1. The average of first five multiples of 3 is:
Multiples of 3 are 3, 6, 9, 12, 15. Sum = 45. Average = 45/5 = 9.
2. If 20% of a number is 120, then 120% of that number will be:
If 20% = 120, then 1% = 6. Therefore, 120% = 120 * 6 = 720.
3. A train 100 meters long is running at the speed of 30 km/hr. The time taken by it to pass a man standing near the railway line is:
Speed = 30 * (5/18) = 25/3 m/s. Time = Distance / Speed = 100 / (25/3) = 12 seconds.
4. What is the value of x in the equation 3x + 7 = 22?
3x = 22 - 7 => 3x = 15 => x = 5.
5. The ratio of 45 to 75 in its simplest form is:
Divide both by their HCF (15). 45/15 = 3 and 75/15 = 5. So, 3:5.
6. A person bought a shirt for Rs. 500 and sold it for Rs. 600. What is the profit percentage?
Profit = 600 - 500 = 100. Profit % = (100/500) * 100 = 20%.
7. If the radius of a circle is doubled, its area becomes:
Area = Ï€r². If r becomes 2r, Area = Ï€(2r)² = 4Ï€r². Thus, it becomes 4 times.
8. Find the HCF of 12, 18, and 24.
Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Highest Common Factor is 6.
9. A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is:
Let son's age be x. Man's age = x + 24. In 2 years: (x+24+2) = 2(x+2) => x + 26 = 2x + 4 => x = 22.
10. What is the sum of the first 50 natural numbers?
Formula: n(n+1)/2. So, 50(51)/2 = 25 * 51 = 1275.
11. If 5 men can build a wall in 12 days, how many days will it take 10 men to build the same wall?
Inverse proportion: M1D1 = M2D2. 5 * 12 = 10 * D2 => 60 = 10 * D2 => D2 = 6.
12. The decimal equivalent of 3/8 is:
3 divided by 8 = 0.375.
13. A car travels 180 km in 3 hours. What is its speed in meters per second?
Speed = 180/3 = 60 km/hr. In m/s: 60 * (5/18) = 300/18 = 16.67 m/s.
14. What is the LCM of 15, 20, and 30?
Multiples of 30: 30, 60... 60 is divisible by both 15 and 20. So, LCM is 60.
15. A rectangular field has a length of 20m and a width of 15m. What is its perimeter?
Perimeter = 2(Length + Width) = 2(20 + 15) = 2(35) = 70m.
16. If the price of a book is reduced by 25%, it becomes Rs. 75. What was the original price?
75% of Original Price = 75. So, Original Price = 75 / 0.75 = 100.
17. Solve: (0.5 * 0.5) + (0.5 / 0.5) = ?
(0.5 * 0.5) = 0.25. (0.5 / 0.5) = 1. Sum = 1.25.
18. The sum of three consecutive integers is 72. The largest integer is:
x + (x+1) + (x+2) = 72 => 3x + 3 = 72 => 3x = 69 => x = 23. Largest is x+2 = 25.
19. What is 15% of 200?
(15/100) * 200 = 15 * 2 = 30.
20. A sum of money doubles itself in 10 years at simple interest. What is the rate of interest?
Interest = Principal. I = PRT/100 => P = (P * R * 10) / 100 => 1 = R/10 => R = 10%.
21. If the side of a square is increased by 50%, its area increases by:
New side = 1.5s. New area = (1.5s)² = 2.25s². Increase = 2.25 - 1 = 1.25 or 125%.
22. Which of the following is a prime number?
97 has no factors other than 1 and itself. (33=3*11, 81=9*9, 91=7*13).
23. A clock strikes once at 1 o'clock, twice at 2 o'clock, and so on. How many times will it strike in 12 hours?
Sum of 1 to 12 = n(n+1)/2 = 12(13)/2 = 6 * 13 = 78.
24. If a:b = 2:3 and b:c = 4:5, then a:c is:
a/c = (a/b) * (b/c) = (2/3) * (4/5) = 8/15.
