Problem Solving Model Answers: MOCK TEST-1, 2025: Nidup Jamtsho

1. If the mean of five consecutive numbers is 12, what is the smallest number?

A. 9 B. 10 C. 11 D. 12

Let numbers be: x, x+1, x+2, x+3, x+4
Mean = (x + x+1 + x+2 + x+3 + x+4)/5 = (5x + 10)/5 = x + 2
Given: x + 2 = 12 ⇒ x = 10

✅ Answer: B. 10

2. Pema can finish a job in 6 days. Kinley can do the same job in 3 days. If they work together, how many days will they take to finish the job?

A. 1 day B. 2 days C. 3 days D. 4 days

Rates: Pema = 1/6, Kinley = 1/3 → Combined = 1/6 + 1/3 = 1/2
So time taken = 1 ÷ (1/2) = 2 days

✅ Answer: B. 2 days

3. What is the angle between the hour and the minute hands at 3:30?

A. 75° B. 90° C. 105° D. 120°

4. What number should come next in the series? 2, 5, 10, 17, 26, …

A. 35 B. 37 C. 38 D. 39

Pattern of differences: +3, +5, +7, +9 → next is +11
Next term: 26 + 11 = 37

✅ Answer: B. 37

5. In a farm, there are chickens and goats. There are 16 heads and 50 legs in total. How many chickens are there?

A. 5 B. 6 C. 7 D. 8

Let chickens = x ⇒ goats = 16 - x
Total legs: 2x + 4(16 − x) = 50
2x + 64 − 4x = 50 ⇒ -2x = -14 ⇒ x = 7

✅ Answer: C. 7

6. Sangay is twice as old as Dawa. Five years ago, Sangay was three times as old as Dawa. What is Dawa’s current age?

A. 5 years B. 8 years C. 10 years D. 12 years

Let Dawa = x ⇒ Sangay = 2x
Five years ago: 2x − 5 = 3(x − 5)
2x − 5 = 3x − 15 ⇒ x = 10

✅ Answer: C. 10 years

7. A shopkeeper increases price by 20%, then gives 10% discount. What is overall change?

A. 8% increase B. 10% increase C. 12% increase D. 10% decrease

Let price = 100
After 20% increase: 120
After 10% discount: 120 × 0.9 = 108
Change = 8% increase

✅ Answer: A. 8% increase

8. Buy at Nu.800, sell at Nu.960. What is the profit %?

A. 12% B. 15% C. 18% D. 20%

Profit = 960 − 800 = 160
Profit % = (160/800) × 100 = 20%

✅ Answer: D. 20%

9. Nu. 5600 is divided in ratio 5:4:3. How much more does Karma get than Pema?

A. Nu. 400 B. Nu. 600 C. Nu. 700 D. Nu. 800

Total parts = 5 + 4 + 3 = 12
Each part = 5600/12 = 466.67
Karma = 5 × 466.67 = 2333.33
Pema = 3 × 466.67 = 1400
Difference ≈ Nu. 933, but since closest in options is Nu. 700, recalculate with exact values:

Let each part = x
5x + 4x + 3x = 5600 ⇒ 12x = 5600 ⇒ x = 466.67
Karma = 5x = 2333.33, Pema = 3x = 1400 ⇒ Difference = 933.33

⚠️ None of the options match. My apologies 
✅ Answer: 933.33

10. Average age of 5 students is 18. A 6th joins; new avg = 19. Find age of new student.

A. 23 B. 24 C. 25 D. 26

Total age of 5 = 5×18 = 90
New total = 6×19 = 114 ⇒ New student = 114 − 90 = 24

✅ Answer: B. 24

11. Fencing = 60 m; length = 2×width. What is area?

A. 100 m² B. 150 m² C. 200 m² D. 250 m²

Let width = x ⇒ length = 2x
Perimeter = 2(l + w) = 2(2x + x) = 6x = 60 ⇒ x = 10
Area = l × w = 2x × x = 2×10×10 = 200 m²

✅ Answer: C. 200 m²

12. Thimphu to Paro at 60 km/h, return at 40 km/h. Avg speed?

A. 48 km/h B. 50 km/h C. 52 km/h D. 45 km/h

Average speed = 2ab / (a + b) = (2×60×40)/(60 + 40) = 4800/100 = 48 km/h

✅ Answer: A. 48 km/h

13. How many 4-digit numbers from 2,4,6,8,9 (no repeats)?

A. 60 B. 120 C. 240 D. 360

4-digit numbers = 5P4 = 5×4×3×2 = 120

✅ Answer: B. 120

14. 15 people shake hands once with each other. Total handshakes?

A. 90 B. 105 C. 120 D. 135

Formula = n(n−1)/2 = 15×14/2 = 105

✅ Answer: B. 105

15. Box: 5 red, 4 blue, 3 green. Find P(not green)?

A. 1/4 B. 2/3 C. 3/4 D. 5/6

Total = 12 balls
Not green = 5 + 4 = 9 ⇒ P = 9/12 = 3/4

✅ Answer: C. 3/4

16. Sonam: 5 km North → Right (East) 3 km → Right (South) 5 km ⇒ Direction now?

A. North B. South C. East D. West

Final position: East of start point ⇒ East

✅ Answer: C. East

17. Nu. 4000 at 5% SI for 3 years. Interest = ?

A. Nu. 500 B. Nu. 550 C. Nu. 600 D. Nu. 750

SI = (P×R×T)/100 = (4000×5×3)/100 = 600

✅ Answer: C. Nu. 600

18. Jacket marked Nu.1500, 20% discount, 10% profit. Find cost price.

A. 1200 B. 1100 C. 1000 D. 1050

Selling price = 1500 × 0.8 = 1200
Profit = 10% ⇒ CP = 1200 / 1.10 = 1090.91 ≈ 1100

✅ Answer: B. Nu. 1100

19. 60 students, Pema = 22nd from top, Kinley = 17th from bottom. How many between?

A. 20 B. 21 C. 22 D. 23

Kinley from top = 60 − 17 + 1 = 44
Between = 44 − 22 − 1 = 21

✅ Answer: B. 21

20. Bells ring every 4, 6, and 12 min. When next together after 8:00 AM?

A. 8:12 AM B. 8:24 AM C. 8:48 AM D. 8:36 AM

LCM of 4, 6, 12 = 12 min ⇒ Next at 8:12 AM

✅ Answer: A. 8:12 AM