1. A does half as much work as B does in one sixth of the time. If together they take 20 days to complete the work, then what is the time taken by B to complete the work independently.
a) 80 days
b) 100 days
c) 120 days
d) 140 days
e) None of these
Sol. Let B take X days to complete the work then in one –sixth of the time i.e. x/6 days. Now A do half work as done by B so A will take twice the time i.e. 2*x/6 = x/3 to complete the job alone
So 1/x + 3/x = 1/20
x = 80 days
2. A contractor undertakes to make a mall in 60 days and he employs 30 men. After 30 days it is found that only one- third of the work is completed. How many extra men should he employ so that the work is completed on time?
a) 20men
b) 25men
c) 30men
d) 40men
e) None of these
Sol. Let total work is w and it is given that one-third of the work is completed after 30 days. Means
M*D = 30*30 = w/3, so total work = 30*30*3
2700 = 30*30 + (30+p)*30, so we get P = 30 (p = additional men)
3. 50 men could complete a work in 200 days. They worked together for 150 days, after that due to bad weather the work is stopped for 25 days. How many more workers should be employed so as to complete the work in time?
a) 25
b) 35
c) 50
d) 60
e) None of these
Sol. Let additional workers be P,
(50*150)/(50*200) = 3/4 of the work is already completed and now only 1/4 of the work is to be done. So,
1/4 = ((50 + P) * 25)/50*200, solve for p, we get P = 50
4. P and Q were assigned to do a work for an amount of 1200. P alone can do it in 15 days while Q can do it in 12 days. With the help of R they finish the work in 6 days. Find the share if C.
a) 100
b) 120
c) 140
d) 160
e) None of these
Sol. 1/15 + 1/12 + 1/c = 1/6, we got C = 60 (it means C will take 60 days to complete the work alone)
so ratio of work done by P:Q:R = 4:5:1
so c share = (1/10)*1200 = 120
5. A can do a work in 32 days. P who is 60 percent more efficient than A. Find how much time they will take together to do the same work?
a) 150/13 days
b) 160/13 days
c) 170/3 days
d) 190/3 days
e) None of these
Sol. A’s one day work = 1/32 so P one day work = (160/100)*1/32 = 1/20, so P will take 20 days to complete the work.
So Both A and P will take = (32*20)/52 = 160/13 days
6. P does half as much work as Q in three-fourth of the time. If together they take 24 days to complete the work, how much time shall P take to complete the work?
a) 50 days
b) 60 days
c) 70 days
d) 80 days
e) None of these
Sol. Let Q take x days to complete the work, so P will take 2*3/4 of X day to complete the work i.e. 3x/2 days
1/x + 2/3x = 1/24, we get x = 40 days, so P will take = 3/2 of 40 = 60 days.
7. P and Q together can complete a job in 90days, Q and R takes 60 days to complete the same work and P and R will take 45 days to complete the same work. How much time will P, Q and R will take to complete the work together.
a) 40 days
b) 42 days
c) 36 days
d) 44 days
e) None of these
Sol. ( 1/90 + 1/60 + 1/45)*1/2 = (1/P +1/Q + 1/R) = 1/40
so 40 days.
8. A and B undertake to complete a piece of work for Rupees 1200. A can do it in 8 days, B can do it in 12 days and with the help of C they complete the work in 4 days. Find the share of C?
a) 100
b) 200
c) 300
d) 400
e) None of these
Sol. 1/8 + 1/12 + 1/C = 1/4, we get C = 24 days
now efficiency of A, B and C are in the ratio of 1/8 :1/12 : 1/24
3:2:1, so share of C is 1/6 * 1200 = 200
9. A piece of work has to be completed in 50 days, a number of men are employed but it is found that only half of the work is done in 30 days, then an additional 20 men were joined to complete the work on time. How many men initially put to work?
a) 30
b) 35
c) 40
d) 45
e) None of these
Sol. Suppose Initially X men get employed. Half work is done in 30 days it means full work will be done by X men in 60 days. Now,
Work done = 1/2 = [20*(x + 20)]/60X
X = 40.
10. P can do a piece of work in 20 days. Q is 25 percent more efficient than P. In how many days half the work is completed when both are working simultaneously?
a) 41/9
b) 40/9
c) 39/9
d) 43/9
e) None of these
Sol. Q is 25 percent more efficient so he will complete the work in 16 days
(1/20 + 1/16)*t = 1/2.
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