Unit-5:
(a)Alligation
(b)Time and work, work and wages and pipes and cisterns
(c)Time and distance, trains and streams
Q1.
18 men can do a work in 10 days . How many men are needed to complete the work in 36 days?
(a) 8 men (b) 5 men
(c) 6 men (d) 7 men
Solution.
M1D1W2 = M2D2W1
18 x 10 = 36M2
M2 = 5 men
Solution
Q2.
A and B together can do a piece of work in 8 days and A alone can do it in 12 days. In how many days can B alone do it ?
(a) 20 days (b) 16 days (c) 12 days (d) 24 days
Solution.
=
8 x 12/ 12 - 8
= 24 days
Solution
Q3.
x and y can do a work in 12 days , y and z in 15 days , z and x in 20 days . How long x will take seperately to do the same work.
(a) 60 days (b) 30 days (c) 10 days (d) 40 days
Solution.
time taken by x + y + z = 10 days
So,x can do the work in (x + y + z) - (y + z)
=
10 x 15/ 15 - 10
= 30 days
Solution
Q4.
A certain number of men complete work in 50 days. If there were 5 men more, The work could be finished in 5 days less. How many men were
originally there ?
(a) 35 days (b) 40 days (c) 30days (d) 45 days
Solution.
M1D1 = M2D2
(x) x 50 = (x + 5)45
x = 45
Solution
Q5.
Pipe A can fill a tank in 20 hrs, pipe B alone can fill it in 10 hrs and pipe C can empty the full tank in 30 hrs. If all the pipes
are opened together, how much time will be needed to make the tank fill.
(a) 30 hrs (b) 60/7hrs (c) 20 hrs
(d) 20/7 hrs
Solution.
= 1/10 + 1/20 - 1/30 = 60/7
Solution
Q6.
Two pipes x and y can fill a tank in 5 hrs and 10 hrs respectively. If both the pipes are opened simultaneously after how much time should y
be closed so that the tank is full in 8 hrs.
(a) 1 hrs (b) 2 hrs (c) 3 hrs (d) 4 hrs
Solution.
let y be closed after t hrs.
t(1/5 + 1/10) + (8 - t)/10 = 1
t(3/10) + (8 - t)/10 = 1
(3t + 8 - t)/10 = 1
2t + 8 = 10
2t = 2
t = 1
Solution
Q7.
Two runners cover the same distance at the rate of 15 km and 18 km per hour respectively. Find the distance travelled when one takes a minutes longer
than the other
(a) 30 km/hr (b) 13.5 km/hr (c) 14 km/hr (d) 20 km/hr
Solution.
Distance =
multiplication of speeds/ difference of speeds
x difference in time to cover distance
=
15 x 18/ 18 - 15
x
9/ 60
= 13.5 km/hr
Solution
Q8.
Two cars run to a place at the speeds of 45 km/hr and 50 km/hr respectively. If the second cars takes 5 hrs less than the first for journey
, find the length of the journey.
(a) 1890 km (b) 2000 km (c) 2400 km (d) 2250 km
Solution.
45 x 50/ 5
x 5
= 2250 km
Solution
Q9.
A can row a certain distance downstream in 6 hrs and return the same distance in 9 hrs . If the stream flows at the rate of 3 km/hr. find
the speed of A in still water.
(a) 20 km/hr (b) 15 km/hr (c) 10 km/hr (d) 5 km/hr
Solution.
m be the speed of boat in still water,z is the speed of stream.
s1 t1 = s2 t2
6(m + z) = 9(m -z)
6(m + 3) = 9(m - 3)
6m + 18 = 9m - 27
45 = 3m
m = 15
Solution
Q10.
A man can row 9 km/hr in still water. In a stream which is flowing at 2 km/hr it takes him 5 hrs to row to a place and back. How far is the place ?
(a) 24/7 km (b) 77 km (c) 77/9 km (d) 18 km
Solution.
x/7 + x/11 = 2
11x + 7x = 77 x 2
18 x = 77 x 2
x = (77 x 2)/18
= 77/9 km
Solution
