Time and Work
- A particular job can be completed by a team of 10 men in 12 days. The same job can be completed by a team of 10 women in 6 days. How many days are needed to complete the job if the two teams work together?
-
View Hint View Answer Discuss in Forum
According to question,
10 men’s one day’s work = 1 12 ∴ 1 man one day’s work = 1 = 1 12 × 10 120
Similarly,1 woman one day’s work = 1 = 1 6 × 10 60 ∴ (1 man + 1 woman)’s one day’s work = 1 + 1 120 60 (1 man + 1 woman)’s one day’s work = 1 + 2 = 3 = 1 120 120 40
Correct Option: A
According to question,
10 men’s one day’s work = 1 12 ∴ 1 man one day’s work = 1 = 1 12 × 10 120
Similarly,1 woman one day’s work = 1 = 1 6 × 10 60 ∴ (1 man + 1 woman)’s one day’s work = 1 + 1 120 60 (1 man + 1 woman)’s one day’s work = 1 + 2 = 3 = 1 120 120 40 ∴ (10 men + 10 women)’s one day’s work = 10 = 1 40 4
Therefore, both the teams can finish the whole work in 4 days.
- A and B can do a piece of work in 72 days. B and C can do it in 120 days, A and C can do it in 90 days. In how many days all the three together can do the work ?
-
View Hint View Answer Discuss in Forum
(A + B)’s 1 day’s work = 1 72
(B + C)’s 1 day’s work = 1 120
(C + A)’s 1 day’s work = 1 90
On adding all three2 (A + B + C)'s 1 days work = 1 + 1 + 1 72 120 90 2 (A + B + C)'s 1 days work = 5 + 3 + 4 = 1 360 30 ∴ (A+B+C)’s 1 day’s work = 1 60
∴ (A+B+C) will do the work in 60 days.
Second method to solve this question ,
Here , x = 72 , y = 120 , z = 90Time taken = 2xyz xy + yz + zx
Correct Option: C
(A + B)’s 1 day’s work = 1 72
(B + C)’s 1 day’s work = 1 120
(C + A)’s 1 day’s work = 1 90
On adding all three2 (A + B + C)'s 1 days work = 1 + 1 + 1 72 120 90 2 (A + B + C)'s 1 days work = 5 + 3 + 4 = 1 360 30 ∴ (A+B+C)’s 1 day’s work = 1 60
∴ (A+B+C) will do the work in 60 days.
Second method to solve this question ,
Here , x = 72 , y = 120 , z = 90Time taken = 2xyz xy + yz + zx Time taken = 2 × 72 × 120 × 90 72 × 120 +120 × 90 +72 × 90 = 1555200 8640 + 10800 + 6480 = 1555200 = 60 days 25920
- A and B can do a work in 12 days, B and C in 15 days and C and A in 20 days. If A, B and C work together, they will complete the work in :
-
View Hint View Answer Discuss in Forum
According to question,
A and B can do a work in 12 days∴ (A + B)’s one day’s work = 1 12
Similarly,(B + C)’s one day’s work = 1 15 and (C + A)’s one day’s work = 1 20
On adding all three,∴ 2 (A + B + C)’s one days’s work = 1 + 1 + 1 12 15 20 2 (A + B + C)’s one days’s work = 10 + 8 + 6 = 1 120 5 ⇒ (A + B + C)’s one days’s work = 1 10
∴ A, B and C together can finish the whole work in 10 days.
Second method to solve this question ,
Here , x = 12 , y = 15 , z = 20Time taken = 2xyz xy + yz + zx
Correct Option: C
According to question,
A and B can do a work in 12 days∴ (A + B)’s one day’s work = 1 12
Similarly,(B + C)’s one day’s work = 1 15 and (C + A)’s one day’s work = 1 20
On adding all three,∴ 2 (A + B + C)’s one days’s work = 1 + 1 + 1 12 15 20 2 (A + B + C)’s one days’s work = 10 + 8 + 6 = 1 120 5 ⇒ (A + B + C)’s one days’s work = 1 10
∴ A, B and C together can finish the whole work in 10 days.
