multiplied by (100+R)/100 to go forward, so multiply by 100/(100+R) to go back.
• Fraction table shortcut memory hook: 1/8 = 12.5, 1/6 = 16.67, 1/3 = 33.33 — remember as 12.5, double it is 25 (1/4), double again is 50 (1/2). Going up in half steps helps recall the series.

• RRB Group D typically asks 2-3 direct percentage questions — one on finding X% of Y, one on percentage increase/decrease, and sometimes one reverse percentage. Do not overthink these.
• Percentage questions in RRB Group D are often wrapped inside profit-loss or discount problems. Identifying the base value correctly is the key step before solving.
• Calculation speed is critical. Practise converting between fractions and percentages mentally using the fraction table. This alone can save 30-40 seconds per question.
• Watch for the word 'by' vs 'to' — price increased BY 20% means add 20% to original; price increased TO 120 means the final value is 120. These are different and both appear in papers.
• Successive percentage change questions often appear as a two-step word problem about population or salary — recognise the pattern and apply the a + b + ab/100 formula directly to save time.