Time & Work, General Mathematics

Question: A certain number of men complete a piece of work in 60 days. If there were 8 men more, the work could be finished in 10 days less. How man were originally there ?
A
`30`

B
`32`

C
`36`

D
`40`

Note: solution: Originally, let there be `X`men. More men, Less days `:. (x + 8) : x :: 60 :50` So, `x + 8/x = 60/50` or `x = 40`. Hence, there were `40` men, originally.
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Question: The rates of working of A and B are in the ratio 5 : 6. The number of days taken by them to finish the work are in the ratio :
A
`5 : 6`

B
`25 : 36`

C
`6 : 5`

D
None of these

Note: solution: Ratio of number of days `= 1/5 : 1/6` `= 6 : 5`.
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Question: If 1 man or 2 women or 3 boys can do a piece of work in 44 days, then the same piece of work will be done by 1 man, 1 woman and 1 boy in :
A
`21` days

B
`24` days

C
`26` days

D
`33` days

Note: solution: `1` woman `-= 1/2` man `& 1` boy `-= 1/3` man. `:.`(1 man + 1 woman + 1 boy) `-= (1 + 1/2 + 1/3)` men Now, 1 man can do the work in `44` days `:. 11/6` men can do it in `(44 xx 6/11)` `= 24` days.
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Question: 8 men can dig a pit in 20 days. If a man works half as much again as a boy, then 4 men and 9 boys can dig a similar pit in :
A
`10` days

B
`12` days

C
`15` days

D
`16` days

Note: solution: `1` man `-= 3/2` boys. So, (`4` men `+ 9` boys )`-= 15` boys. Also, `8` men `-= (3/2 xx 8)` boys `= 12` boys. More boys, less days. `15 : 12 :: 20 : x` `:. x = ((12 xx 20)/15)` `= 16`.
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Question: A does half as much work as B and C does half as much work as A and B together. If C alone can finish the work in 40 days, then together all will finish the work in :
A
`13 1/3` days

B
`15` days

C
`20` days

D
`30` days

Note: solution: `C`alone can finish the work in `40` days. `:. (A + B)` can do it in `20` days. `:. (A + B)'s 1` day's work `= 1/20`. `A's 1` day's work : `B's 1` day's work `= 1/2 : 1` `= 1 : 2`. `:. A's 1` day's work `= (1/20 xx 1/3)` `= 1/60`. [Divide `1/20` in the ratio 1 : 2] `B's 1` day's work `= (1/20 xx 2/3)` `= 1/30`. `(A + B + C)'s 1` day's work `= (1/60 + 1/30 + 1/40)` `= 9/120` `=3/40`. `:.` All the three together will finish it in `40/3` `=13 1/3` days.
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Question: A and B can separately do a piece of work in 20 and 15 days respectively. They worked together for 6 days, after which B was replaced by C. If the work was finished in next 4 days, then the number of days in which C alone could do the work will be :
A
`60`

B
`40`

C
`35`

D
`30`

Note: solution: `(A + B)'s 6` day's work `= 6(1/20 + 1/15)` `= 7/10`. `(A + C)'s 4` day's work `= 3/10`. `(A + C)'s 1` day's work `= 3/40` `A's 1` day's work `= 1/20` `:. C's 1` day's work `=(3/40 - 1/20)` `=1/40`. Hence, C alone can finish the work in `40` days.
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Question: A, B and C can do a piece of work in 36, 54 and 72 days respectively. They started the work but A left 8 days before the completion of the work while B left 12 days before the completion. The number of days for which C worked is :
A
`4`

B
`8`

C
`12`

D
`24`

Note: solution: Suppose the work was finished in `x` days. Then A's `(x - 8)` day's work `+ B's (x - 12)` day's work `+ C's x` day's work `= 1` `(x - 8)/36 + (x - 12)/54 + x/72 = 1 iff 6(x - 8) + 4(x - 12) + 3x = 216` `:. 13x = 312 iff x = 24`.
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Question: A certain number of men complete a piece of work in 60 days. If there were 8 men more, the work could be finished in 10 days less. How man were originally there ?

Question: The rates of working of A and B are in the ratio 5 : 6. The number of days taken by them to finish the work are in the ratio :

Question: If 1 man or 2 women or 3 boys can do a piece of work in 44 days, then the same piece of work will be done by 1 man, 1 woman and 1 boy in :

Question: 8 men can dig a pit in 20 days. If a man works half as much again as a boy, then 4 men and 9 boys can dig a similar pit in :

Question: A does half as much work as B and C does half as much work as A and B together. If C alone can finish the work in 40 days, then together all will finish the work in :

Question: A and B can separately do a piece of work in 20 and 15 days respectively. They worked together for 6 days, after which B was replaced by C. If the work was finished in next 4 days, then the number of days in which C alone could do the work will be :

Question: A, B and C can do a piece of work in 36, 54 and 72 days respectively. They started the work but A left 8 days before the completion of the work while B left 12 days before the completion. The number of days for which C worked is :