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1. A train travels 18 km/hr. How many meters will it travel in 12 minutes.
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?
3. If the height of a cylinder is 7 cm and the radius is 3 cm, then the surface area of the cylinder is?
4. Jack purchases a calculator for $ 350 and sells for $420.Then the percentage of profit is
5. The average of 6 numbers is 8. What is the 7th number, so that its average will become 10?
6. Find the number of prime factors of 6 ¹⁰ × 7
¹⁷ × 55 ²⁷
7. If 12 man can do a piece of work in 36 days. Within how many days 18 men can do the same work?
8. If two dice are rolled, what is the probability of getting same number on both the dies?
9.The sum of reciprocal of (3/2) and the reciprocal of 3 is
10. It is 9 hours now in a 12 hour clock. What will be the time after 18 hours?
Explanation for question No 1 |
Distance traveled by the train in one hour = 18 km
From this we need to find the distance in meters . 1000 m = 1 km 1 hour = 60 minutes Distance traveled by the train in 60 minutes = 18000 m Distance traveled by the train in 1 minute = 18000/60 Distance traveled by the train in 1 minute = 300 m Distance traveled by the train in 12 minutes = 300 x 12 = 3600 m So the correct answer for this question is 3600 m option A |
Explanation for question No 2 |
The average age of 30 kids is 9 years
Let x be the age of teacher 9 = sum of ages of 30 kids/30 Sum of ages of 30 kids = 30 x 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 x 31 = 270 + x 310 = 270 + x x = 310 - 270 x = 40 Therefore age of teacher 40 years So the correct answer for this question is 40 years option C |
Explanation for question No 3 |
Height of the cylinder = 7 cm
Radius of the cylinder = 3 cm Curved surface area of cylinder = 2 Π r h = 2 x (22/7) x 7 x 3 = 2 x 22 x 3 = 44 x 3 = 132 cm ^{2} So the correct answer for this question is 132 cm ^{2} option C |
Explanation for question No 4 |
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) x 100 = (70/350) x 100 = (1/5) x 100 = 20 % So the correct answer for this question is 20 % ^{2} option B |
Explanation for question No 5 |
The average of 6 numbers is 8
Average = Sum of numbers/Number of terms 8 = Sum of numbers/6 6x8 = Sum of 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 correct answer for this question is 22 option B |
Explanation for question No 6 |
= 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 correct answer for this question is 91 option B |
Explanation for question No 7 |
This situation comes under the topic inverse proportion Let X be the number of days taken by 18 men to complete the same work. 12 x 36 = 18 x X 12 x 36 /18 = X 24 = X Therefore the number of days taken by 18 men to complete the same work = 24 days So the correct answer for this question is 24 days option B |
Explanation for question No 8 |
Sample space S = {{1,1)(1,2)(1,3)(1,4)(1,5) (1,6)
= {2,1)(2,2)(2,3)(2,4)(2,5) (2,6) = {3,1)(3,2)(3,3)(3,4)(3,5) (3,6) = {4,1)(4,2)(4,3)(4,4)(4,5) (4,6) = {5,1)(5,2)(5,3)(5,4)(5,5) (5,6) = {6,1)(6,2)(6,3)(6,4)(6,5) (6,6)} n(S) = 36 Let A be the event of getting the same number on both the dies A = {(1,1)(2,2)(3,3)(4,4)(5,5)(6,6)} n(A) = 6 probability of getting the same number on both dies = n(A)/n(S) = 6/36 = 1/6 So the correct answer for this question is 1/6 option C |
Explanation for question No 9 |
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 option A |
Explanation for question No 10 |
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. Step1: Add 18 to 9 Step2: Divide the result by the divisor 12 Step3: Take the remainder 9 + 18 = 27 When 27 is divided by 12, the remainder is 3 Hence, the time after 18 hours will be 3 hours. So the correct answer for this question is 3 hours option C |