Problem 1 :

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

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

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

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

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 cm2

So, the answer is 132 cm2

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%

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

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

Problem 6 :

Find the number of prime factors of 610 × 717 × 5527

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

=  6 10 × 7 17 × 5527

=  (2 x 3) 10 × 7 17 × (5 x 11)27

=  210 x 310 × 7 17 × 527 x 1127

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

=  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

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

The distance covered in both cases are same.

Time  =  Distance / Speed

T1  =  Distance / 25

T2  =  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

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

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 :

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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