'A' and 'B' can do a piece of work in 25 days and 30 days respectively. Both start the work together but 'A' leaves the work 8 days before its completion. Find the time in which the work is finished.

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- anonymous

'A' can do 1/25 job per day
'B' can do 1/30 job per day
part of job done in 8 days=8(1/25 + 1/30)
part of job done in rest of days (by 'B' alone)=1-[8(1/25 + 1/30)]
days consumed to finish job by 'B'=(1/25)*[1-[8(1/25 + 1/30)]]
total days to finish job=8+(1/25)*[1-[8(1/25 + 1/30)]]

- anonymous

do calculations youself>>make yourself useful

- anonymous

Now, the time taken by A and B to complete 22/30th work is \[\frac{ 22 }{ 30 }\times \frac{ 210 }{ 11}\]
And for the total, number of days, you'll have to add an 8 it.

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## More answers

- sasogeek

stgreen, A leaves the job 8 days BEFORE COMPLETION.... not 8 days after they began.... so that's how long they would've taken to finish minus 8... correct?

- anonymous

oh right i didn't see that

- anonymous

8/25+1/30=53/150

- anonymous

1-53/150=97/150*30

- anonymous

It's 14 + 8 = 22 days, I think.

- anonymous

no ....

- anonymous

if both work they take 14 days to finish

- anonymous

so A left after 6 days

- anonymous

'A' can do 1/25 job per day
'B' can do 1/30 job per day
part of job done in 6 days=6(1/25 + 1/30)
part of job done in rest of days (by 'B' alone)=1-[6(1/25 + 1/30)]
days consumed to finish job by 'B'=(1/25)*[1-[6(1/25 + 1/30)]]
total days to finish job=6+(1/25)*[1-[6(1/25 + 1/30)]]

- anonymous

is it done now?

- anonymous

1-8/25=17/25

- anonymous

^what was that??

- anonymous

a s work for 8 days

- anonymous

Oh, now I get it.
No. of days A and B take to do 1 work: 1/25 + 1/ 30 = 11/ 150= 150/11
In one day, B can do : 8/30th of work.
So, the remaining work is done by both A and B. The remaining work is : 22/30
Now, the time taken by A and B to complete 22/30th work is :\[ \frac{ 22 }{ 30 } \times \frac{ 150 }{ 11 } = 10 days.\]
So, total = 10 + 8 = 18 days.

- phi

I would use rate * time = "distance" or in this case
\[ \frac{\text{jobs}}{\text{day}}\cdot { \text{days} }= \text{# of jobs} \]
let T = total number of days for the job. B works for all T days, A works for T-8 days
we have
\[ \frac{1}{25} \cdot (T-8) + \frac{1}{30} T = 1 \]
multiply both sides by 30*25 to "clear" the denominators
\[ 30 (T-8) + 25 T= 750 \\ 55T = 990 \\ T= 18 \]

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