Math Question

[Dencology]

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Question: Rama is able to do a job in 10 days working alone and Anil is able to do the same job in 20 days, working alone

(i). How long will they take to do the job if both of them work together ?
this is just 10*20/30 = 20/3

but how do you do the next one?

(ii)If they work alternately How many days it would take to complete the job (provided Rama starts)?

 

[godzilla0120]

13 days
7 days for Rama
6 days for Anil

x/10 + y/20 = 1

x = number of days Rama works
y = number of days Anil works

hence there are two variables, you need two equations.

here is the part when it gets tricky.
since you know they alternate between the days.
so either x = y or x = y +1 (Rama starts working first)

x = y does not work because it turns out to be a fraction
so it has to be x = y + 1 for the second equation

don't know if this kind of logic helps or not.

 

[Streetwolf]

Question: Rama is able to do a job in 10 days working alone and Anil is able to do the same job in 20 days, working alone

(i). How long will they take to do the job if both of them work together ?
this is just 10*20/30 = 20/3

but how do you do the next one?

(ii)If they work alternately How many days it would take to complete the job (provided Rama starts)?

Every 2 days they cycle and do 1/10 + 1/20 = 3/20 amount of work. So it takes 20/3 = 6 and 1/3 cycles of 2 to finish. So after 6 full cycles there is 1/10 of the work left which would be Rama's part. That means Rama does 7 days and Anil does 6.

 

[Dencology]

hey, i don't understand your explaniation, would you explain it in a different way, i mean i don't understand how you got from 3/20 to 20/3 and where did you get 6?

 

[Streetwolf]

hey, i don't understand your explaniation, would you explain it in a different way, i mean i don't understand how you got from 3/20 to 20/3 and where did you get 6?

In 2 days (1 cycle) they do 3/20 of the job. How long does it take to do the full job (1 job)? Their rate is 3/20 job/cycle * 'x' cycles = 1 job. Solve for x and you get 1 / (3/20) which is 20/3 cycles. As a shortcut, if you have the time it takes to do a portion of the job and you want to know how long to do the full job, you just take the reciprocal of the rate they do the job to get the answer.

20/3 cycles is 6 and 1/3 cycles. As I stated in the other post, 1 cycle = the first person doing work on the first day and the second person doing work on the following day. Then it repeats. Since you need to go through 6 and 1/3 cycles to finish the job fully, you could do 6 full cycles which would be 12 days. Since each cycle does 3/20 of the work, 6 cycles does 18/20 = 9/10 of the work. That means you need to do 1/10 of the work after 6 full cycles (12 days). Since the first person to do work each cycle does 1/10 of the work per day, that would finish the job. So it takes the first person 7 days and the second person 6 days.