Mental Reasoning 3- 30 Arithmetical Reasoning Practice Set with Step-by-Step Explanations

Mental Reasoning 3- 30 Arithmetical Reasoning Practice Set with Step-by-Step Explanations

ARITHMETICAL REASONING PRACTICE SET (30 QUESTIONS)

Arithmetical Reasoning Practice-PART A: Problems on Ages (आयु संबंधी प्रश्न)

Q1. Father is 3 times son’s age. After 15 years, he will be twice son’s age. Find son’s present age.

Q 1 -Father is 3 times son’s age. After 15 years, he will be twice son’s age.
Let son = x → Father = 3x
3x + 15 = 2(x + 15) → 3x + 15 = 2x + 30 → x = 15
✅ Son = 15 years, Father = 45 years
Hindi: पिता की उम्र पुत्र की उम्र से 3 गुना है, 15 वर्ष बाद दो गुना होगी → पुत्र = 15 वर्ष।

Q2. The sum of father and son’s age is 60. Five years ago, father’s age was 5 times the son’s age. Find their ages.

Let father = x, son = y
→ x + y = 60
→ x – 5 = 5(y – 5) ⇒ x – 5 = 5y – 25 ⇒ x = 5y – 20
Substitute: 5y – 20 + y = 60 ⇒ 6y = 80 ⇒ y = 13⅓, x = 46⅔
✅ Father = 47 yrs, Son = 13 yrs
Hindi: पिता = 47 वर्ष, पुत्र = 13 वर्ष।

Q3. The ratio of ages of A and B is 3:5. After 10 years, it becomes 5:7. Find their present ages.

Let A=3x, B=5x
(3x+10)/(5x+10)=5/7 ⇒ 7(3x+10)=5(5x+10)
→ 21x+70=25x+50 ⇒ 4x=20 ⇒ x=5
✅ A=15, B=25
Hindi: A=15 वर्ष, B=25 वर्ष।

Q4. 5 years ago, the ratio of a father and son’s age was 7:3. 5 years hence, ratio will be 9:5. Find their present ages.

Let present ages = 7x, 3x
→ (7x+5)/(3x+5)=9/5 ⇒ 5(7x+5)=9(3x+5)
→ 35x+25=27x+45 ⇒ 8x=20 ⇒ x=2.5
✅ Father=17.5 yrs, Son=7.5 yrs
Hindi: पिता=17.5 वर्ष, पुत्र=7.5 वर्ष।

Q5. The average age of a family of 4 is 25. A child of 5 years is born. Find new average.

Sum before = 4×25=100
Now total = 100+5=105, members=5
Average=105/5=✅ 21
Hindi: नया औसत = 21 वर्ष।

Arithmetical Reasoning Practice-PART B: Average, Ratio, Percentage (औसत, अनुपात, प्रतिशत)

Q6. Average of 6 numbers is 15. If one number is 21, what is the average of the remaining 5 numbers?

Sum = 6×15=90 → remaining = 90–21=69
Average = 69/5 = ✅ 13.8
Hindi: शेष 5 संख्याओं का औसत = 13.8

Q7. Divide ₹1200 between A and B in ratio 2:3.

Sum of parts = 5
A = 1200×(2/5)=480
B = 720
✅ A=₹480, B=₹720

Q8. What percent of 80 is 20?

(20/80)×100 = ✅ 25%

Q9. A number increases from 40 to 50. Find percent increase.

Increase =10 → % = (10/40)×100=✅ 25%

Q10. A scored 60 marks out of 80. Find % marks.

= (60/80)×100 = ✅ 75%

Arithmetical Reasoning Practice-PART C: Profit, Loss, Interest (लाभ, हानि, ब्याज)

Q11. CP=₹200, Profit=20%. Find SP.

SP = (120/100)×200 = ✅ ₹240

Q12. CP=₹400, Loss=10%. Find SP.

SP = (90/100)×400 = ✅ ₹360

Q13. Find SI on ₹1000 for 3 years at 10%.

SI=(1000×10×3)/100=✅ ₹300

Q14. Find CI on ₹1000 for 2 years @10%.

CI=1000[(1.1)²–1]=1000(1.21–1)=✅ ₹210

Q15. If SP=₹660 and Profit=10%, find CP.

CP = (100×660)/110 = ✅ ₹600

Arithmetical Reasoning Practice-PART D: Time, Speed, Distance / Work (समय, गति, कार्य)

Q16. Speed = 60 km/h, Time = 2 h → Find Distance.

D = 60×2 = ✅ 120 km

Q17. Distance = 90 km, Speed = 45 km/h → Find Time.

T = 90/45 = ✅ 2 hours

Q18. A can do a work in 10 days, B in 15 days. In how many days will they finish together?

(10×15)/(10+15)=✅ 6 days

Q19. A can do work in 12 days, B in 8 days. In how many days will work finish if both work together for 3 days?

1 day work = 1/12+1/8=5/24
In 3 days → 15/24=5/8 done
Remaining =3/8
B alone → 8×(3/8)=3 days
✅ Total = 6 days

Q20. A car travels 60 km/h for 2 hours, then 80 km/h for 1 hour. Find average speed.

Total distance = 120 + 80 = 200 km
Total time = 3 hr
Average speed = 200/3 = ✅ 66.67 km/h

Arithmetical Reasoning Practice-PART E: Partnership / Numbers / Logical Arithmetic

Q21. A invests ₹10,000 for 12 months, B invests ₹15,000 for 8 months. Find profit ratio.

10,000×12 : 15,000×8 = 120000 : 120000
✅ 1 : 1

Q22. The sum of two numbers is 50 and difference is 10. Find numbers.

x+y=50, x–y=10 → 2x=60 → x=30, y=20
✅ 30 and 20

Q23. If 2 + 3 = 10, 4 + 5 = 40, 6 + 7 = ?

Logic: (a+b)×a
→ (6+7)×6 = 13×6=✅ 78

Q24. If 8 × 2 + 3 = 19, and ‘×’ means ‘+’, ‘+’ means ‘×’. Find answer.

8 + 2 × 3 = 8 + 6 = ✅ 14

Q25. Replace ‘*’ by suitable sign: 12 * 3 * 4 = 24

Try × and ÷ ⇒ 12 ÷ 3 × 4 = 4×4=✅16 ❌
Try × and – ⇒ 12×3–4=36–4=✅32 ❌
Try ÷ and + ⇒ 12÷3+4=4+4=✅8 ❌
Try + and × ⇒ 12+3×4=✅24
Answer: +, ×

Arithmetical Reasoning Practice-PART F: Miscellaneous Arithmetic Logic & Puzzles

Q26. Find number whose double is 10 more than its triple.

2x = 3x + 10 ⇒ x = -10 ✅

Q27. Find 2 consecutive numbers whose sum is 37.

Let numbers = x, x+1 → 2x+1=37 ⇒ x=18
✅ Numbers = 18, 19

Q28. If 4 is coded as 20, 5 as 30, 6 as 42, find code for 7.

Pattern: n × (n+1)
→ 4×5=20, 5×6=30, 6×7=42 → 7×8=✅ 56

Q29. Find number that is 15 more than twice of 20.

2×20+15=✅55

Q30. If sum of 3 consecutive even numbers = 90, find numbers.

Let = x, x+2, x+4 → 3x+6=90 ⇒ x=28
✅ Numbers: 28, 30, 32

Exam Tip Summary

✅ Translate words → equation
✅ Note relation: difference stays constant in Age
✅ Always write unit (years, km, ₹)
✅ For reasoning-type, test logical patterns
✅ Revise formulas daily for speed