ALL Mixed

Pema is 4 years older than Deki. After 6 years, the sum of their ages will be 40. What are their current ages?

Let Deki = x → Pema = x + 4
(x + 6) + (x + 4 + 6) = 40
x + 6 + x + 10 = 40 → 2x + 16 = 40 → x = 12
Deki = 12, Pema = 16

✅ Answer: Pema = 16 years, Deki = 12 years

Calendar

If 5th April 2025 is a Saturday, what day will 5th April 2026 be?

Solution:
2025 is not a leap year → adds 1 day
Saturday + 1 = Sunday

✅ Answer: Sunday

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Clock

At what time between 2 and 3 o’clock will the hands of the clock be at a right angle?

Solution:
Right angle = 90°
Angle between hands = |(30×H − (11/2)×M)|
Between 2 & 3 → H = 2
So: |60 − 5.5M| = 90
Case 1: 60 − 5.5M = 90 → M = −5.45 ❌
Case 2: 5.5M − 60 = 90 → 5.5M = 150 → M = 27.27 minutes

✅ Answer: At approximately 2:27

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Average

The average age of 5 friends is 16. If Sonam joins the group, the average becomes 17. What is Sonam’s age?

Solution:
Total of 5 = 5×16 = 80
New total = 6×17 = 102
Sonam = 102 − 80 = 22 years

✅ Answer: 22 years

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Area

Find the area of a triangle with base 14 cm and height 12 cm.

Solution:
Area = ½ × base × height = ½ × 14 × 12 = 84 cm²

✅ Answer: 84 cm²

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Volume and Surface Area

A cylindrical water tank in Mongar has a radius of 7 m and height of 4 m. Find the volume. (Use π = 22/7)

Solution:
Volume = πr²h = 22/7 × 7 × 7 × 4 = 616 m³

✅ Answer: 616 m³

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Permutation and Combination

How many 3-letter codes can Kinley form using the letters A, B, C, D if no letter repeats?

Solution:
P(4,3) = 4 × 3 × 2 = 24

✅ Answer: 24 codes

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Numbers

The sum of two numbers is 150. If one number is 20% more than the other, find the numbers.

Solution:
Let smaller = x → larger = 1.2x
x + 1.2x = 150 → 2.2x = 150 → x = 68.18
Other = 150 − 68.18 = 81.82

✅ Answer: 68.18 and 81.82

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Problems on Numbers

A number when divided by 7 leaves remainder 4. When the same number is divided by 5, the remainder is 1. What is the smallest such number?

Solution:
Let number be x
x ≡ 4 mod 7 → x = 7a + 4
Now, 7a + 4 ≡ 1 mod 5 → 7a ≡ −3 ≡ 2 mod 5 → a = 4
x = 7×4 + 4 = 32

✅ Answer: 32

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Problems on H.C.F. and L.C.M.

The H.C.F. of two numbers is 16, and their L.C.M. is 240. If one number is 48, find the other.

Solution:
HCF × LCM = a × b
16 × 240 = 48 × x → x = (16×240)/48 = 80

✅ Answer: 80