Question : A number is increased by 20% and then decreased by 25%. If the resulting number is 360, what was the original number?
400
420
450
480
Correct Answer : 400
Question : A, B and C can complete a work in 12, 18 and 24 days respectively. They work together for 4 days, after which A leaves. In how many more days will B and C complete the remaining work?
4⅖ days
4⁸⁹⁄₁₀₁ days
4⁶⁄₇ days
5 days
Correct Answer : 4⁸⁹⁄₁₀₁ days
Question : A train 240 m long crosses a platform 360 m long in 30 seconds. If the same train crosses a man running at 6 m/s in the opposite direction in 12 seconds, what is the speed of the train?
24 m/s
26 m/s
28 m/s
30 m/s
Correct Answer : 24 m/s
Question : A sum of ₹8,000 amounts to ₹9,680 in 2 years when compounded annually. What is the annual rate of interest?
8%
9%
10%
12%
Correct Answer : 10%
Question : The average of 15 numbers is 42. The average of the first 8 numbers is 39 and that of the last 8 numbers is 46. If the 8th number is excluded from both groups, what is the average of the remaining 14 numbers?
41
42
43
44
Correct Answer : 42
Question : A mixture contains milk and water in the ratio 7:3. If 20 litres of the mixture are removed and replaced with water, the ratio becomes 7:5. What was the original quantity of the mixture?
120 litres
140 litres
160 litres
180 litres
Correct Answer : 140 litres
Question : A shopkeeper marks an article 40% above its cost price and allows two successive discounts of 10% and 5%. If the selling price is ₹5,985, what is the cost price?
₹4,750
₹5,000
₹5,250
₹5,500
Correct Answer : ₹5,000
Question : The radius of a cylindrical vessel is increased by 20% while its height is decreased by 10%. By what percentage does its volume change?
19.6% increase
24% increase
29.6% increase
32% increase
Correct Answer : 29.6% increase
Question : A man travels from A to B at 40 km/h and returns from B to A at 60 km/h. If the total time taken is 5 hours, what is the distance between A and B?
100 km
110 km
120 km
125 km
Correct Answer : 120 km
Question : The HCF and LCM of two numbers are 12 and 420 respectively. If one number is 84, what is the other number?
48
60
72
84
Correct Answer : 60
Question : A person spends 75% of his income. His income increases by 20% and his expenditure increases by 10%. By what percentage does his saving increase?
40%
45%
50%
55%
Correct Answer : 50%
Question : The area of a triangle is 216 cm² and its sides are in the ratio 3:4:5. What is the length of the largest side?
12 cm
15 cm
18 cm
20 cm
Correct Answer : 18 cm
Question : A boat travels 36 km downstream in 3 hours and the same distance upstream in 6 hours. What is the speed of the boat in still water?
8 km/h
9 km/h
10 km/h
12 km/h
Correct Answer : 9 km/h
Question : The present ages of A and B are in the ratio 5:7. After 6 years, their ages will be in the ratio 3:4. What is B's present age?
36 years
40 years
42 years
48 years
Correct Answer : 42 years
Question : A sum is divided among A, B and C in the ratio 5:7:9. If C receives ₹1,440 more than A, what is the total sum?
₹6,720
₹7,140
₹8,400
₹9,240
Correct Answer : ₹6,720
Question : A rectangular field has perimeter 280 m. If its length is increased by 10% and breadth is decreased by 10%, the area decreases by 24 m². What is the original area?
4,800 m²
4,896 m²
4,900 m²
5,040 m²
Correct Answer : 4,896 m²
Question : A can do a work in 15 days and B can do it in 20 days. They work on alternate days, beginning with A. In how many days will the work be completed?
16⅔ days
17 days
17⅓ days
18 days
Correct Answer : 17⅓ days
Question : The difference between compound interest and simple interest on a sum at 10% per annum for 3 years is ₹248. What is the principal?
₹7,500
₹8,000
₹8,500
₹9,000
Correct Answer : ₹8,000
Question : The diagonal of a rectangular field is 25 m and its length exceeds its breadth by 5 m. What is the area of the field?
250 m²
300 m²
350 m²
375 m²
Correct Answer : 300 m²
Question : A vessel contains 80 litres of a milk-water mixture in the ratio 3:1. How much water must be added so that the ratio of milk to water becomes 3:2?