25. The angle of a triangle are in ratio 2:3:4. The largest angle is:
2x + 3x + 4x = 180 => 9x = 180 => x = 20. Largest angle = 4 * 20 = 80°.
26. What is the value of (2^3)^2?
(2^3)^2 = 2^(3*2) = 2^6 = 64.
27. A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price?
Loss = 15% of 1400 = 210. SP = 1400 - 210 = 1190.
28. The average of 7 numbers is 5. If one number is removed, the average becomes 4. What was the removed number?
Total of 7 numbers = 7 * 5 = 35. Total of 6 numbers = 6 * 4 = 24. Removed number = 35 - 24 = 11.
29. How many minutes are there in 2/5 of an hour?
(2/5) * 60 minutes = 2 * 12 = 24 minutes.
30. If x = 2 and y = 3, find the value of x^2 + 2xy + y^2.
This is (x+y)^2. (2+3)^2 = 5^2 = 25.
31. What is the probability of getting an even number when a fair die is rolled?
Even numbers on a die: 2, 4, 6 (3 outcomes). Total outcomes: 6. Probability = 3/6 = 1/2.
32. 0.003 * 0.02 = ?
3 * 2 = 6. Total decimal places = 3 + 2 = 5. So, 0.00006.
33. A container has 40 liters of milk. 4 liters are replaced by water. What is the percentage of water in the container?
(4/40) * 100 = 10%.
34. The square root of 0.0016 is:
√(16/10000) = 4/100 = 0.04.
35. If 3 men or 6 women can do a piece of work in 16 days, in how many days can 12 men and 8 women do the same work?
3M = 6W => 1M = 2W. 12M + 8W = 24W + 8W = 32W. If 6W do it in 16 days, 32W do it in (6 * 16)/32 = 3 days.
36. Find the missing number in the series: 2, 6, 12, 20, 30, ?
Differences are 4, 6, 8, 10. Next difference is 12. 30 + 12 = 42.
37. A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?
CP of 6 = 1. Gain = 20%. SP of 6 = 1.2. If Rs. 1.2 buys 6, then Rs. 1 buys 6/1.2 = 5.
38. The difference between the largest and smallest 3-digit numbers is:
Largest 3-digit = 999. Smallest 3-digit = 100. Difference = 899.
39. If 1/x = 0.5, then x = ?
1/x = 1/2 => x = 2.
40. What is the area of a triangle with base 10cm and height 8cm?
Area = 1/2 * base * height = 1/2 * 10 * 8 = 40.
41. A person covers 1/3 of his journey at 20 km/h and the rest at 40 km/h. If total distance is 60 km, total time taken is:
1/3 of 60 = 20 km (at 20 km/h = 1 hr). Rest = 40 km (at 40 km/h = 1 hr). Total = 2 hours.
42. If the sum of two numbers is 10 and their difference is 2, the numbers are:
x+y=10, x-y=2. Adding: 2x=12 => x=6. Then y=4.
43. What is the value of 10% of 20% of 500?
20% of 500 = 100. 10% of 100 = 10.
44. How many degrees are in a circle?
A full rotation in a circle is exactly 360 degrees.
45. If 12x = 144, then x/2 = ?
12x = 144 => x = 12. x/2 = 6.
46. A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 40 marks. The maximum marks are:
Passing marks = 125 + 40 = 165. 33% of X = 165 => X = (165 * 100) / 33 = 500.
47. The smallest prime number is:
2 is the smallest prime number and the only even prime number.
48. Simplify: 10 + 10 * 10 / 10
Using BODMAS: 10 * 10 / 10 = 100 / 10 = 10. Then 10 + 10 = 20.
49. What is the sum of angles in a quadrilateral?
Any 4-sided polygon (quadrilateral) has interior angles that sum to 360 degrees.
50. A man walks 3 km North, then 4 km East. How far is he from his starting point?
Using Pythagoras theorem: √(3² + 4²) = √(9 + 16) = √25 = 5 km.
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