1.Three years ago the average age of a family of four was 29 years. The father in the family is four years elder to the mother. The daughter is two years elder to the son. The mother’s age is three years more than thrice the age of her daughter. The present age of the father is _
(a) 48 years
(b) 50 years
(c) 52 years
(d) 54 years
2.Two pipes A and B can fill a tank in one hour, and one hour and 30 minutes respectively. The third pipe C can empty the tank in two hours and thirty minute. Initially when the tank in empty, the pipes A and B are opened for thirty minutes and then closed. Now the time taken by pipe C to empty the tank is ____________.
(a) 1 1/6 hours
(b) 1 5/6 hours
(c) 2 1/12 hours
(d) 2 1/3 hours
3.The average marks of a class of students in Mathematics examination is 72. But later it was found that the marks of two students were entered as 65 and 78 instead of 56 and 87 respectively. What is the correct average marks of the class in Mathematics?
(a) 64
(b) 68
(c) 72
(d) Cannot be determined
4.Arjun covered the distance between A and B travelling by a motor cycle at 60 kmph for two hours, by bus at 50 kmph for three hours and finally by a taxi which travelled at 70 kmph for three hours. The average speed of Arjun for the entire journey is
(a) 55 kmph
(b) 60 kmph
(c) 65 kmph
(d) 70 kmph
5.Ten litres of milk solution contains milk and water in the ratio of 4 : 1. Find the quantity of solution that should be replaced with water so that the resultant solution has milk and water in the ratio 3 : 2.
(a) 1.5 lt
(b) 2.5 lt
(c) 3.5 lt
(d) 4.5 lt
6.Ten men working eight hours a day can finish a piece of work in 15 days. Eight women working at six hours a day can finish the work in 30 days. In how many days can five men and four women working at eight hours a day finish the work by working together?
(a) 18 days
(b) 20 days
(c) 24 days
(d) 25 days
7.A certain sum of money is to be divided among 10 men, 15 women and 20 boys such that each man gets double the amount of each woman. Each woman gets thrice the amount each boy gets. If the total amount distributed is Rs. 50, 000, then the amount each man gets is
(a) Rs. 1,200
(b) Rs. 1,500
(c) Rs. 1,800
(d) Rs. 2,400
8.In an auditorium there are 500 people of whom men and women are in the ratio of 3 : 2. Later 48 women and 96 men entered the auditorium. The new ratio of number of men to the number of women is _____________,
(a) 33 : 96
(b) 66 : 53
(c) 99 : 62
(d) 121 : 98
9.Kishore started a business with a capital of Rs. 36, 000. After three months Ramesh joined him with a capital of Rs. 48,000. Three months later Suresh joined them with a capital of Rs. 96,000 and the three stayed till the end of the first year. They earned a profit of Rs. 8, 400. The share of Ramesh in the profit is ___________.
(a) Rs. 2,520
(b) Rs. 3,200
(c) Rs. 3,600
(d) Rs. 4,000
10.If (2)^x (3)^y = 216 then the value of (x + y)^2 is _____________.
(a) 36
(b) 64
(c) 100
(d) 144
Answers and SOLUTION
1.(c)
2.(c) Given that
Pipe A can fill half the tank in half an hour,
Pipe B can fill the 1/3rd tank in one hour 30 minutes.
The part of the tank filled by the pipes A and B in 30 minutes is = 1/2 + 1/3 = 5/6
so Time taken by pipe C to empty (5/6)th of tank is
=>(5/6) (2 1/2) = 5/6 = 5/2 = 25/12 = 2 1/12 hrs.
3.(c) Let’n be the strength of the class and A be the correct average
=>From the given information we can write,
nA = n (72) + (56 – 65) + (87 – 78)
=> nA = 72 n – 9 + 9
=> A = 72
so The correct average of the class is 72 marks.
4.(b) Distance covered by Arjun on motor cycle is (60) * 2 = 120km
Distance covered by him on Bus = (50) * 3 = 150 km
Distance covered by him on Taxi = (70) * 3 = 210 km
so Total distance covered by him in 8 hours = 120 + 150 + 210 = 480 km
so The average speed of Arjun over the entire journey = 480/8 = 60 kmph.
5.(b)
6.(a)
7.(d) Let the amount each child gets be x.
Amount each women gets = 3 x,
Amount each man gets = 2(3x) = 6x
Total amount distributed = 10 (6x) + 15 (3x) + 20 (x)
=> 60x + 45x + 20 x
=> 125x = Rs. 50, 000
X = 50, 000/125 = 400
so Amount each man gets = 6 (400) = 24,00
8.(c)Number of men initially present in the Auditoorium = 3/5 * 500 = 300
Number of women initially present in the Auditorium = 2/5*(500) = 200
After 48 women and 96 men entered, the new
ratio of number of men to the number of women = (300 + 96)/(200 + 48)
= 396/248 = 99/62 = 99 : 62
9.(a)
10.(a) Given that
(2)^x (3)^y=216 =8 ×27= (2)^3 (3)^3
=> x = 3 and y = 3
so (x+y)^2 = (3+3)^2= (6)^2=36
1.(c)
2.(c) Given that
Pipe A can fill half the tank in half an hour,
Pipe B can fill the 1/3rd tank in one hour 30 minutes.
The part of the tank filled by the pipes A and B in 30 minutes is = 1/2 + 1/3 = 5/6
so Time taken by pipe C to empty (5/6)th of tank is
=>(5/6) (2 1/2) = 5/6 = 5/2 = 25/12 = 2 1/12 hrs.
3.(c) Let’n be the strength of the class and A be the correct average
=>From the given information we can write,
nA = n (72) + (56 – 65) + (87 – 78)
=> nA = 72 n – 9 + 9
=> A = 72
so The correct average of the class is 72 marks.
4.(b) Distance covered by Arjun on motor cycle is (60) * 2 = 120km
Distance covered by him on Bus = (50) * 3 = 150 km
Distance covered by him on Taxi = (70) * 3 = 210 km
so Total distance covered by him in 8 hours = 120 + 150 + 210 = 480 km
so The average speed of Arjun over the entire journey = 480/8 = 60 kmph.
5.(b)
6.(a)
7.(d) Let the amount each child gets be x.
Amount each women gets = 3 x,
Amount each man gets = 2(3x) = 6x
Total amount distributed = 10 (6x) + 15 (3x) + 20 (x)
=> 60x + 45x + 20 x
=> 125x = Rs. 50, 000
X = 50, 000/125 = 400
so Amount each man gets = 6 (400) = 24,00
8.(c)Number of men initially present in the Auditoorium = 3/5 * 500 = 300
Number of women initially present in the Auditorium = 2/5*(500) = 200
After 48 women and 96 men entered, the new
ratio of number of men to the number of women = (300 + 96)/(200 + 48)
= 396/248 = 99/62 = 99 : 62
9.(a)
10.(a) Given that
(2)^x (3)^y=216 =8 ×27= (2)^3 (3)^3
=> x = 3 and y = 3
so (x+y)^2 = (3+3)^2= (6)^2=36
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