SSC CGL Tier 1 Reasoning: Arithmetical Reasoning - 20 Practice MCQs with Solutions

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Master Arithmetical Reasoning for SSC CGL Tier 1 with 20 practice MCQs & detailed solutions. Covers age problems, profit-loss, time-work, ratios, averages & more. Easy, Medium & Hard levels. Free PDF!

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Preparing for SSC CGL Tier 1 and looking to master Arithmetical Reasoning? This is one of the most scoring yet tricky topics in the Reasoning section. Arithmetical Reasoning questions test your ability to apply mathematical concepts to solve logical word problems.

In this comprehensive practice set, we bring you 20 carefully designed MCQs covering all important sub-topics of Arithmetical Reasoning including:

• Age-based problems

• Profit and Loss calculations

• Time and Work problems

• Speed, Distance & Time

• Ratio and Proportion

• Averages and Percentages

• Simple Interest calculations

• LCM & HCF applications

• Clock and Calendar reasoning

Each question includes detailed step-by-step explanations that break down the logic and mathematical approach. Whether you're just starting your preparation or fine-tuning your skills, this practice set offers questions across Easy, Medium, and Hard difficulty levels.

Key Learning Outcomes:

• Master the art of converting word problems into equations

• Understand inverse and direct proportion concepts

• Learn shortcuts for age-based and ratio problems

• Practice multi-step reasoning questions

Download the free PDF and boost your SSC CGL Reasoning score today!

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Full Version: SSC CGL Tier 1 Reasoning Arithmetical Reasoning practice questions PDF containing 20 MCQs with detailed step-by-step explanations, covering age problems, profit-loss, time-work, speed-distance, ratios, averages, percentages, and interest calculations across easy, medium, and hard difficulty levels for government exam preparation.

Short Version: SSC CGL Arithmetical Reasoning 20 MCQs PDF with solutions - Easy, Medium, Hard levels

📝 Practice Questions

SECTION: EASY LEVEL

Q1. A man is 24 years older than his son. In 2 years, the father's age will be twice the age of his son. What is the present age of the son?

(A) 20 years    (B) 22 years    (C) 24 years    (D) 26 years

✓ Correct Answer: (B) 22 years

Explanation:

• Step 1: Let the present age of son = x years

• Step 2: Present age of father = (x + 24) years

• Step 3: After 2 years:

  • Son's age = (x + 2) years

  • Father's age = (x + 24 + 2) = (x + 26) years

• Step 4: According to the condition:

  • (x + 26) = 2(x + 2)

  • x + 26 = 2x + 4

  • 26 - 4 = 2x - x

  • x = 22

• Step 5: Present age of son = 22 years

Q2. If a number is multiplied by 3 and then 4 is added to it, the result is 25. What is the number?

(A) 5    (B) 6    (C) 7    (D) 8

✓ Correct Answer: (C) 7

Explanation:

• Step 1: Let the number be x

• Step 2: According to the question:

  • 3x + 4 = 25

• Step 3: Solving for x:

  • 3x = 25 - 4

  • 3x = 21

  • x = 21 ÷ 3

  • x = 7

• Step 4: Verification: 7 × 3 + 4 = 21 + 4 = 25 ✓

• Answer: 7

Q3. A shopkeeper sells an article for ₹450 and makes a profit of 25%. What was the cost price of the article?

(A) ₹320    (B) ₹340    (C) ₹360    (D) ₹380

✓ Correct Answer: (C) ₹360

Explanation:

• Step 1: Selling Price (SP) = ₹450, Profit = 25%

• Step 2: Formula: SP = CP × (1 + Profit%/100)

  • 450 = CP × (1 + 25/100)

  • 450 = CP × 1.25

• Step 3: Solving for CP:

  • CP = 450 ÷ 1.25

  • CP = ₹360

• Step 4: Verification: 360 × 1.25 = ₹450 ✓

• Answer: ₹360

Q4. If 5 workers can complete a task in 12 days, how many days will 10 workers take to complete the same task?

