**Problem 1 :**

A train travels 18 km/hr. How many meters will it travel in 12 minutes.

(A) 3600 (B) 4200 (C) 5100

**Answer :**

Speed of the train = 18 km/hr

Speed of train in m/sec = 18 ⋅ (5/18)

= 5 m/sec

12 minutes = 12 (60)

= 720 seconds

Distance covered in 720 seconds = time taken (Speed)

= 720(5)

= 3600 m

So, the distance covered is 3600 m.

**Problem 2 :**

The average age of 30 kids is 9 years. If the age of teacher is included, the average age becomes 10 years. What is the age of teacher?

(A) 26 (B) 58 (C) 40

**Answer :**

The average age of 30 kids is 9 years

Let x be the age of teacher

Average age = Sum of ages/Total number of ages

9 = sum of ages of 30 kids/30

Sum of ages of 30 kids = 30 ⋅ 9

= 270

Sum of ages of kids and teacher = 270 + x

Average age of kids and teacher = (270 + x)/31

10 = (270 + x)/31

10 (31) = 270 + x

310 = 270 + x

x = 310 - 270

x = 40

So, the required age is 40 years.

**Problem 3 :**

If the height of a cylinder is 7 cm and the radius is 3 cm, then the surface area of the cylinder is ?

(A) 150 (B) 132 (B) 143

**Answer :**

Height of the cylinder = 7 cm

Radius of the cylinder = 3 cm

Curved surface area of cylinder = 2 Π r h

= 2 ⋅ (22/7) ⋅ 7 ⋅ 3

= 2 ⋅ 22 ⋅ 3

= 44 ⋅ 3

= 132 cm^{2}

So, the answer is 132 cm^{2}

**Problem 4 :**

Jack purchases a calculator for $350 and sells for $420.Then the percentage of profit is

(A) 10% (B) 20% (C) 50%

**Solution :**

Cost price of a calculator = $350

Selling price of the calculator = $420

Profit = Selling price - Cost price

= 420 - 350

= 70

profit percentage = (profit/cost price) ⋅ 100

= (70/350) ⋅ 100

= (1/5) ⋅ 100

= 20%

So, the answer is 20%

**Problem 5 :**

The average of 6 numbers is 8. What is the 7th number, so that its average will become 10 ?

(A) 15 (B) 22 (C) 12

**Answer :**

The average of 6 numbers is 8

Average = Sum of numbers/Number of terms

8 = Sum of 6 numbers/6

6(8) = Sum of 6 numbers

Sum of 6 numbers = 48

If 7th term is added with this total, its average will become 10

Let x be the 7th term

(48 + x)/7 = 10

48 + x = 70

x = 70 - 48

x = 22

So, the answer is 22.

**Problem 6 :**

Find the number of prime factors of 6^{10} × 7^{17} × 55^{27}

(A) 100 (B) 91 (C) 64

**Answer :**

= 6 ^{10} × 7 ^{17} × 55^{27}

= (2 x 3) ^{10} × 7 ^{17} × (5 x 11)^{27}

= 2^{10} x 3^{10} × 7 ^{17} × 5^{27} x 11^{27}

Total number of prime factors = 10 + 10 + 17 + 27 + 27

= 91

So, the answer is 91.

**Problem 7 :**

If 12 man can do a piece of work in 36 days. Within how many days 18 men can do the same work ?

(A) 27 (B) 24 (C) 22

**Answer :**

Work done = Number of days ⋅ number of men

= 36 ⋅ 12

= 432 ---(1)

Work done = Number of days ⋅ 18 ----(2)

432 = Number of days ⋅ 18

Number of days = 432 / 18

Number of days = 24

So, the required number of days is 24.

**Problem 8 :**

A man traveled from the village to the post office at the rate of 25 kmph and walked back at the rate of 4 kmph. If the entire journey took 5 hours 48 minutes, determine the distance of the post office from that village.

(A) 20 (B) 13 (C) 20

**Answer :**

The distance covered in both cases are same.

Time = Distance / Speed

T_{1} = Distance / 25

T_{2} = Distance / 4

5 hours 48 minutes = 5 4/5 hours

29/5 = (Distance / 25) + (Distance / 4)

29/5 = (4 Distance + 25 Distance) / 100

(29/5) ⋅ (100/29) = Distance

Distance = 20 km

**Problem 9 :**

The sum of reciprocal of (3/2) and the reciprocal of 3 is

(A) 2 (B) 1 (C) 5

**Answer :**

Reciprocal of 3/2 is 2/3

reciprocal of 3 is 1/3

Sum of these two numbers = (2/3) + (1/3)

= (2 + 1)/3

= 3/3

= 1

So, the correct answer for this question is 1

**Problem 10 :**

It is 9 hours now in a 12 hour clock. What will be the time after 18 hours ?

(A) 2 (B) 4 (C) 3

**Answer :**

Now, the time is 9 hours. We want to know the time after 18 hours.

To get answer for our question, we have to do the following steps.

**Step 1 :**

Add 18 to 9

**Step 2 :**

Divide the result by the divisor 12

**Step 3 :**

Take the remainder

9 + 18 = 27

When 27 is divided by 12, the remainder is 3

The time after 18 hours will be 3 hours. So the answer is 3 hours.

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