Time and Work
- A and B together can do a piece of work in 12 days which B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days, C takes up and finishes it alone in 13 days. In how many days, C alone can do the work ?
-
View Hint View Answer Discuss in Forum
(A + B)'s one day work = 1/12
(B + C)'s one day work = 1/16
Now, from the question,
A's 5 days work + B's 7 days work + C's 13 days work = 1Correct Option: C
(A + B)'s one day work = 1/12
(B + C)'s one day work = 1/16
Now, from the question,
A's 5 days work + B's 7 days work + C's 13 days work = 1
⇒ A's 5 days work + B's 5 days work + B's 2 days work + C's 2 days work + C's 11 days work = 1
(A + B)'s 5 days work + (B + C)'s 2 days work + C's 11 days work = 1
⇒ 5/12 + 2/16 + C's 11 days work = 1
⇒ C's 11 days work = 1 - (5/12 + 2/16) = 11/24
⇒ C's 1 day work = (11/24) x 11 = 1/24
Hence, C can do this work in 24 days.
- Rohit, Harsh and Sanjeev are three typists, who working simultaneously, can type 216 pages in four hours . In one hour, Sanjeev can type as many pages more than Harsh as Harsh can type more than Rohit. During a period of five hours, Sanjeev can type as many passages as Rohit can, during seven hours. How many pages does each of them type per hour ?
-
View Hint View Answer Discuss in Forum
Let Rohit, Harsh and Sanjeev can type x, y and z pages respectively in 1 h.
Therefore, they together can type 4(x + y + z) pages in 4 h
∴ 4(x + y + z) = 216
⇒ x + y + z = 54 .....(i)
Also, z - y = y - x
i.e., 2y = x + z ......(ii)Correct Option: D
Let Rohit, Harsh and Sanjeev can type x, y and z pages respectively in 1 h.
Therefore, they together can type 4(x + y + z) pages in 4 h
∴ 4(x + y + z) = 216
⇒ x + y + z = 54 .....(i)
Also, z - y = y - x
i.e., 2y = x + z ......(ii)
From Eqs. (i) and (ii), we get
3y = 54
⇒ y = 18
From Eq. (ii), x + z = 36 ....(iv)
From Eqs. (iii) and (iv),
we get x = 15 and z = 21
- A conveyer belt delivers baggage at the rate of 3 tonne in 5 min and a second conveyer belt delivers baggage at the rate of 1 tonne in 2 min. How much time will it take to get 33 tonne of baggage using both conveyer belts ?
-
View Hint View Answer Discuss in Forum
The weight of baggage deliver in 1 min by 1st belt = 3/5 tonne
The weight of baggage deliver in 1 min by 2nd belt = 1/2 tonne
The weight of baggage deliver in 1 min by both belt = 3/5 + 1/2 = 11/10 tonne
So, the two belts delivers 1 tonne in 10/11 min.Correct Option: B
The weight of baggage deliver in 1 min by 1st belt = 3/5 tonne
The weight of baggage deliver in 1 min by 2nd belt = 1/2 tonne
The weight of baggage deliver in 1 min by both belt = 3/5 + 1/2 = 11/10 tonne
So, the two belts delivers 1 tonne in 10/11 min.
Hence, required time to deliver 33 tonne = (10/11) x 33 = 30 min
- Two pipes A and B can each fill a tank in 40 and 60 min, respectively. There is an outlet C. If all the 3 pipes are opened up, the tank will be filled in 30 min. How much time will it take for C alone to empty the full tank ?
-
View Hint View Answer Discuss in Forum
Work done by C in one min = (1/40 + 1/60) - 1/30 = 1/120
Correct Option: B
Work done by C in one min = (1/40 + 1/60) - 1/30 = 1/120
Hence, C can empty the tank in 120 min or 2 h.
