1. A 280 metre long train moving with an average speed of 108 km/h crosses a platform in 12 seconds. A man crosses the same platform in 10 seconds. What is the speed of the man?
(a) 5 m/s
(b) 8 m/s
(c) 12 m/s
(d) Cannot be determined
2. The compound interest on a certain sum of money for 20 years at 10% per annum is Rs. 420. Find the simple interest at the same rate and for the same time.
(a) Rs. 400
(b) Rs. 500
(c) Rs. 450
(d) Rs. 550
3. A jar contains a mixture of 2 liquids A and B in the ratio 4:1. When 10 litres of the mixture is taken out and 10 litres of liquid B is poured into the jar, the ratio becomes 2:3. How many litres of the liquid A was contained in the jar?
(a) 17 litres
(b) 16 litres
(c) 18 litres
(d) 15 litres
4. Two men X and Y working separately can mow the field in 8 and 12 hrs respectively. If they work in stretches of one hour alternately, X beginning at 9a.m., when will the mowing be finished?
(a) 6p.m
(b) 15/2pm
(c) 7p.m
(d) 13/2pm
5. In what time would a cistern be filled by three pipes whose diameters are 1cm, 11/3cm, 2cm, running together, when the largest alone will fill it in 61minutes, the amount of water flowing in by each pipe being proportional to the square of its diameter?
(a) 36 minutes
(b) 37minutes
(c) 38 minutes
(d) 35minutes
6. Work done by A in one day is half of the work done by B in one day. Work done by B is half of the work done by C in one day. If C alone can complete the work in 7 days, in how many days will A, B and C together will complete the work?
(a) 28
(b) 14
(c) 4
(d) 21
7. Three times a number is 20% more than twice another number when increased by 105. If twice the first number increased by 36 is 20% less than three times of the second number, then what is the first number?
(a) 150
(b) 162
(c) 180
(d) None of these
8.The simple interest accrued on an amount of Rs. 25,000 at the end of three years is Rs. 7,500. What would be the compound interest accrued on the same amount at the same rate in the same period?
(a) Rs. 7,750
(b) Rs. 8,275
(c) Rs. 8,500
(d) Rs. 8,250
9. Aman won a competition and so he got some prize money. He gave Rs. 2000 less than the half of prize money to his son and Rs. 1000 more than the two third of the remaining to his daughter. If both they got same amount, what is the prize money Aman got?
(a) 20000
(b) 25000
(c) 26000
(d) None of these
10. The stream of a boat when travelling downstream is 32 km/hr, whereas when travelling upstream it is 28km/hr. what is the speed of boat in still water?
(a) 27km/hr
(b) 30km/hr
(c) 31km/hr
(d) Cannot be determined
Answers with solutions :
1.(b)
Speed of train = 108km/hr= (108*5/18) m/sec
If the length of the platform be x meters, then
x+280/12 =30
x+ 280 = 360
x=(360-280)=80
then 80/10 = 8 m/s
2.(a)
3.(b)
4.(d)
5.(a) In one minute the pipe of 2cm diameter fills 1/61 of the cistern.
In one minute the pipe of 1cm diameter fills 1/61* 1/4 of the cistern
In one minute the pipe of 11/3 cm diameter fills 1/61* 4/9 of the cistern
In one minute (1/61+1/(61*4)+4/(61*9))=1/36 of the cistern is filled.
The whole cistern is filled in 36 minutes
6.(c)Work done by C in one day = 1/7
Work done by B in one day = 1/2*1/7=1/14
Work done by A in one day = 1/2*1/14=1/28
Work done by A, B and C in one day = 7/28=1/4
7.(b) Let the two numbers be x and y.
3x = 1.2( 2y +105)
3x = 2.4y +126 ………………..(1)
2x +36 = 0.8(3y)
2x +36 =2.4y ………………..(2)
x = 162
8.(b)
9.(c) Assume Aman got x rupees.
He gave x/2 - 2000 to his son.
