1. ‘x’ number of men can finish a piece
of work in 30 days. If there were 6
men more, the work could be finished in 10 days less. The actual number of men
2. 8 men can complete a piece of work in
20 days. 8 women can complete the same work in 32 days. In how many days will 5
men and 8 women together complete the same work?
4. 15 Men take 20
days to complete a job working 8 hours a day. The number of hours a day should
20 men take to complete the job in 12 days is:
piece of work for Rs. 1,200. The first person can complete the work in 8 days,
second person in 12 days and third person in 16 days. They complete the work
with the help of a fourth person in 3 days. What does the fourth person get?
Sol. Let the fourth person complete the entire work in x days.
Now, according to the question:
⇒1/x=1/3-1/8-1/12-1/16=(16 – 6 – 4 – 3)/48=1/16
∴ x = 16
Ratio of wages =1/8 ∶1/12 ∶1/16 ∶1/16=6∶4∶3∶3
Sum of ratios = 6 + 4 + 3 + 3
∴ Fourth person’s share =3/16×1200 =Rs. 225.
7. A can do a piece
of work in 20 days and B in 30 days. They work together for 7 days and then
both leave the work. Then C alone finishes the remaining work in 10 days. In
how many will C finish the full work?
Sol.(c) Work done by A and B in 7 days
Remaining work =1-7/12=5/12
∴ Time taken by C =12/5×10= 24 days
9. A farmer can
plough a filed working 6 hours per day in 18 days. The worker has to work how
many hours per day to finish the same work in 12 days?
Days. B starts the work and works only for 3 days. Thereafter A completes the
job. He will finish it in:
Time taken by B in doing the same work = 15 days
B’s 3 days’ work =3/15=1/5
Remaining work =1-1/5=4/5
∴ Time taken by A in finishing the remaining work =(35×4/5)=28 days
12. 2 men and 4 boys
can do a piece of work in 10 days, while 4 men and 5 boys can do it in 6 days.
Men and boys are paid wages according to their output. If the daily wage of a
man is Rs. 40, then the ratio of daily wages of a man and a boy will be:
∴ required ratio = 40 : 16 = 5 : 2
employed to do a work for Rs. 5750. P and Q together finished 19/23 of work and Q and R together finished 8/23 of work. Wage of Q in rupees, is:
Work done by (P + Q) =19/23 …(ii)
Work done by (Q + R) =8/23 …(iii)
From equations (ii) + (iii) – (i)
Q =19/23+8/23-1=(27 – 23)/23=4/23
∴ Wages of Q =4/23×5750 = Rs. 1000
of work in 12 days and B and C together in 15 days. If A is twice as good a
workman as C, then in how many days will B alone complete the same work?