Examples(Set 2) - Time and Work

6.$5$ men and $10$ women can complete a work in $12$ days. $15$ men and 60 women can complete a work in 3 days. $5$ men and $16$ women can do the same work in:

A. 10 days
B. 12 days
C. 8 days
D. 2 days

Answer: Option A

Explanation:

Assume 1 man does 1m unit of work in a day, 1 woman does 1w unit of work in a day.

5 men and 10 women complete the work in 12 days. 

Therefore, total work is =12(5m+10w)

15 men and 60 women complete the work in 3 days. 

Therefore, total work is =3(15m+60w)

12(5m+10w)=3(15m+60w)

m=4w

Total work =3(15m+60w)

=3(60w+60w)

=360w   

work done by 5 men and 16 women complete the work in x days. 

total work is =x(5m+16w)

=x(36w)  

360w =x(36w)

x=10 

7. P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10days. R alone needs 50 days to complete the same work. then Q alone can do it in:
A. 30 days
B. 20 days
C. 25 days
D. 15 days

Answer: Option C

Explanation:
Amount of work P can do in 1 day = 1/ P

Amount of work Q can do in 1 day = 1/Q

Amount of work R, can do in 1 day = 1/ 50

Amount of work P and Q can do in 1 day
= 1/P+1/Q =1/10

given: 1/P=1/Q+1/50 (P can do a work in the same time in which Q and R together can do it)

solving both equations
1/Q=1/25
Q=25 days

8.A can do a piece of work in 6 hours. A and C together can do it in just 3 hours, while B and C together need 2 hours to finish the same work. B alone can complete the work in:
A. 6 hours
B. 3 hours
C. 5 hours
D. 2 hours

Answer: Option B

Explanation:
Amount of work A can do in 1 hour
1/A= 1/6

Amount of work A and C can do together in 1 hour
1/A+1/C= 1/3

Amount of work B and C can do together in 1 hour
1/B+1/C= 1/2

solving above equations
1/B=1/3
B=3
B alone will take 3 hours

9.A completes 80 % of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?
A. 31 days
B. 22 days
C. 26 days
D. 37 and 1 2 days

Answer: Option D

Explanation:
Work done by A in 20 days
= 80/ 100
= 4/ 5
Work done by A in 1 day
= ( 4/ 5 )/ 20
= 1/ 25
Work done by A and B in 3 days
= 20/ 100
= 1/ 5 (because remaining 20 % is done in 3 days by A and B)
Work done by A and B in 1 day = (1/ 5)/3
=1/15
Work done by B in 1 day
= 1/ 15 − 1/ 25 = 2/ 75
Therefore, B can complete the work in 75/ 2 days
= 37 and 1/ 2 days

10.Machine P can print one lakh books in 8 hours. Machine Q can print the same number of books in 10 hours while machine R can print the same in 12 hours. All the machines started printing at 9 a.m. Machine P is stopped at 11 a.m. and the remaining two machines complete work. Approximately at what time will the printing of one lakh books be completed?
A. 11 a.m.
B. 3 p.m.
C. 1 p.m.
D. 2 p.m.

Answer: Option C

Explanation: Work done by P in 1hour =1/8
Work done by Q in 1hour = 1/10
Work done by R in 1hour =1/12

P worked for 2 hrs = 2*1/8

suppose Q and R worked for 'x' hrs then,

2*1/8+(1/10)*x+(1/12)x = 1
x=4.09

9+4.09 = 1pm