Question

Ram and Shyam together can do a piece of work in 20 days while Shyam and Kishore can do it in 15 days while Ram and Kishore take 12 days to complete the same piece of work calculate the number of days each person will take to finish a work by working alone

Answer 1

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Answer 2

Answer:

Number of days taken by each people is as follows

Ram = 20 days

Shyam = 60 days

Kishore = 30 days

Step-by-step explanation:

Given, Ram(R) and Shyam(S) together can do a piece of work in 20 days, Shyam and Kishore(K) can do it in 15 days, Ram and Kishore take 12 days

To find: number of days taken by each person to finish the work by working alone

R+S= 20 (3 units)

S+K= 15  (4 units)

K+R= 12 (5 units)

LCM of 12, 15, 20 is 60

5+4+3 = 12 units

2R+ 2S+ 2K will complete 12 units of work

so R+ S+ K will complete only 6 units of the work

and S+ K will complete 4 units of work

So, Ram can complete 2 units of work in one day

So, the number of days required by Ram to complete work = $\frac{60}{2}$ = 30 days

Similarly, R+ S+ K = 6 and K+R = 5

⇒ S = 1 unit in one day

thus to complete 60 units, Shyam will take 60 days

And:  R+ S+ K = 6 and R+S= 3

⇒ K = 3 units in one day

Thus, Kishore will take $\frac{60}{3}$ = 30 days to complete the work if he work alone

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