Second method to solve this question ,
Here , x = 12 , y = 15 , z = 20Time taken = 2xyz xy + yz + zx Time taken = 2 × 12 × 15 × 20 12 × 15 + 15 × 20 + 20 × 12 Time taken = 24 × 300 180 + 300 + 240 Time taken = 7200 = 10 days. 720
- A can do a piece of work in 120 days and B can do it in 150 days. They work together for 20 days. Then B leaves and A alone continues the work. 12 days after that C joins A and the work is completed in 48 days more. In how many days can C do it if he works alone?
-
View Hint View Answer Discuss in Forum
A’s 1 day’s work
= 1 120 B’s 1 day’s work = 1 150
(A + B)’s 1 day’s work= 1 + 1 = 5 + 4 = 3 120 150 600 200
(A + B) work together for 20 days
Hence, (A + B)’s 20 days’ work= 20 × 3 = 3 200 10
After 20 days B leaves, and A alone works for 12 days
∴ A’s 12 days’ work= 1 × 12= 2 120 10
Now, after 12 days, C joins A and the work is finished in 48 days. It means A works for 48 days more.
∴ A’s 48 days’ work= 1 × 48 = 2 120 5
∴ Total work done by A and B together= 3 + 1 + 2 10 10 5 = 3 + 1 + 4 = 4 10 5
∴ Remaining work= 1 - 4 = 1 5 5
This part of work, i.e., 1/5 is done by C in 48 days∴ C’s 48 days’ work = 1 5
∴ C’s 1 day’s work= 1 = 1 5 × 48 240
Hence, C alone can finish the work in 240 days.Correct Option: C
A’s 1 day’s work
= 1 120 B’s 1 day’s work = 1 150
(A + B)’s 1 day’s work= 1 + 1 = 5 + 4 = 3 120 150 600 200
(A + B) work together for 20 days
Hence, (A + B)’s 20 days’ work= 20 × 3 = 3 200 10
After 20 days B leaves, and A alone works for 12 days
∴ A’s 12 days’ work= 1 × 12= 2 120 10
Now, after 12 days, C joins A and the work is finished in 48 days. It means A works for 48 days more.
∴ A’s 48 days’ work= 1 × 48 = 2 120 5
∴ Total work done by A and B together= 3 + 1 + 2 10 10 5 = 3 + 1 + 4 = 4 10 5
∴ Remaining work= 1 - 4 = 1 5 5
This part of work, i.e., 1/5 is done by C in 48 days∴ C’s 48 days’ work = 1 5
∴ C’s 1 day’s work= 1 = 1 5 × 48 240
Hence, C alone can finish the work in 240 days.
- A can complete a work in 10 days, B can complete the same work in 20 days and C in 40 days. A starts working on the first day, B works for second day and C works for third day. Again A works for fourth day and B for fifth day and so on. If they continued working in the same way, in how many days will the work be completed?
-
View Hint View Answer Discuss in Forum
A’s work for the first day
= 1 10
B’s work for the second day= 1 20
C’s work for the third day= 1 40
Work done in 3 days by them together= 1 + 1 + 1 10 20 40 = 4 + 2 + 1 = 7 40 40
Hence, 7/40 part of work will be completed in 3 days.= 7 × 5 i.e 35 40 40
part of work will be completed in 3 × 5 or 15 days.
Remaining work= 1 - 35 = 5 = 1 40 40 8
Now, A will work on 16th day.
The remaining work after 16 days= 1 - 1 = 5 - 4 = 1 8 10 40 40
Again, B will work on 17th day.
∵ B completes the work in 20 days.
∴ B will complete 1/40 part of work in= 20 × 1 = 1 day 40 2
Hence, Total time taken in completion of work= 15 + 1 + 1 = 16 1 day 2 2 Correct Option: B
A’s work for the first day
= 1 10
B’s work for the second day= 1 20
C’s work for the third day= 1 40
Work done in 3 days by them together= 1 + 1 + 1 10 20 40 = 4 + 2 + 1 = 7 40 40
Hence, 7/40 part of work will be completed in 3 days.= 7 × 5 i.e 35 40 40
part of work will be completed in 3 × 5 or 15 days.
Remaining work= 1 - 35 = 5 = 1 40 40 8
Now, A will work on 16th day.
The remaining work after 16 days= 1 - 1 = 5 - 4 = 1 8 10 40 40
Again, B will work on 17th day.
∵ B completes the work in 20 days.
∴ B will complete 1/40 part of work in= 20 × 1 = 1 day 40 2
Hence, Total time taken in completion of work= 15 + 1 + 1 = 16 1 day 2 2