20 litres
24 litres
30 litres
40 litres
Correct Answer : 20 litres
Question : A trader sells an article at a profit of 25%. Had he purchased it for 20% less and sold it for ₹60 less, his profit would have been 50%. What was the original cost price?
₹400
₹500
₹600
₹750
Correct Answer : ₹600
Question : The mean of 7 consecutive odd integers is 35. What is the product of the smallest and largest integers?
961
1,023
1,089
1,155
Correct Answer : 1,089
Question : A cistern can be filled by pipes A and B in 20 minutes and 30 minutes respectively. Pipe C can empty it in 60 minutes. If all three pipes are opened simultaneously, how long will it take to fill the cistern?
12 minutes
15 minutes
18 minutes
20 minutes
Correct Answer : 15 minutes
Question : If x + 1/x = 4, where x > 0, find x^3 + 1/x^3.
52
56
58
60
Correct Answer : 52
Question : A number is first increased by 25% and then decreased by 20%. If the final value is 600, what was the original number?
580
600
620
640
Correct Answer : 600
Question : A and B can complete a work in 18 days and 24 days respectively. They work together for 6 days, after which A leaves. In how many more days will B complete the remaining work?
8 days
9 days
10 days
12 days
Correct Answer : 10 days
Question : A train running at 72 km/h crosses a platform in 25 seconds and a man standing on the platform in 10 seconds. What is the length of the platform?
250 m
300 m
350 m
400 m
Correct Answer : 300 m
Question : The compound interest on a certain sum at 10% per annum for 2 years is ₹1,260. What is the simple interest on the same sum at the same rate for 3 years?
₹1,800
₹1,890
₹2,000
₹2,100
Correct Answer : ₹1,800
Question : The average of 12 numbers is 35. If two numbers, 42 and 48, are replaced by 30 and 36 respectively, what will be the new average?
32
33
34
35
Correct Answer : 33
Question : A mixture contains milk and water in the ratio 5:2. If 14 litres of water are added to it, the ratio becomes 5:3. What was the original quantity of the mixture?
84 litres
98 litres
112 litres
126 litres
Correct Answer : 98 litres
Question : An article is marked 50% above its cost price. After allowing a discount of 20%, the shopkeeper earns a profit of ₹120. What is the cost price?
₹1,000
₹1,200
₹1,500
₹1,800
Correct Answer : ₹1,200
Question : If the roots of 3x^2 - 11x + 6 = 0 are alpha and beta, find alpha^2 + beta^2.
49/9
61/9
73/9
85/9
Correct Answer : 73/9
Question : The radius of a circle is increased by 10%. By what percentage does its area increase?
10%
20%
21%
22%
Correct Answer : 21%
Question : A man covers 240 km partly by car at 60 km/h and partly by train at 80 km/h. If the total time taken is 3.5 hours, what distance did he travel by car?
80 km
100 km
120 km
140 km
Correct Answer : 120 km
Question : The HCF of two numbers is 16 and their LCM is 240. If one number is 48, what is the other number?
60
72
80
96
Correct Answer : 80
Question : A person's expenditure is 80% of his income. If his income increases by 25% and expenditure increases by 20%, by what percentage does his saving increase?
35%
40%
45%
50%
Correct Answer : 45%
Question : If tan theta + cot theta = 10, find tan^2 theta + cot^2 theta.
96
98
100
102
Correct Answer : 98
Question : The sides of a triangle are in the ratio 5:12:13 and its perimeter is 60 cm. What is its area?
120 cm^2
150 cm^2
180 cm^2
240 cm^2
Correct Answer : 120 cm^2
Question : A boat covers 48 km downstream in 4 hours and the same distance upstream in 6 hours. What is the speed of the boat in still water?
8 km/h
9 km/h
10 km/h
12 km/h
Correct Answer : 10 km/h
Question : The present ages of A and B are in the ratio 4:5. After 8 years, their ages will be in the ratio 5:6. What is A's present age?
24 years
28 years
32 years
36 years
Correct Answer : 32 years
Question : A sum of ₹7,200 is divided among A, B and C in the ratio 2:3:4. What is the difference between C's share and A's share?
