Top 50 - Part 2

1. Ratio

If:

A : B = 2 : 3
B : C = 4 : 5

find A:B:C.

A) 8:12:15 B) 2:4:5 C) 8:6:15 D) 4:6:5

Answer: A) 8:12:15

Make B common:

2:3 = 8:12

4:5 = 12:15

Therefore:

A:B:C = 8:12:15

2. Work Efficiency

A is twice as efficient as B. If B takes 18 days to complete a work, how many days does A take?

A) 6 B) 9 C) 12 D) 15

Answer: B) 9 days

If A is twice as efficient, A takes half the time:

18/2 = 9

3. Work

A and B together finish a work in 10 days. A alone takes 15 days. How many days does B alone take?

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

Answer: C) 30 days

Together = 1/10
A = 1/15

B = 1/10 - 1/15
  = 3/30 - 2/30
  = 1/30

Therefore:

B = 30 days

4. Speed Conversion

Convert 72 km/h into metres per second.

A) 18 m/s B) 20 m/s C) 22 m/s D) 25 m/s

Answer: B) 20 m/s

72 × 5/18 = 20 m/s

5. Average Speed

A person travels 60 km at 30 km/h and another 60 km at 60 km/h. Find the average speed.

A) 35 km/h B) 40 km/h C) 45 km/h D) 50 km/h

Answer: B) 40 km/h

Total distance:

120 km

Time:

60/30 = 2 hours
60/60 = 1 hour

Total = 3 hours

Average:

120/3 = 40 km/h

6. Simple Interest

At what rate will ₹5,000 earn ₹1,000 simple interest in 4 years?

A) 4% B) 5% C) 6% D) 8%

Answer: B) 5%

SI = PRT/100

1000 = 5000 × R × 4 / 100

R = 5%

7. Compound Interest

The compound interest on ₹10,000 at 10% for 2 years is ₹2,100. What is the amount?

A) ₹11,000 B) ₹12,000 C) ₹12,100 D) ₹12,500

Answer: C) ₹12,100

Amount = Principal + CI
       = 10000 + 2100
       = ₹12,100

8. Mixture

A 30-litre mixture contains milk and water in the ratio 4:1. How much water must be added to make the ratio 2:1?

A) 5 L B) 8 L C) 10 L D) 12 L

Answer: C) 10 L

Initially:

Milk = 24 L
Water = 6 L

For ratio 2:1:

24 : Water = 2 : 1

Water = 12 L

Already 6 L exists.

Therefore added:

12 - 6 = 6 L

So the correct answer is 6 L, which is missing from the options.

Corrected answer: 6 L.

9. Partnership

A invests ₹10,000 for 12 months and B invests ₹15,000 for 8 months. Find their profit-sharing ratio.

A) 1:1 B) 2:1 C) 3:2 D) 4:3

Answer: A) 1:1

A = 10000 × 12 = 120000
B = 15000 × 8 = 120000

Therefore:

A:B = 1:1

10. Ages

A father is 3 times as old as his son. After 10 years, he will be twice as old. Find the son’s present age.

A) 5 B) 10 C) 15 D) 20

Answer: B) 10 years

Let son’s age = x.

Father = 3x.

After 10 years:

3x + 10 = 2(x + 10)

3x + 10 = 2x + 20

x = 10

11. HCF

Find the HCF of 72 and 108.

A) 18 B) 24 C) 36 D) 54

Answer: C) 36

72 = 2³ × 3²
108 = 2² × 3³

HCF = 2² × 3²
    = 36

12. LCM

Find the LCM of 15 and 20.

A) 30 B) 45 C) 60 D) 75

Answer: C) 60

15 = 3 × 5
20 = 2² × 5

LCM = 2² × 3 × 5
    = 60

13. Remainder

What is the remainder when 2¹⁰ is divided by 7?

A) 1 B) 2 C) 3 D) 4

Answer: A) 1

Pattern:

2¹ = 2
2² = 4
2³ = 8 → 1

Cycle = 3.

10 ÷ 3 gives remainder 1

Therefore:

2¹⁰ → remainder 2

So the correct answer is actually B) 2.

Answer: B) 2

14. Divisibility

Which of the following is divisible by 11?

A) 121 B) 125 C) 132 D) 145

Answer: A) 121

121 ÷ 11 = 11

15. Pipes

Pipe A fills a tank in 10 hours and pipe B in 15 hours. How long do they take together?

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

Answer: B) 6 hours

1/10 + 1/15
= 3/30 + 2/30
= 5/30
= 1/6

16. Boats

A boat moves downstream at 18 km/h and upstream at 10 km/h. Find stream speed.

A) 2 B) 4 C) 6 D) 8

Answer: B) 4 km/h

Stream speed
= (18 - 10)/2
= 4 km/h