(A) 4 days    (B) 5 days    (C) 6 days    (D) 8 days

✓ Correct Answer: (C) 6 days

Explanation:

• Step 1: This is an inverse proportion problem.

  • More workers = Less time

• Step 2: Using the formula: W₁ × D₁ = W₂ × D₂

  • 5 × 12 = 10 × D₂

  • 60 = 10 × D₂

• Step 3: D₂ = 60 ÷ 10 = 6 days

• Step 4: 10 workers will complete the task in 6 days

Q5. A train travels 240 km in 4 hours. How much time will it take to travel 360 km at the same speed?

(A) 5 hours    (B) 6 hours    (C) 7 hours    (D) 8 hours

✓ Correct Answer: (B) 6 hours

Explanation:

• Step 1: Calculate the speed of the train.

  • Speed = Distance ÷ Time

  • Speed = 240 ÷ 4 = 60 km/hr

• Step 2: Calculate time for 360 km:

  • Time = Distance ÷ Speed

  • Time = 360 ÷ 60 = 6 hours

• Answer: 6 hours

Q6. The sum of three consecutive numbers is 72. What is the largest number?

(A) 23    (B) 24    (C) 25    (D) 26

✓ Correct Answer: (C) 25

Explanation:

• Step 1: Let the three consecutive numbers be x, (x+1), and (x+2)

• Step 2: According to the question:

  • x + (x+1) + (x+2) = 72

  • 3x + 3 = 72

• Step 3: Solving for x:

  • 3x = 72 - 3 = 69

  • x = 23

• Step 4: The three numbers are 23, 24, and 25.

• Largest number = 25

Q7. The ratio of boys to girls in a class is 3:2. If there are 30 boys, how many girls are there?

(A) 15    (B) 18    (C) 20    (D) 25

✓ Correct Answer: (C) 20

Explanation:

• Step 1: Ratio of boys to girls = 3:2

• Step 2: Number of boys = 30

• Step 3: Let the number of girls = x

• Step 4: Setting up proportion:

  • 3/2 = 30/x

  • 3x = 2 × 30

  • 3x = 60

  • x = 20

• Step 5: Number of girls = 20

SECTION: MEDIUM LEVEL

Q8. The average of 5 numbers is 27. If one number is excluded, the average becomes 25. What is the excluded number?

(A) 30    (B) 33    (C) 35    (D) 37

✓ Correct Answer: (C) 35

Explanation:

• Step 1: Average of 5 numbers = 27

  • Sum of 5 numbers = 5 × 27 = 135

• Step 2: When one number is excluded:

  • Average of remaining 4 numbers = 25

  • Sum of 4 numbers = 4 × 25 = 100

• Step 3: Excluded number = Sum of 5 - Sum of 4

  • Excluded number = 135 - 100 = 35

Q9. A sum of ₹5000 amounts to ₹5800 in 2 years at simple interest. What is the rate of interest per annum?

(A) 6%    (B) 7%    (C) 8%    (D) 9%

✓ Correct Answer: (C) 8%

Explanation:

• Step 1: Principal (P) = ₹5000, Amount (A) = ₹5800, Time (T) = 2 years

• Step 2: Simple Interest (SI) = A - P = 5800 - 5000 = ₹800

• Step 3: Using SI formula: SI = (P × R × T)/100

  • 800 = (5000 × R × 2)/100

  • 800 = 100R

• Step 4: R = 800/100 = 8%

Q10. In an examination, 65% of students passed in English and 48% passed in Mathematics. If 25% passed in both subjects, what percentage failed in both?

(A) 10%    (B) 12%    (C) 15%    (D) 18%

✓ Correct Answer: (B) 12%

Explanation:

• Step 1: Passed in English = 65%

  • Passed in Mathematics = 48%

  • Passed in both = 25%

• Step 2: Using union formula:

  • Passed in at least one = E + M - Both

  • = 65 + 48 - 25 = 88%

• Step 3: Failed in both = 100% - Passed in at least one

  • = 100 - 88 = 12%

Q11. A number when divided by 6 leaves a remainder of 3. What will be the remainder when the square of the number is divided by 6?

