Time & Work, General Mathematics

Question: A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately, A beginning, in how many days the work will be completed ?
A
$10 1/2$

B
$10 1/3$

C
$10 1/4$

D
$10 2/3$

Note: solution: $(A + B)'s 2$ day's work $= (1/9 + 1/12)$ $= 7/36$ . Work done in 5 pairs of days $= (5 xx 7/36)$ $= 35/36$ . Remaining work $= (1 - 35/36)$ $= 1/36$ . On 11th day, it is A's turn. $1/9$ work is done by him in 1 day. $1/36$ work id done by him in $(9 xx 1/36)$ $= 1/4$ day. $:.$ Total time taken $= 10 1/4$ days.
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Question: A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately, A beginning, in how many days the work will be completed ?
A
$1o 1/2$

B
$10 1/3$

C
$10 1/4$

D
$10 2/3$

Note: solution: $(A + B)'s 2$ day's work $= (1/9 + 1/12)$ $= 7/36$ . Work done in 5 pairs of days $= (5 xx 7/36)$ $= 35/36$ . Remaining work $= (1 - 35/36)$ $= 1/36$ . On 11th day, it is A's turn. $1/9$ work is done by him in 1 day. $1/36$ work id done by him in $(9 xx 1/36)$ $= 1/4$ day. $:.$ Total time taken $= 10 1/4$ days.
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Question: A,B and C can do a piece of work in 11 days, 20 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by B and C on alternate days ?
A
7 days

B
8 days

C
9 days

D
10 days

Note: solution: (A + B)'s 1 day's work $= (1/11 + 1/20)$ $= 31/220$ . (A + C)'s 1 day's work $= (1/11 + 1/55)$ $= 6/55$ . Work done in 2 days $= (31/220 + 6/55)$ $= 55/220$ $= 1/4$ . Now, $1/4$ work is done in 2 days. $:.$ Whole work will be done in $(4 xx 2)$ $= 8$ days.
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Question: Machines A and B produce $8000$ clips in 4 and 6 hours respectively. If they work alternately for 1 hour, A starting first, then $8000$ clips will be produced in :
A
$4 1/3$ hours

B
$4 2/3$ hrs

C
$5 1/3$ hrs

D
$5 2/3$ hrs

Note: solution: (A + B)'s 2 hour's work $= (1/4 + 1/6)$ $= 5/12$ . (A +B)'s 4 hour's work $= (5/12 xx 2)$ $= 10/12$ $= 5/6$ . Remaining work $= (1 - 5/6)$ $= 1/6$ . Now, it is A's turn. $1/4$ work is done by A in 1 hour $1/6$ work is done by A in $(4 xx 1/6)$ $= 2/3$ hours. Total time taken $= 4 2/3$ hours.
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Question: A father can do a job as fast as his two sons working together. If one son does the job in 3 hours and the other in 6 hours, how many hours does it take the father to do the job ?
A
$1$

B
$2$

C
$3$

D
$4$

Note: solution: Father's 1 hour's work $= (1/3 + 1/6 )$ $= 1/2$ . $:.$ Time taken by father to complete the work $= 2$ hours.
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Question: A sum of money is sufficient to pay A's wages for 21 days and B's wages for 28 days. The same money is sufficient to pay the wages of both for :
A
$12$ days

B
$14$ days

C
$12 1/4$ days

D
$24 1/2$ days

Note: solution: Let total money be Rs. $x$ . A's 1 day's wages $= x/21$ , B's 1 day's wages $= x/28$ . $:. (A + B)$ 's 1 day's wages $= (x/21 + x/28)$ $= x/12$ . $:.$ Money is sufficient to pay the wages of both for $12$ days.
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Question: A alone can finish apiece of work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of total wages of Rs. 225, the amount (in rupees) that A will get, is :
A
$90$

B
$112.50$

C
$135$

D
$150$

Note: solution: A's wages : B's wages = A's 1 day's work : B's 1 day's work $= 1/10 : 1/15 : 3 : 2$ . A's wages $= Rs. (225 xx 3/5)$ $= Rs. 135$ .
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Question: A can do a piece of work in 6 days and B alone can do it in 8 days. A and B undertook to do it for Rs. $640$ . With the help of C, they finished it in 3 days. How much is paid to C ?
A
$Rs. 75$

