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Start here: 3 easy methods that solve most questions

You do not need a formula for every chapter. Most percentage, profit and loss, ratio and time and work questions give way to three plain methods: pretend the number is 100, pretend the job has a convenient size, or try the answer options. Learn these first. The shortcuts come later.

Practise (10 questions) Present as slides

Why this topic matters

You do not need to be 'good at maths' for placement aptitude. You need three habits: start from 100, pick a convenient total, and try the options.

These three methods are the fastest way in for anyone who finds formulas scary. They work on percentages, profit and loss, discount, ratio, time and work, pipes, ages and number puzzles: more than half of a typical quantitative paper. Every later chapter points back to them.

Method 1: pretend the number is 100

Many questions never tell you the starting price, salary or population. They only talk in percentages. So choose the starting number yourself, and choose 100, because a percentage of 100 is just that many rupees.

Then apply each change in order, as plain numbers. At the end, compare with 100.

+201000100%
Start at 100. A 20% rise adds 20, not '20%'
Example 1A shopkeeper raises a price by 25% and then gives a 20% discount. What is the overall change?
  1. Start at 100.No price is given, so we choose a friendly one.
  2. 25% rise: 100 + 25 = 125.25% of 100 is 25.
  3. 20% discount on 125: 20% of 125 = 25, so 125 - 25 = 100.The discount is on the NEW price, not on 100.
  4. Back to 100: no change.
Example 2A's salary is 20% more than B's. By what percent is B's salary less than A's?
  1. Let B = 100. Then A = 120.The sentence compares A to B, so B is the base.
  2. B is 20 less than A.Difference stays 20.
  3. As a percent of A: 20/120 × 100 = 16.67%.'Less than A' means A is now the base.

Method 2: pick a convenient total

When a job, a tank or an amount has no size, give it one. Choose the LCM (lowest common multiple) of the numbers in the question, so everyone's share per day comes out whole.

Now 'A finishes in 10 days' simply means 'A does 3 units a day' if the job is 30 units. Adding people is plain addition.

A3/dayB2/dayJob30 units
Job = LCM(10, 15) = 30 units. A does 3 a day, B does 2
Example 1A can finish a job in 12 days and B in 18 days. How long will they take together?
  1. Job = LCM(12, 18) = 36 units.Both 12 and 18 divide 36, so no fractions.
  2. A: 36/12 = 3 units a day. B: 36/18 = 2 units a day.Units per day = total / days.
  3. Together: 5 units a day.Working together, their daily work adds.
  4. 36 / 5 = 7.2 days.

Method 3: try the options

Multiple-choice questions give you the answer, hidden among three wrong ones. When setting up an equation feels hard, put each option into the question and see which one fits.

Start with the middle option. If it is too big, the answer is one of the smaller options, so you only need one more try.

Example 1The sum of two numbers is 45 and their difference is 9. The larger number is: (a) 25 (b) 27 (c) 29 (d) 31
  1. Try 27: the other number is 45 - 27 = 18.The sum fixes the other number.
  2. Difference: 27 - 18 = 9. It fits.Check the second condition.
  3. Answer: 27.
Exam tipTrying options is not cheating. In an exam it is often the quickest correct method.

Formula summary

Method 1: take 100
When the question has no starting number, start with 100. Percent changes become plain rupees.
Method 2: pick a convenient total
When the job size or quantity is unknown, choose the LCM of the numbers given. Everything becomes a whole number.
Method 3: try the options
When setting up an equation feels hard, put each option into the question. The one that fits is the answer.
Which method?
Percent, profit, discount, price rise: Method 1. Time and work, pipes, ratio sharing: Method 2. Ages, numbers, 'find x': Method 3.

Shortcuts and tricks

Method 1: take 100

Use it when: Percent, profit and loss, discount, successive increase or decrease.

  1. Call the starting value 100.
  2. Apply each change as plain rupees: +20% of 100 is +20.
  3. Read the answer straight off. The final number minus 100 is the percent change.
ExampleA price goes up 20%, then down 20%. Net change?
  1. Start at 100.
  2. Up 20%: 100 + 20 = 120.
  3. Down 20% of 120 = 24: 120 - 24 = 96.
  4. 96 - 100 = -4, so a 4% fall.

Method 2: pick a convenient total

Use it when: Time and work, pipes and cisterns, anything with 'together'.

  1. Take the total work as the LCM of the days given.
  2. Each person's work per day = total / their days.
  3. Add the per-day work of people working together, then divide the total by it.
ExampleA finishes a job in 10 days, B in 15 days. Together?
  1. LCM of 10 and 15 = 30 units of work.
  2. A does 30/10 = 3 units a day. B does 30/15 = 2 units a day.
  3. Together 5 units a day.
  4. 30 / 5 = 6 days.