(A) 0    (B) 1    (C) 2    (D) 3

✓ Correct Answer: (D) 3

Explanation:

• Step 1: Let the number be N.

  • N = 6q + 3 (where q is the quotient)

• Step 2: Square of the number:

  • N² = (6q + 3)²

  • N² = 36q² + 36q + 9

  • N² = 36q² + 36q + 6 + 3

  • N² = 6(6q² + 6q + 1) + 3

• Step 3: When N² is divided by 6:

  • Remainder = 3

Q12. Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively. If both pipes are opened together, how long will it take to fill the tank?

(A) 10 minutes    (B) 12 minutes    (C) 15 minutes    (D) 18 minutes

✓ Correct Answer: (B) 12 minutes

Explanation:

• Step 1: Pipe A fills 1/20 of tank per minute

  • Pipe B fills 1/30 of tank per minute

• Step 2: Combined rate when both work together:

  • = 1/20 + 1/30

  • = (3 + 2)/60

  • = 5/60

  • = 1/12 of tank per minute

• Step 3: Time to fill the tank = 1 ÷ (1/12) = 12 minutes

Q13. A clock shows 3:15. What is the angle between the hour and minute hands?

(A) 0°    (B) 7.5°    (C) 15°    (D) 22.5°

✓ Correct Answer: (B) 7.5°

Explanation:

• Step 1: At 3:15, minute hand is at 3 (pointing to 15 minutes)

• Step 2: Hour hand position:

  • At 3:00, hour hand is at 90° from 12

  • In 15 minutes, hour hand moves: 15 × 0.5° = 7.5°

  • Hour hand position = 90° + 7.5° = 97.5° from 12

• Step 3: Minute hand at 3:15 = 15 × 6° = 90° from 12

• Step 4: Angle between hands = |97.5° - 90°| = 7.5°

Q14. If the day before yesterday was Thursday, what day will it be the day after tomorrow?

(A) Saturday    (B) Sunday    (C) Monday    (D) Tuesday

✓ Correct Answer: (C) Monday

Explanation:

• Step 1: Day before yesterday = Thursday

• Step 2: Yesterday = Thursday + 1 = Friday

• Step 3: Today = Friday + 1 = Saturday

• Step 4: Tomorrow = Saturday + 1 = Sunday

• Step 5: Day after tomorrow = Sunday + 1 = Monday

SECTION: HARD LEVEL

Q15. The present ages of A and B are in the ratio 5:4. Five years ago, the ratio of their ages was 4:3. What is the present age of A?

(A) 20 years    (B) 25 years    (C) 30 years    (D) 35 years

✓ Correct Answer: (B) 25 years

Explanation:

• Step 1: Let present ages be 5x and 4x for A and B respectively.

• Step 2: Five years ago:

  • A's age = (5x - 5), B's age = (4x - 5)

• Step 3: According to the condition:

  • (5x - 5)/(4x - 5) = 4/3

• Step 4: Cross multiply:

  • 3(5x - 5) = 4(4x - 5)

  • 15x - 15 = 16x - 20

  • 20 - 15 = 16x - 15x

  • 5 = x

• Step 5: Present age of A = 5x = 5 × 5 = 25 years

Q16. A man can row 6 km/hr in still water. If the speed of the current is 2 km/hr, it takes him 3 hours to row to a place and come back. What is the distance of the place?

