Top 50 - Part 1

1. Partnership

A and B invest in the ratio 3:5. If the total profit is ₹4,000, find B’s share.

A) ₹1,200 B) ₹2,000 C) ₹2,500 D) ₹3,000

Answer: C) ₹2,500

Total parts = 8

B = 5/8 × 4000
  = ₹2,500

2. Ages

The present ages of A and B are in the ratio 4:5. Their total age is 45. Find A’s age.

A) 18 B) 20 C) 25 D) 30

Answer: B) 20

Total parts = 9

One part = 45/9 = 5

A = 4 × 5 = 20

3. HCF and LCM

The HCF of two numbers is 6 and their LCM is 72. If one number is 18, find the other.

A) 20 B) 24 C) 30 D) 36

Answer: B) 24

Use:

First × Second = HCF × LCM

18 × x = 6 × 72

18x = 432

x = 24

4. Remainder

What is the remainder when 125 is divided by 7?

A) 5 B) 6 C) 4 D) 3

Answer: A) 6

7 × 17 = 119

125 - 119 = 6

Therefore the answer is actually B) 6.

5. Divisibility

Which number is divisible by both 3 and 5?

A) 125 B) 135 C) 142 D) 154

Answer: B) 135

135 ÷ 3 = 45
135 ÷ 5 = 27

6. Pipes

A pipe fills a tank in 8 hours. A second pipe empties it in 12 hours. If both are opened together, how long will the tank take to fill?

A) 12 hours B) 18 hours C) 24 hours D) 30 hours

Answer: C) 24 hours

Fill = 1/8
Empty = 1/12

Net = 1/8 - 1/12
    = 3/24 - 2/24
    = 1/24

Therefore:

24 hours

7. Boats and Streams

A boat’s speed in still water is 15 km/h and stream speed is 3 km/h. Find its downstream speed.

A) 12 B) 15 C) 18 D) 20

Answer: C) 18 km/h

Downstream = Boat + Stream
           = 15 + 3
           = 18 km/h

8. Train

A 200-metre train travels at 72 km/h. How long does it take to cross a pole?

A) 8 sec B) 10 sec C) 12 sec D) 15 sec

Answer: B) 10 seconds

72 km/h = 72 × 5/18
        = 20 m/s

Time = 200/20
     = 10 sec

9. Permutation

How many 3-digit numbers can be formed using 1, 2, 3, 4 without repetition?

A) 12 B) 18 C) 24 D) 36

Answer: C) 24

4 choices × 3 choices × 2 choices

= 24

10. Combination

From 6 employees, how many ways can 3 employees be selected?

A) 15 B) 18 C) 20 D) 24

Answer: C) 20

⁶C₃
= 6!/(3!3!)
= 20

11. Probability

A bag contains 3 red balls and 2 blue balls. One ball is selected randomly. What is the probability of getting a red ball?

A) 2/5 B) 3/5 C) 1/2 D) 3/4

Answer: B) 3/5

Favorable = 3
Total = 5

P = 3/5

12. Algebra

If:

x + y = 15
x - y = 5

find x.

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

Answer: C) 10

Add the equations:

x + y = 15
x - y =  5
-----------
2x    = 20

x = 10

13. Geometry

The angles of a triangle are in the ratio 2:3:4. Find the largest angle.

A) 60° B) 70° C) 80° D) 90°

Answer: C) 80°

Total parts = 2 + 3 + 4 = 9

One part = 180/9 = 20°

Largest = 4 × 20
        = 80°

14. Mensuration

Find the circumference of a circle with radius 7 cm. Use π = 22/7.

A) 22 cm B) 44 cm C) 49 cm D) 154 cm

Answer: B) 44 cm

Circumference = 2πr

= 2 × 22/7 × 7

= 44 cm

15. Data Interpretation

The number of candidates selected by a company is:

Year	Selected
2022	100
2023	120
2024	150
2025	180

What is the percentage increase from 2022 to 2025?

A) 60% B) 70% C) 80% D) 90%

Answer: C) 80%

Increase = 180 - 100 = 80

Percentage = 80/100 × 100
           = 80%

16. Successive Discount

An article is discounted by 20% and then by 10%. What is the effective discount?

A) 28% B) 30% C) 32% D) 25%

Answer: A) 28%

Take price = 100

After 20% discount = 80

10% of 80 = 8

Final = 72

Discount = 28%

17. Profit with Discount

An article marked at ₹1,000 is sold after a 10% discount. If its cost price is ₹800, find the profit percentage.

A) 10% B) 12.5% C) 15% D) 20%

Answer: B) 12.5%

SP = 1000 - 10%
   = 900

Profit = 900 - 800
       = 100

Profit % = 100/800 × 100
         = 12.5%

18. Average

The average of 10 numbers is 30. If one number, 45, is removed, what is the new average?

A) 27.5 B) 28 C) 28.33 D) 29

Answer: C) 28.33

Original total = 10 × 30 = 300

New total = 300 - 45
          = 255

Numbers remaining = 9

Average = 255/9
        = 28.33