₹1,200
₹1,400
₹1,600
₹1,800
Correct Answer : ₹1,600
Question : If a:b = 4:5 and b:c = 10:7, then a:c is:
5:7
7:8
8:7
9:10
Correct Answer : 8:7
Question : A rectangular garden is 60 m long and 40 m broad. A path of uniform width is constructed inside it along all four sides. If the area of the remaining portion is 1,584 m^2, what is the width of the path?
2 m
3 m
4 m
5 m
Correct Answer : 3 m
Question : If x - 1/x = 3, where x > 0, find x^2 + 1/x^2.
7
9
11
13
Correct Answer : 11
Question : A sum of money becomes ₹13,310 in 3 years at 10% per annum compound interest. What was the principal?
₹9,000
₹10,000
₹11,000
₹12,000
Correct Answer : ₹10,000
Question : A can complete a work in 16 days and B in 24 days. They work together for 4 days, after which A leaves. How many more days will B take to complete the remaining work?
12 days
13 days
14 days
15 days
Correct Answer : 14 days
Question : A train 180 m long crosses another train 220 m long running in the opposite direction at 54 km/h in 16 seconds. What is the speed of the second train?
72 km/h
81 km/h
90 km/h
99 km/h
Correct Answer : 36 km/h
Question : An article is sold at a profit of 20%. If both its cost price and selling price are increased by ₹100, the profit percentage becomes 16 2/3%. What was the original cost price?
₹400
₹500
₹600
₹750
Correct Answer : ₹500
Question : The average of 8 numbers is 45. If one number is excluded, the average becomes 42. What is the excluded number?
63
66
69
72
Correct Answer : 66
Question : A vessel contains 90 litres of a mixture of milk and water in the ratio 7:2. How much mixture should be removed and replaced with water so that the ratio becomes 7:3?
10 litres
12 litres
15 litres
18 litres
Correct Answer : 10 litres
Question : A shopkeeper allows two successive discounts of 15% and 10% on an article marked at ₹4,000. If he still earns a profit of 20%, what is the cost price?
₹2,450
₹2,550
₹2,650
₹2,750
Correct Answer : ₹2,550
Question : If the roots of 2x^2 - 9x + 4 = 0 are alpha and beta, find 1/alpha + 1/beta.
2
9/4
4/9
9/2
Correct Answer : 9/4
Question : The length of a rectangle is increased by 20% and its breadth is decreased by 20%. What is the percentage change in its area?
4% increase
4% decrease
8% decrease
No change
Correct Answer : 4% decrease
Question : A man travels 180 km at a certain speed. If his speed were 15 km/h more, he would take 1 hour less. What is his original speed?
30 km/h
45 km/h
50 km/h
60 km/h
Correct Answer : 45 km/h
Question : The product of two numbers is 4320 and their HCF is 12. If one number is 144, what is the other number?
24
30
36
48
Correct Answer : 30
Question : A man's income is 25% more than his expenditure. If his income increases by 20% and expenditure increases by 10%, his savings increase by ₹1,500. What was his original expenditure?
₹4,000
₹4,500
₹5,000
₹5,500
Correct Answer : ₹5,000
Question : If sec theta + tan theta = 3, find sec theta - tan theta.
1/9
1/3
2/3
3
Correct Answer : 1/3
Question : The area of a rhombus is 240 cm^2 and one of its diagonals is 16 cm. Find the length of its other diagonal.
24 cm
28 cm
30 cm
32 cm
Correct Answer : 30 cm
Question : A boat travels 30 km upstream and 44 km downstream in a total of 8 hours. If the speed of the stream is 2 km/h, what is the speed of the boat in still water?
8 km/h
10 km/h
12 km/h
14 km/h
Correct Answer : 10 km/h
Question : The present ages of A and B are in the ratio 7:9. Five years ago, their ages were in the ratio 3:4. What is B's present age?
36 years
40 years
45 years
54 years
Correct Answer : 45 years
Question : A sum is divided among A, B and C such that A receives 2/3 of B and B receives 3/4 of C. If C receives ₹1,800, what is the total amount distributed?