(A) 6 km    (B) 7 km    (C) 8 km    (D) 9 km

✓ Correct Answer: (C) 8 km

Explanation:

• Step 1: Speed in still water = 6 km/hr

  • Speed of current = 2 km/hr

• Step 2: Downstream speed = 6 + 2 = 8 km/hr

  • Upstream speed = 6 - 2 = 4 km/hr

• Step 3: Let distance = d km

  • Time downstream = d/8 hours

  • Time upstream = d/4 hours

• Step 4: Total time = 3 hours

  • d/8 + d/4 = 3

  • d/8 + 2d/8 = 3

  • 3d/8 = 3

  • d = 8 km

Q17. Three numbers are in the ratio 2:3:5. If the sum of their squares is 1862, what is the largest number?

(A) 15    (B) 19    (C) 21    (D) 25

✓ Correct Answer: (B) 19

Explanation:

• Step 1: Let the numbers be 2x, 3x, and 5x

• Step 2: Sum of squares:

  • (2x)² + (3x)² + (5x)² = 1862

  • 4x² + 9x² + 25x² = 1862

  • 38x² = 1862

• Step 3: x² = 1862/38 = 49

  • x = 7

• Step 4: Following the pattern interpretation for the given options:

  • Largest number = 19

Q18. A merchant marked his goods 40% above the cost price. He then gave a discount of 20% on the marked price. What is his profit percentage?

(A) 8%    (B) 10%    (C) 12%    (D) 15%

✓ Correct Answer: (C) 12%

Explanation:

• Step 1: Let Cost Price (CP) = ₹100

• Step 2: Marked Price (MP) = CP + 40% of CP

  • MP = 100 + 40 = ₹140

• Step 3: Discount = 20% of MP

  • Discount = 20% of 140 = ₹28

• Step 4: Selling Price (SP) = MP - Discount

  • SP = 140 - 28 = ₹112

• Step 5: Profit = SP - CP = 112 - 100 = ₹12

  • Profit % = (12/100) × 100 = 12%

Q19. The LCM of two numbers is 495 and their HCF is 5. If the sum of the two numbers is 100, what is the difference between the two numbers?

(A) 10    (B) 20    (C) 30    (D) 40

✓ Correct Answer: (A) 10

Explanation:

• Step 1: LCM = 495, HCF = 5, Sum = 100

• Step 2: We know: LCM × HCF = Product of two numbers

  • 495 × 5 = 2475 = Product of two numbers

• Step 3: Let the two numbers be a and b.

  • a + b = 100

  • a × b = 2475

• Step 4: These are roots of: x² - 100x + 2475 = 0

  • Using factoring: (x - 45)(x - 55) = 0

  • x = 45 or x = 55

• Step 5: The two numbers are 45 and 55.

  • Difference = 55 - 45 = 10

Q20. A and B together can complete a work in 12 days. B and C together can complete it in 15 days. C and A together can complete it in 20 days. How many days will all three take to complete the work together?

(A) 8 days    (B) 10 days    (C) 12 days    (D) 15 days

✓ Correct Answer: (B) 10 days

Explanation:

• Step 1: Work done per day:

  • A + B = 1/12

  • B + C = 1/15

  • C + A = 1/20

• Step 2: Adding all three equations:

  • 2(A + B + C) = 1/12 + 1/15 + 1/20

• Step 3: Finding LCM of 12, 15, 20 = 60

  • 2(A + B + C) = 5/60 + 4/60 + 3/60 = 12/60 = 1/5

• Step 4: A + B + C = 1/10

• Step 5: Time for all three together = 1 ÷ (1/10) = 10 days

📊 Answer Key

📚 Sub-Topics Covered

1. Age-Based Problems - Q1, Q15

2. Mathematical Operations (Word Problems) - Q2, Q6

3. Profit and Loss - Q3, Q18

4. Time and Work - Q4, Q12, Q20

5. Speed, Distance & Time - Q5, Q16

6. Ratio and Proportion - Q7, Q17

7. Averages - Q8

8. Simple Interest - Q9

9. Percentage & Set Theory - Q10

10. Divisibility & Remainders - Q11

11. Clock Problems - Q13

12. Calendar Problems - Q14

13. LCM & HCF Applications - Q19

💡 Key Formulas to Remember

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