Arithmetic Formula Guide for SSC Exams
Rahul Kumar
SSC Exam Expert & Content Editor
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Arithmetic is the biggest part of SSC Quantitative Aptitude, and it is built on a small set of formulas. This arithmetic formula guide for SSC gives the formulas of percentage, profit and loss, simple and compound interest, average, speed, time and work, boats and alligation, each with a solved example.
Percentage
| Formula | Meaning |
|---|---|
| Percentage = (part / whole) × 100 | Basic percentage |
| Net change of two successive changes a% and b% = a + b + ab/100 | Use a minus sign for a decrease |
| Fraction to percentage | 1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5% |
Profit, Loss and Discount
| Formula | Meaning |
|---|---|
| Profit = SP − CP and Loss = CP − SP | SP is the selling price and CP the cost price |
| Profit % = (Profit / CP) × 100 | Profit on the cost price |
| SP = CP × (100 + Profit %) / 100 | Selling price when profit is known |
| Discount = Marked price − SP | Discount % is on the marked price |
| Two successive discounts a% and b% = a + b − ab/100 | Single equivalent discount |
Simple and Compound Interest
| Formula | Meaning |
|---|---|
| SI = (P × R × T) / 100 | P is the principal, R the rate and T the time in years |
| Amount = P + SI | Total money |
| Amount in CI = P(1 + R/100)^n | n is the number of years |
| CI = Amount − P | Compound interest |
Average
| Formula | Meaning |
|---|---|
| Average = Sum of the observations / Number of observations | Basic average |
| Sum = Average × Number | To find the total |
Speed, Time and Distance
| Formula | Meaning |
|---|---|
| Speed = Distance / Time | Basic formula |
| km/h to m/s: multiply by 5/18 | 72 km/h = 20 m/s |
| m/s to km/h: multiply by 18/5 | 10 m/s = 36 km/h |
| Average speed for equal distances = 2xy / (x + y) | x and y are the two speeds |
| Train crossing a pole: time = length of train / speed | Platform: (train + platform length) / speed |
| Relative speed: sum for opposite directions and difference for the same direction | For trains and runners |
| Downstream speed = boat + stream; upstream speed = boat − stream | For boats and streams |
Time and Work
| Formula | Meaning |
|---|---|
| Work done by A in one day = 1 / days taken by A | One-day work |
| A and B together take xy / (x + y) days | x and y are their separate days |
| Work = Efficiency × Time | Use total work as the LCM of days |
Alligation
Quantity of cheaper : Quantity of dearer = (d − m) : (m − c), where c is the cost of the cheaper, d the cost of the dearer and m the cost of the mixture.
Solved Examples
Example 1. Find the compound interest on 1000 rupees at 10% for 2 years.
Amount = 1000 × 1.1 × 1.1 = 1210. CI = 1210 − 1000 = 210 rupees.
Example 2. A does a work in 10 days and B in 15 days. In how many days will they finish it together?
(10 × 15) / (10 + 15) = 150 / 25 = 6 days.
Example 3. A man goes 40 km/h and returns 60 km/h over the same distance. What is the average speed?
2 × 40 × 60 / (40 + 60) = 4800 / 100 = 48 km/h.
Example 4. Find the single discount equal to successive discounts of 10% and 20%.
10 + 20 − (10 × 20)/100 = 30 − 2 = 28%.
Quick Tips
- Write the formula first, then put in the numbers.
- Learn the fraction to percentage table by heart.
- Use total work as the LCM in time and work questions.
- Check the unit (km/h or m/s) before you calculate.
Quick Revision Points
- Profit % = (Profit / CP) × 100.
- SI = PRT / 100 and Amount in CI = P(1 + R/100)^n.
- km/h to m/s: multiply by 5/18.
- A and B together take xy/(x + y) days.
- Average speed for equal distances = 2xy/(x + y).
Practice Questions With Answers
- Find the simple interest on 1000 rupees at 5% for 2 years.
Answer: 100 rupees - Find the compound interest on 1000 rupees at 10% for 2 years.
Answer: 210 rupees - Convert 72 km/h into m/s.
Answer: 20 m/s - Find the average speed for equal distances at 40 km/h and 60 km/h.
Answer: 48 km/h - A does a work in 10 days and B in 15 days. In how many days will they do it together?
Answer: 6 days - Find the profit % if CP is 200 rupees and SP is 250 rupees.
Answer: 25% - Find the single discount equal to successive discounts of 10% and 20%.
Answer: 28% - A 100 m long train runs at 36 km/h. How long does it take to cross a pole?
Answer: 10 seconds - The speed of a boat is 8 km/h and of the stream is 2 km/h. Find the downstream speed.
Answer: 10 km/h - Find the average of 10, 20 and 30.
Answer: 20
How to Practise This Chapter
Write each formula on a card, with a solved example on the back, and revise the cards every day. Then test yourself with our practice papers and the previous year papers page. See all guides on the Formula Guide page, and also read the Mathematics notes and Quantitative Aptitude notes. The next guide is Geometry and Mensuration.
Frequently Asked Questions
Why should I learn formulas by heart?
Formulas save time in the exam, and a quick start gives you more time for the difficult questions.
What is the formula for profit percentage?
Profit percentage is profit divided by the cost price, multiplied by 100.
What is the formula for simple interest?
Simple interest is principal times rate times time, divided by 100.
What is the formula for compound interest?
Amount = P times (1 + R/100) to the power n, and CI = Amount minus P.
How do I convert km/h into m/s?
Multiply by 5/18.
How do I find the average speed for equal distances?
Use 2xy divided by (x + y).
How do I find the time taken by two persons together?
Use xy divided by (x + y) days.
What is the formula of two successive discounts?
Single discount = a + b minus ab/100.
What is alligation?
It is a method to find the ratio in which two items of different prices are mixed.
Is Arithmetic important for SSC exams?
Yes. Arithmetic questions form the largest part of the Quantitative Aptitude section.
How should I revise the formulas?
Write them on cards, solve one example for each and revise every day.
How many questions come from this topic in SSC exams?
Many questions in the Quantitative Aptitude section are based on Arithmetic, but the number changes from exam to exam.
Rahul Kumar
SSC Exam Expert & Content Editor
Rahul is a senior SSC exam strategist with 8+ years of experience helping aspirants crack CGL, CHSL and MTS exams. He writes in-depth notification breakdowns, exam pattern guides and preparation strategies.