General Mathematics

Question: A is thrice as good a workman as B and takes 10 days less to do a piece of work than B takes. B alone can do the whole work in:
A12 days

B15 days

C20 days

D30 days

Note: solution:
Ratio of times taken by `A & B = 1 : 3`.
If difference of time is 2 days, B takes 3 days.
If difference of time is 10 days, B takes `(3/2 xx 10)`
                                                               = `15` days.

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Question: A can do a piece of work in 14 days which B can do in 21 days. They begin together but 3 days before the completion of the work, A leaves  off. The total number of days to complete the work is :
A`6 3/5`

B`8 1/2`

C`10 1/5`

D`13 1/2`

Note: solution:
B's 3 day's  work =`(1/21 xx 3)`
                            = `1/7`.
Remaining work =`(1 - 1/7)`
                          = `6/7`
`(A + B)`'s 1 day's work = `(1/14 + 1/21)`
                                       =`5/42`.
Now, `5/42` work is done by A & B in 1 day.
`:. 6/7` work in done by A &  B in `(42/5 xx 6/7)`
                                                      =`36/5` days.
`:.` Total time taken = `(3 + 36/5)` days 
                                 = `10 1/5` days.

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Question: If Ramesh,  Suresh and Harish can do a piece of work in 15 days, 10 days and 6 days respectively, how long will they take to do it, if all the three work at it together ?
A3 days

B`3 1/2` days

C`3 9/20` days

D`3 3/20` days

Note: solution:
(Ramesh + Suresh + Harish)'s 1 day's work = `(1/15 + 1/10 + 1/6)`
                                                                      =`12/30`
                                                                      =`1/3`.
So, all the tree will finish the work in 3 days.

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Question: A and B can do a piece of work in 72 days; B and C do it in 120 days; A and C can do it in 90 days. In what time can A alone do it ?
A150 days

B120 days

C100 days

D80 days

Note: solution:
`(A + B )`'s 1 day's work =`1/721`,
`(B + C)`'s  1day's work =` 1/120`,
`(A + C)`'s  1day's work =`1/90`.
Adding `2(A + B + C)`'s 1 day's work = `(1/72 + 1/120 + 1/90)`
                                                            =`12/360`
                                                            =`1/30`.
`:. (A + B + C)`'s 1 day's work =`1/60`.
     A's 1 day's work =`(1/60 - 1/120)`
                               =`1/120`.
`:.` A alone can finish the work in 120 days.

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Question: A and B can do a piece of work in 5 days; B and C can do it in 7 days; A and C can do it in 4 days. Who among these will take the least time if put to do it alone ?
AA

BB

CC

DData inadequate

Note: solution:
`(A + B)`'s 1 day's work = `1/5`;
`(B + C)`'s 1 day's work = `1/7` and
`(A + C)`'s 1 day's work = `1/4`.
`2(A + B + C)`'s 1 day's work =`(1/5 + 1/7 + 1/4)`
                                                =`83/140`.
`(A + B + C)`'s 1 day's work = `83/280`.
 C's 1 day's work =`(83/280 - 1/5)`
                            = `27/280`.
 A's 1 day's work =`(83/280 - 1/7)`
                           =`43/280`.
 B's 1 day's work =`(83/280 - 1/4)`
                           =`13/280.`
Thus time taken by A, B, C is `280/43` days, `280/13` days, `280/27` days respectively.
Clearly, the time taken by A is least.

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Question: If A, B and C together can finish a piece of work in 4 days; A alone can do it in 12 days and B in 18 days, then C alone Can do it in:
A21 days

B16 days

C14 days

D9 days

Note: solution:
`(A + B + C)`'s 1 day's work =`1/4`
`(A + B)`'s 1 day's work =`(1/12 + 1/18)`
                               =`5/36`.
 C's 1 day's work =`(1/4 - 5/36)`
                            =`4/36`
                            =`1/9`.
`:.`C alone can finish the work in 9 days.

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Question: A and B can do a piece of work in 18 days; B and C can do it in 24 days; A and C can do it in 36 days. In how many days can they do it all working together ?
A12

B13

C16

D26

Note: solution:
`(A + B)`'s 1 day's work =`1/18`,
`(B + C)`'s 1 day's work =`1/24` and
`(A + C)`'s 1 day,s work =`1/36`.
`:. 2 (A + B + C)`'s 1 day's work =`(1/18 + 1/24 + 1/36)`
                                                    =`9/72`
                                                    =`1/8`
`:. (A + B + c)`'s 1 day's work =`1/16`.
Hence, all working together can do the work in 16 days.

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Question: 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 finishes in 13 days. In how many days C alone will  do the work?
A16

B24

C36

D48

Note: solution:
`(A + B)'s 5`days' work `+(B +C)`s 2 day's work `+ C's 11`day's work = 1.
`5/12 + 2/16 + C's 11` day's work = 1
`C's 11` day's work = `11/24`
`C's 1` day's work  `= (11/24 xx 1/11)`
                              `= 1/24`.
`:.`C alone can finish it in 24 days.

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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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