Time & Work, General Mathematics

Question: A is twice as good a workman as B and together they complete a work in 15 days. In how many days can the work be completed by B alone?
A`22 1/2`

B`30`

C`37 1/2`

D`45`

Note: solution:
(A's 1 day's work) : (B's 1 day's work) `=2 :1`.
`(A + B)`'s 1 day's work `= 1/15`.
Divide `1/15` in the ratio `2:1`.
B's 1 day's work `=(1/15 xx 1/3)`
                             `=1/45`.
`:.` B alone can finish the work in 45 days.

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Question: 45 men can complete a work in 16 days. Six days after they started working, 30 more men joined them. How many days will they now take to complete the remaining work ?
A4

B5

C6

D8

Note: solution:
`(45 xx 16)` men can complete the work in 1 day.
`:. 1` man's 1 day's work `= 1/720`.
`45` men's   6 day's work `= (1/16 xx 6)`
                                          `= 3/8`.
Remaining work `= (1 - 3/8)`
                          `= 5/8`.
`75` men's 1 day's work `= 75/720`
                                        `= 5/48`.
Now `5/48` work is done by them in 1 day.
`:. 5/8` work is done by them in `(48/5 xx 5/8)`
                                                     `= 6 `days.

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Question: 12 men can complete a work in 18 days. Six days after they started working, 4 men joined them. How many days will all of them take to finish the remaining work ?
A9

B10

C12

D15

Note: solution:
`(12 xx 18)` men can complete the work in 1 day.
`:. 1` man's 1 day's work `= 1/216`.
`12`men's 6 day's work `= (1/18 xx 6)`
                                        `= 1/3`.
Remaining work `=(1 - 1/3)`
                           `= 2/3`.
`16` men's 1 day's work `= 16/216`
                                        `= 2/27`.
`2/27` work is done by them in 1 day.
`2/3` work is done by them in `(27/2 xx2/3)`
                                                 `= 9` days.

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Question: Twelve men can complete a work  in 8 days. Three days after they started the work, 3 more men joined. In how many days will all of them together complete the remaining work ?
A2

B4

C5

D6

Note: solution:
`1` man's 1 day's work `= 1/96`.
`12` men's 3 day's work `= (1/8 xx 3)`
                                    `=  3/8`.
Remaining work `= (1 - 3/8)`
                          `= 5/8`.
`15` men's 1 day's work `= 15/96`.
Now, `15/96` work is done by them in 1 day
`:. 5/8` work is done by them in `(96/15 xx 5/8)`
                                                    `= 4` days.

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Question: A, B and C are employed to do a piece of work for Rs. 529. A and C are supposed to finish `19/23` of the work together. How much shall be paid to B ?
ARs. 82

BRs. 92

CRs. 300

DRs. 437

Note: solution:
Work done by B `= (1 - 19/23)`
                          `= 4/23`.
`:. (A + B) : B = 19/23 : 4/23`
                      `= 19 : 4`.
`:. B`'s share `= Rs. (529 xx 4/23)`
                                `= R's 92`.

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Question: A job is completed by 10 men in 20 days and by 20 women in 15 days. How many days will it take for 5 men and 10 women to finish that work ?
A`17 1/2`

B`17 1/7`

C`17`

D`17 1/120`

Note: solution:
Let 1 men's 1 day's work `= x` & 1 woman's 1 day's work `= y`.
Then, `10x = 1/20` and `20y = 1/15`.
So, `x = 1/200 and y = 1/300`.
`:.`(5 men + 10 women)'s 1 day's work `= (5/200 + 10/300)`
                                                      `= 7/120`.
So, they will finish the work in `120/7`
                                         `= 17 1/7`days.

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Question: A piece of work can be done by 6 men and 5 women in 6 days or 3 men and 4 women in 10 days. It can be done by 9 men and 15 women in :
A1 day

B2 days

C3 days

D4 days

Note: solution:
Let 1 man's 1 day's work `= x & 1` woman's 1 day's work `= y`.
Then, `6x + 5y = 1/6, 3x +4y = 1/10`.
On solving, we get `x = 1/54` and `y = 1/90`.
(9 men + 15 women )'s 1 day's work `= (9/54 + 15/90)`
                                               `= 1/3`.
`:.` They will finish the work in 3 days.

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Question: 4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how many days will 10 women working together finish it ?
A`24`

B`32`

C`36`

D`40`

Note: solution:
Let 1 men's 1 day's work `= x & 1` woman's 1 day's work `= y`.
Then, `4x + 6y = 1/8` and `3x + 7y = 1/10`.
Solving, we get :` y = 1/400`.
`:. 10` women's 1 day' work `= 10/400`
                                           `= 1/40`.
`:. 10` women will finish the work in `40` days.

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Question: 12 children take 16 days to complete a work which can be completed by 8 adults in 12 days. 16  adults started working and after 3 days 10 adults  left and 4 children joined them. How many days will it take them to complete the remaining work ?
A`6`

B`8`

C`4`

D`3`

Note: solution:
Let 1 chile's 1 day's work `= x & 1` adult's 1 day's work `= y`.
Then, `12x = 1/16 or x = 1/192 and 8y = 1/12 or y = 1/96`.
Work done in 3 days `=(16 xx 1/96 xx3)`
                               ` = 1/2`.
Work left `= (1 - 1/2)`
               `= 1/2`.
(6 adults + 4 children)'s 1 day's work `= (6/96 + 4/192)`
                                                       `= 1/12`.
`1/2` work is done by them in 1 day.
`1/2` work is done by them in `(12 xx 1/2)`
                                             `= 6`days.

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Question: Ram can do  a piece of work  in 8 days which Shyam can  finish in 12 days. If they work at it on alternate days with Ram beginning, in how many days, the work will be finished ?
A`9 1/3`

B`9 1/2`

C`9 1/24`

D`10 1/3`

Note: solution:
(Ram + Shyam)'s 2 days work `= (1/8 + 1/12)`
                                             `= 5/24`.
Their 8 day's work `= (5/24 xx 4)`
                            `= 5/6`.
Their 9 day's work `=(5/6 + 1/8)`
                           `= 23/24`.
Remaining work `= (1 - 23/24)`
                        `= 1/24`.
Now it is Shyam's turn.
`1/12` work is done by him in 1 day.
`1/24` work is done by him in `(12 xx 1/24)`
                                            `= 1/2` day.
`:.` Total time taken `= 9 1/2` days.

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