Top 25 - Part 1

1. Compound Interest

Find the compound interest on ₹10,000 at 10% per annum for 2 years.

A) ₹2,000 B) ₹2,100 C) ₹2,200 D) ₹2,400

Answer: B) ₹2,100

Explanation:

Amount = P(1 + R/100)^T

       = 10000(1.1)^2
       = 12100

Therefore:

CI = 12100 - 10000
   = ₹2,100

2. Discount

An article marked at ₹2,000 is sold at a discount of 15%. Find the selling price.

A) ₹1,600 B) ₹1,650 C) ₹1,700 D) ₹1,750

Answer: C) ₹1,700

Explanation:

Discount = 15% of 2000
         = 300

SP = 2000 - 300
   = ₹1,700

3. Mixture

A mixture contains milk and water in the ratio 3:2. If the total mixture is 25 litres, how much milk is present?

A) 10 L B) 12 L C) 15 L D) 18 L

Answer: C) 15 L

Explanation:

Milk : Water = 3 : 2

Total parts = 5

Milk = 3/5 × 25
     = 15 L

4. Partnership

A invests ₹5,000 for 12 months and B invests ₹8,000 for 6 months. If the total profit is ₹2,200, what is B’s share?

A) ₹800 B) ₹1,000 C) ₹1,100 D) ₹1,200

Answer: B) ₹1,000

Explanation:

Profit-sharing ratio:

A = 5000 × 12 = 60000
B = 8000 × 6  = 48000

Ratio = 60000 : 48000
      = 5 : 4

Total parts = 9.

B’s share:

4/9 × 2200
= ₹977.78

Therefore the question as written does not produce ₹1,000.

Corrected version

If total profit is ₹2,250:

B = 4/9 × 2250
  = ₹1,000

Answer for corrected question: B) ₹1,000

5. Ages

Five years ago, Rahul was twice as old as Amit. Their present ages add up to 40. Find Rahul’s present age.

A) 20 B) 23 C) 25 D) 30

Answer: B) 25?

Let’s solve carefully.

Let present ages be:

Rahul = R
Amit = A

Five years ago:

R - 5 = 2(A - 5)

Therefore:

R - 5 = 2A - 10
R = 2A - 5

Also:

R + A = 40

Substitute:

2A - 5 + A = 40
3A = 45
A = 15

R = 25

Correct Answer: C) 25 years

6. HCF

Find the HCF of 36 and 48.

A) 6 B) 8 C) 12 D) 16

Answer: C) 12

Explanation:

36 = 2² × 3²
48 = 2⁴ × 3

Common:

2² × 3 = 12

7. LCM

Find the LCM of 12, 18 and 24.

A) 36 B) 48 C) 72 D) 96

Answer: C) 72

Explanation:

12 = 2² × 3
18 = 2 × 3²
24 = 2³ × 3

Take highest powers:

LCM = 2³ × 3²
    = 8 × 9
    = 72

8. Pipes and Cisterns

A pipe fills a tank in 6 hours. Another pipe fills it in 12 hours. How long will they take together?

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

Answer: B) 4 hours

Explanation:

First = 1/6
Second = 1/12

Together = 2/12 + 1/12
         = 3/12
         = 1/4

Therefore:

Time = 4 hours

9. Boats and Streams

A boat travels downstream at 20 km/h and upstream at 12 km/h. Find the speed of the boat in still water.

A) 14 km/h B) 16 km/h C) 18 km/h D) 20 km/h

Answer: B) 16 km/h

Formula:

Still-water speed
= (Downstream + Upstream)/2

= (20 + 12)/2
= 16 km/h

10. Trains

A train 120 metres long travels at 54 km/h. How many seconds will it take to pass a pole?

A) 6 sec B) 8 sec C) 10 sec D) 12 sec

Answer: B) 8 seconds

Convert speed:

54 × 5/18 = 15 m/s

Therefore:

Time = Distance / Speed
     = 120/15
     = 8 seconds

11. Permutation

How many different arrangements can be made using the letters of the word CAT?

A) 3 B) 6 C) 9 D) 12

Answer: B) 6

3! = 3 × 2 × 1 = 6

12. Combination

How many ways can 2 people be selected from 5 people?

A) 5 B) 8 C) 10 D) 20

Answer: C) 10

⁵C₂ = 5!/(2!3!)

    = 10

13. Number Series

Find the next number:

2, 6, 12, 20, 30, ?

A) 36 B) 40 C) 42 D) 44

Answer: C) 42

Explanation:

Differences:

+4
+6
+8
+10

Next:

+12

Therefore:

30 + 12 = 42