B
$Rs. 80$

C
$Rs. 120$

D
$Rs. 160$

Note: solution: C's 1 day's work $= 1/3 - (1/6 + 1/8)$ $= (1/3 - 7/24)$ $= 1/24$ . $:. A : B : C = 1/6 : 1/8 : 1/24$ $= 4 : 3 : 1$ $:.$ C's share $= Rs. (640 xx 1/8)$ $= Rs. 80$ .
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Question: A, B and C together earn $Rs. 300$ per day, while A and C together earn $Rs. 188$ and B and C together earn $Rs. 152$ . The daily earning of C is :
A
$Rs. 150$

B
$Rs. 112$

C
$Rs. 68$

D
$Rs. 40$

Note: solution: B's daily earning $= Rs. (300 - 188)$ $= Rs. 112$ . A's daily earning $= (300 - 152)$ $= Rs. 148$ . C's daily earning $= [300 - (112 + 148)]$ $= Rs. 40$ .
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Question: Sunil can complete a work in 4 days whereas Dinesh can complete it in 6 days. Ramesh works $1 1/2$ times as fast as Sunil. How many days will it take for the three together to complete the work ?
A
$7/12$

B
$1 5/7$

C
$1 5/12$

D
None of these

Note: solution: Time taken by Ramesh alone $= (2/3 xx 4)$ $= 8/3$ days. Their 1 day's work $= (1/4 + 1/6 + 3/8)$ $= 19/24$ . $:.$ Three together can finish the work in $24/19$ $= 1 5/19$ days.
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Question: A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately, A beginning, in how many days the work will be completed ?

Question: A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately, A beginning, in how many days the work will be completed ?

Question: A,B and C can do a piece of work in 11 days, 20 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by B and C on alternate days ?

Question: Machines A and B produce $8000$ clips in 4 and 6 hours respectively. If they work alternately for 1 hour, A starting first, then $8000$ clips will be produced in :

Question: A father can do a job as fast as his two sons working together. If one son does the job in 3 hours and the other in 6 hours, how many hours does it take the father to do the job ?

Question: A sum of money is sufficient to pay A's wages for 21 days and B's wages for 28 days. The same money is sufficient to pay the wages of both for :

Question: A alone can finish apiece of work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of total wages of Rs. 225, the amount (in rupees) that A will get, is :

Question: A can do a piece of work in 6 days and B alone can do it in 8 days. A and B undertook to do it for Rs. $640$ . With the help of C, they finished it in 3 days. How much is paid to C ?

Question: A, B and C together earn $Rs. 300$ per day, while A and C together earn $Rs. 188$ and B and C together earn $Rs. 152$ . The daily earning of C is :

Question: Sunil can complete a work in 4 days whereas Dinesh can complete it in 6 days. Ramesh works $1 1/2$ times as fast as Sunil. How many days will it take for the three together to complete the work ?

Question: A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately, A beginning, in how many days the work will be completed ?

Question: A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately, A beginning, in how many days the work will be completed ?

Question: A,B and C can do a piece of work in 11 days, 20 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by B and C on alternate days ?

Question: Machines A and B produce 80008000 clips in 4 and 6 hours respectively. If they work alternately for 1 hour, A starting first, then 80008000 clips will be produced in :

Question: A father can do a job as fast as his two sons working together. If one son does the job in 3 hours and the other in 6 hours, how many hours does it take the father to do the job ?

Question: A sum of money is sufficient to pay A's wages for 21 days and B's wages for 28 days. The same money is sufficient to pay the wages of both for :

Question: A alone can finish apiece of work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of total wages of Rs. 225, the amount (in rupees) that A will get, is :

Question: A can do a piece of work in 6 days and B alone can do it in 8 days. A and B undertook to do it for Rs. 640640. With the help of C, they finished it in 3 days. How much is paid to C ?

Question: A, B and C together earn Rs.300Rs. 300 per day, while A and C together earn Rs.188Rs. 188 and B and C together earn Rs.152Rs. 152. The daily earning of C is :

Question: Sunil can complete a work in 4 days whereas Dinesh can complete it in 6 days. Ramesh works 1121 1/2 times as fast as Sunil. How many days will it take for the three together to complete the work ?

Question: Machines A and B produce $8000$ clips in 4 and 6 hours respectively. If they work alternately for 1 hour, A starting first, then $8000$ clips will be produced in :

Question: A can do a piece of work in 6 days and B alone can do it in 8 days. A and B undertook to do it for Rs. $640$ . With the help of C, they finished it in 3 days. How much is paid to C ?

Question: A, B and C together earn $Rs. 300$ per day, while A and C together earn $Rs. 188$ and B and C together earn $Rs. 152$ . The daily earning of C is :

Question: Sunil can complete a work in 4 days whereas Dinesh can complete it in 6 days. Ramesh works $1 1/2$ times as fast as Sunil. How many days will it take for the three together to complete the work ?