₹3,800
₹4,000
₹4,200
₹4,500
Correct Answer : ₹4,200
Question : If a:b = 2:3, b:c = 4:5 and c:d = 10:7, then a:d is:
16:21
8:7
16:35
32:21
Correct Answer : 16:21
Question : A cylindrical tank has radius 7 m and height 10 m. If water is filled at the rate of 22 m^3 per minute, how long will it take to fill the tank? Use pi = 22/7.
10 minutes
12 minutes
14 minutes
16 minutes
Correct Answer : 14 minutes
Question : If x + 1/x = 6, where x > 0, find x^4 + 1/x^4.
1150
1166
1180
1190
Correct Answer : 1180
Question : A number is increased by 30% and then decreased by 30%. If the final number is 637, what was the original number?
625
650
675
700
Correct Answer : 650
Question : A can complete a work in 20 days, B in 30 days and C in 60 days. They start together, but A leaves after 5 days and B leaves 5 days before the work is completed. In how many days is the entire work completed?
12 days
15 days
18 days
20 days
Correct Answer : 15 days
Question : Two trains of lengths 240 m and 160 m are moving in the same direction at 72 km/h and 54 km/h respectively. How much time will the faster train take to completely overtake the slower train?
60 seconds
70 seconds
80 seconds
90 seconds
Correct Answer : 80 seconds
Question : A sum amounts to ₹7,986 in 3 years at 10% per annum compound interest. What is the principal?
₹5,500
₹6,000
₹6,500
₹7,000
Correct Answer : ₹6,000
Question : The average of 20 numbers is 48. If the average of the first 12 numbers is 42 and that of the last 9 numbers is 56, find the 12th number.
48
50
54
60
Correct Answer : 48
Question : A 72-litre mixture contains milk and water in the ratio 5:3. How many litres of water must be added to make the ratio 5:4?
6 litres
8 litres
9 litres
12 litres
Correct Answer : 9 litres
Question : An article is marked 60% above its cost price. After successive discounts of 20% and 10%, the shopkeeper earns a profit of ₹152. What is the cost price?
₹1,200
₹1,400
₹1,600
₹1,800
Correct Answer : ₹1,600
Question : If the roots of 4x^2 - 12x + 5 = 0 are alpha and beta, find alpha^3 + beta^3.
27/2
39/2
45/2
51/2
Correct Answer : 39/2
Question : The side of a square is increased by 15%. By what percentage does its area increase?
30%
32.25%
34.5%
35%
Correct Answer : 32.25%
Question : A man covers a certain distance at 48 km/h. Had he travelled at 60 km/h, he would have taken 1 hour less. Find the distance.
180 km
200 km
220 km
240 km
Correct Answer : 240 km
Question : The HCF of two numbers is 18 and their LCM is 540. If one number is 90, find the other number.
96
108
120
126
Correct Answer : 108
Question : A person's salary is increased by 20% and then decreased by 10%. If his final salary is ₹54,000, what was his original salary?
₹45,000
₹48,000
₹50,000
₹52,000
Correct Answer : ₹50,000
Question : If sin theta + cos theta = 5/4, find sin 2theta.
7/16
9/16
15/16
25/16
Correct Answer : 9/16
Question : The perimeter of a right-angled triangle is 60 cm and its hypotenuse is 25 cm. Find its area.
120 cm^2
150 cm^2
180 cm^2
200 cm^2
Correct Answer : 150 cm^2
Question : A boat takes 5 hours to travel 40 km downstream and 8 hours to travel 48 km upstream. Find the speed of the boat in still water.
8 km/h
9 km/h
10 km/h
12 km/h
Correct Answer : 10 km/h
Question : The present ages of A and B are in the ratio 6:7. After 8 years, their ages will be in the ratio 7:8. What is the present age of A?
42 years
44 years
48 years
54 years
Correct Answer : 48 years
Question : A sum of ₹9,600 is divided among A, B and C in the ratio 3:5:8. If B gives 20% of his share to A, what is A's new share?
₹2,040
₹2,160
₹2,240
₹2,400
Correct Answer : ₹2,240
Question : If a:b = 5:6, b:c = 8:9 and c:d = 12:11, then a:d is:
40:33
20:11
30:11
40:27
Correct Answer : 40:33
Question : A solid sphere of radius 6 cm is melted and recast into small spheres of radius 2 cm each. How many small spheres are formed?
9
18
27
36
Correct Answer : 27