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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