## nithiu 2 years ago '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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1. stgreen

'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)]]

2. stgreen

do calculations youself>>make yourself useful

3. Jas9420

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.

4. 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?

5. stgreen

oh right i didn't see that

6. nithiu

8/25+1/30=53/150

7. nithiu

1-53/150=97/150*30

8. Jas9420

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

9. nithiu

no ....

10. stgreen

if both work they take 14 days to finish

11. stgreen

so A left after 6 days

12. stgreen

'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)]]

13. stgreen

is it done now?

14. nithiu

1-8/25=17/25

15. stgreen

^what was that??

16. nithiu

a s work for 8 days

17. Jas9420

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.

18. 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 $30 (T-8) + 25 T= 750 \\ 55T = 990 \\ T= 18$