SSC Arithmetical Reasoning Questions with Answers and Tricks

Arithmetical reasoning uses simple arithmetic ideas in real-life situations such as money, ages, counting and ratios. These questions appear in SSC CGL, CHSL, MTS and GD papers and are easy to score if you read the problem carefully and form a small equation. This practice paper gives you 21 questions with answers and short solutions.

What Is Arithmetical Reasoning?

In arithmetical reasoning, you are given a short story or a situation with numbers, and you must find the unknown value. There are no new formulas; you only use addition, subtraction, multiplication, division, ratio, percentage and simple equations.

• Read slowly and note the given numbers.
• Choose a variable for the unknown quantity.
• Form an equation from the statement and solve it.

Rules and Shortcut Tricks

• Heads and legs: if there are x two-legged and y four-legged animals, then x + y = heads and 2x + 4y = legs.
• Coins and notes: let the number of one kind be x and the other (total - x), then form the value equation.
• Unitary method: find the value of one unit and then multiply.
• Handshakes: n persons give n(n - 1)/2 handshakes.
• Percentage change in consumption: if the price rises by r%, reduce consumption by r / (100 + r) x 100 percent to keep the expense same.
• Check the answer by putting it back in the question.

Set 1: Money and Counting (Q1–Q7)

Q1. A bag has 5 notes of Rs 100 and 8 notes of Rs 50. Find the total amount.
Answer: Rs 900
Solution: 500 + 400 = 900.

Q2. Ram has twice as many sweets as Shyam. Together they have 36 sweets. How many sweets does Ram have?
Answer: 24
Solution: Shyam has 12 and Ram has 24.

Q3. How many legs are there in 10 hens and 6 goats?
Answer: 44
Solution: 10 x 2 + 6 x 4 = 20 + 24 = 44.

Q4. A has Rs 10 more than B. Together they have Rs 90. How much does A have?
Answer: Rs 50
Solution: B = Rs 40 and A = Rs 50.

Q5. The price of 4 pens is Rs 60. Find the price of 7 pens.
Answer: Rs 105
Trick: One pen = Rs 15, so 7 pens = Rs 105.

Q6. A dozen pencils cost Rs 48. Find the cost of 5 pencils.
Answer: Rs 20
Solution: One pencil = Rs 4.

Q7. A man has 12 coins of Rs 5 and Rs 2 amounting to Rs 42. How many coins of each type does he have?
Answer: 6 coins of Rs 5 and 6 coins of Rs 2
Solution: 5x + 2(12 - x) = 42 gives 3x = 18, so x = 6.

Set 2: Everyday Word Problems (Q8–Q14)

Q8. In a class of 40 students, 25 are girls. Find the ratio of boys to girls.
Answer: 3 : 5
Solution: Boys = 15, so 15 : 25 = 3 : 5.

Q9. A train leaves at 9:45 AM and reaches at 2:10 PM. Find the journey time.
Answer: 4 hours 25 minutes
Solution: From 9:45 to 2:10 PM is 4 h 25 min.

Q10. A car travels 60 km in 1.5 hours. Find its speed.
Answer: 40 km/h
Solution: 60 / 1.5 = 40.

Q11. A shopkeeper buys a pen for Rs 10 and sells it for Rs 12. Find the profit percentage.
Answer: 20%
Solution: Profit = 2 and 2 / 10 x 100 = 20%.

Q12. 5 workers finish a job in 12 days. How many days will 10 workers take?
Answer: 6 days
Solution: More workers take proportionally fewer days.

Q13. The sum of three consecutive numbers is 72. Find the numbers.
Answer: 23, 24 and 25
Solution: The middle number = 72 / 3 = 24.

Q14. The price of sugar rises by 20%. By what percent should consumption be reduced to keep the expense the same?
Answer: 16 2/3%
Trick: 20 / 120 x 100 = 16.67%.

Set 3: Exam-Level Questions (Q15–Q21)

Q15. A farmer has hens and cows. There are 30 heads and 80 legs. How many hens and cows are there?
Answer: 20 hens and 10 cows
Solution: 2x + 4(30 - x) = 80 gives x = 20.

Q16. A father is 4 times as old as his son. The sum of their ages is 50 years. Find their ages.
Answer: Father 40 years and son 10 years
Solution: 5 parts = 50, so 1 part = 10.

Q17. How many squares are there in a 3 x 3 grid (all sizes)?
Answer: 14
Solution: 9 + 4 + 1 = 14.

Q18. How many numbers from 1 to 100 are divisible by 7?
Answer: 14
Solution: 100 / 7 = 14.28, so 14 numbers.

Q19. A watch loses 2 minutes every hour. How many minutes slow will it be after 12 hours?
Answer: 24 minutes
Solution: 2 x 12 = 24.

Q20. One pipe fills a tank in 6 hours and another empties it in 12 hours. In how many hours is the tank filled if both are open?
Answer: 12 hours
Solution: Net rate = 1/6 - 1/12 = 1/12.

Q21. 15 persons shake hands with each other once. How many handshakes are there?
Answer: 105
Trick: 15 x 14 / 2 = 105.

Steps to Solve Arithmetical Reasoning Problems

1. Read the question twice and note what is asked.
2. Write the given data in short with variables.
3. Form one or two simple equations.
4. Solve step by step and check with the options.

Many problems of this type are easy once they are written as an equation. Do not try to solve them in your head. Use the options to test the answer when the equation looks long.

Common Mistakes in Arithmetical Reasoning

• Skipping a number or a condition while reading the problem.
• Forming the equation wrongly (for example mixing legs and heads).
• Not checking the answer.
• Dividing instead of multiplying in the unitary method.
• Ignoring units such as minutes and hours.
• Not using a variable and trying to guess.

How to Practice These 21 Questions

1. Read each question twice.
2. Form an equation before calculating.
3. Solve each set in 7 minutes.
4. Check the answer by substitution.

Related Topics to Study Next

• SSC Reasoning Practice Set
• SSC Percentage Questions with Shortcut Tricks
• Profit and Loss Questions
• SSC Simplification Questions

Frequently Asked Questions

What is arithmetical reasoning?

It is a reasoning topic that uses basic arithmetic to solve everyday word problems.

How do I solve heads and legs questions?

Form two equations from the number of heads and legs and solve them.

What is the formula for handshakes?

For n persons, the number of handshakes is n(n - 1)/2.

What is the unitary method?

It finds the value of one unit first and then multiplies for the required number.

How many such questions come in SSC exams?

One or two questions per shift in the reasoning section.

Is it an easy topic?

Yes. It uses simple maths, but a careful reading of the question is important.

What is a good approach for word problems?

Choose a variable, form an equation and solve.

How do I solve coin and note problems?

Let one kind be x and the other total minus x, then form the value equation.

How do I find the percentage reduction in consumption?

Use r / (100 + r) x 100 when the price rises by r percent.

How can I check my answer quickly?

Put the answer back in the question and check that all conditions are met.

Does it need any formulas?

Only basic ones such as ratio, percentage and equations.

How should I prepare arithmetical reasoning?

Practise one set a day and revise basic arithmetic topics.