And 2/3 ( x/2 + 2000 ) + 1000 to his daughter.
x/2 - 2000 = x/3 + 7000/3
x = 26000
10.(b)
Speed of boat in still water= 1/2(32+28)=60/2=30km/hr
(a) 5 m/s
(b) 8 m/s
(c) 12 m/s
(d) Cannot be determined
2. The compound interest on a certain sum of money for 20 years at 10% per annum is Rs. 420. Find the simple interest at the same rate and for the same time.
(a) Rs. 400
(b) Rs. 500
(c) Rs. 450
(d) Rs. 550
3. A jar contains a mixture of 2 liquids A and B in the ratio 4:1. When 10 litres of the mixture is taken out and 10 litres of liquid B is poured into the jar, the ratio becomes 2:3. How many litres of the liquid A was contained in the jar?
(a) 17 litres
(b) 16 litres
(c) 18 litres
(d) 15 litres
4. Two men X and Y working separately can mow the field in 8 and 12 hrs respectively. If they work in stretches of one hour alternately, X beginning at 9a.m., when will the mowing be finished?
(a) 6p.m
(b) 15/2pm
(c) 7p.m
(d) 13/2pm
5. In what time would a cistern be filled by three pipes whose diameters are 1cm, 11/3cm, 2cm, running together, when the largest alone will fill it in 61minutes, the amount of water flowing in by each pipe being proportional to the square of its diameter?
(a) 36 minutes
(b) 37minutes
(c) 38 minutes
(d) 35minutes
6. Work done by A in one day is half of the work done by B in one day. Work done by B is half of the work done by C in one day. If C alone can complete the work in 7 days, in how many days will A, B and C together will complete the work?
(a) 28
(b) 14
(c) 4
(d) 21
7. Three times a number is 20% more than twice another number when increased by 105. If twice the first number increased by 36 is 20% less than three times of the second number, then what is the first number?
(a) 150
(b) 162
(c) 180
(d) None of these
8.The simple interest accrued on an amount of Rs. 25,000 at the end of three years is Rs. 7,500. What would be the compound interest accrued on the same amount at the same rate in the same period?
(a) Rs. 7,750
(b) Rs. 8,275
(c) Rs. 8,500
(d) Rs. 8,250
9. Aman won a competition and so he got some prize money. He gave Rs. 2000 less than the half of prize money to his son and Rs. 1000 more than the two third of the remaining to his daughter. If both they got same amount, what is the prize money Aman got?
(a) 20000
(b) 25000
(c) 26000
(d) None of these
10. The stream of a boat when travelling downstream is 32 km/hr, whereas when travelling upstream it is 28km/hr. what is the speed of boat in still water?
(a) 27km/hr
(b) 30km/hr
(c) 31km/hr
(d) Cannot be determined
Answers with solutions :
1.(b)
Speed of train = 108km/hr= (108*5/18) m/sec
If the length of the platform be x meters, then
x+280/12 =30
x+ 280 = 360
x=(360-280)=80
then 80/10 = 8 m/s
2.(a)
3.(b)
4.(d)
5.(a) In one minute the pipe of 2cm diameter fills 1/61 of the cistern.
In one minute the pipe of 1cm diameter fills 1/61* 1/4 of the cistern
In one minute the pipe of 11/3 cm diameter fills 1/61* 4/9 of the cistern
In one minute (1/61+1/(61*4)+4/(61*9))=1/36 of the cistern is filled.
The whole cistern is filled in 36 minutes
6.(c)Work done by C in one day = 1/7
Work done by B in one day = 1/2*1/7=1/14
Work done by A in one day = 1/2*1/14=1/28
Work done by A, B and C in one day = 7/28=1/4
7.(b) Let the two numbers be x and y.
3x = 1.2( 2y +105)
3x = 2.4y +126 ………………..(1)
2x +36 = 0.8(3y)
2x +36 =2.4y ………………..(2)
x = 162
8.(b)
9.(c) Assume Aman got x rupees.
He gave x/2 - 2000 to his son.
And 2/3 ( x/2 + 2000 ) + 1000 to his daughter.
x/2 - 2000 = x/3 + 7000/3
x = 26000
10.(b)
Speed of boat in still water= 1/2(32+28)=60/2=30km/hr
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