Method 3: try the options

Use it when: Ages, 'find the number', ratio questions with awkward wording.

  1. Start with the middle option so you learn whether to go higher or lower.
  2. Check every condition in the question, not just one.
  3. Stop at the first option that fits all of them.
ExampleA father is 3 times his son's age. In 10 years he will be twice the son's age. Son's age now? (a) 5 (b) 10 (c) 15 (d) 20
  1. Try 10: father 30. In 10 years: 20 and 40. 40 = 2 × 20. Fits.
  2. Both conditions are checked, so stop here.

Common mistakes

A 20% rise then a 20% fall brings you back to the start.
The fall is taken on the bigger number: 100 → 120 → 96, a 4% loss.
In pipes questions, add every pipe's per-minute amount.
An emptying pipe SUBTRACTS its per-minute amount.
The first option that fits the first sentence is the answer.
Check every condition in the question before you stop.

Before you move on, you should be able to...

  • start at 100 whenever a question gives only percentages
  • turn 'finishes in n days' into units per day using the LCM
  • try the options from the middle when the equation is awkward

Practice questions (10)

Try each one before opening the solution. Or practise them one by one so your score is saved.

easy A shirt costs Rs 400. The shop gives 25% off. What do you pay?
  1. Take 100: 25% off leaves 75.
  2. 75 per 100 means 75/100 of 400 = 300.

Answer: Rs 300

easy Cost price Rs 500, selling price Rs 600. Profit percent?
  1. Profit = 100.
  2. 100 out of 500 = 20 out of 100 = 20%.

Answer: 20%

easy A number is increased by 10% and then by 10% again. Total increase?
  1. Start at 100.
  2. +10% gives 110.
  3. +10% of 110 = 11 gives 121.
  4. 121 - 100 = 21%.

Answer: 21%

easy A can do a job in 12 days and B in 6 days. How long together?
  1. LCM of 12 and 6 = 12 units.
  2. A: 1 a day. B: 2 a day. Together 3 a day.
  3. 12 / 3 = 4 days.

Answer: 4 days

easy Rs 900 is shared between A and B in the ratio 4 : 5. How much does B get?
  1. 4 + 5 = 9 parts.
  2. One part = 900 / 9 = 100.
  3. B gets 5 parts = 500.

Answer: Rs 500

easy The sum of two numbers is 50 and their difference is 10. The larger number? (a) 25 (b) 30 (c) 35 (d) 40
  1. Try 30: the other is 20. Sum 50, difference 10. Fits.

Answer: 30

medium A shopkeeper marks goods 50% above cost and gives a 20% discount. Profit percent?
  1. Cost = 100.
  2. Marked = 150.
  3. 20% off 150 = 30 off, so sells at 120.
  4. Profit 20 on 100 = 20%.

Answer: 20%

medium Pipe A fills a tank in 20 min, pipe B empties it in 30 min. Both open, how long to fill?
  1. LCM of 20 and 30 = 60 litres.
  2. A adds 3 a minute. B removes 2 a minute.
  3. Net 1 a minute.
  4. 60 / 1 = 60 minutes.

Answer: 60 minutes

medium A, B and C finish a job in 10, 12 and 15 days. Together?
  1. LCM of 10, 12, 15 = 60 units.
  2. Per day: 6 + 5 + 4 = 15.
  3. 60 / 15 = 4 days.

Answer: 4 days

medium Five years ago a mother was 4 times her daughter's age. Now the mother is 41. The daughter's age now? (a) 9 (b) 14 (c) 12 (d) 10
  1. Five years ago the mother was 36.
  2. 36 / 4 = 9, so the daughter was 9.
  3. Now 9 + 5 = 14.
  4. Check option (b): 14 - 5 = 9, and 4 × 9 = 36 = 41 - 5. Fits.

Answer: 14

Class plan (2 hours, for trainers)

A tested order for teaching this topic in one 2-hour session. Present mode follows the same order.

15 minWarm-up: five quick percentage questions done the long way; time them.
25 minMethod 1 with four examples: rise then fall, salary comparison, population change, price and spending.
25 minMethod 2: work, pipes, and sharing money, each with the LCM.
20 minMethod 3: options, with the 'start in the middle' rule.
25 minPractice set on the site, timed.
10 minRedo the warm-up with the methods; compare times. Recap.
Where these shortcuts come from →
Start here: 3 easy methods that solve most questionsPractise now