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 ?
A7 days

B8 days

C9 days

D10 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`

DNone 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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