A,B,and C can reap a field in `15^(3/4)` days; B,C and D in 14 days; C,D and A in 18 days; D,A and B in 21 days. In what time can A,B,C and D together reap it?

Explanation

A, B and C can reap the field in = `15 3/4` days
= `63/4` days
(A, B and C)’s 1 day work =`1/(63/4)`
= `4/63`
B, C and D can reap the field in = `14 `days
B, C and D’s 1 day work = `1/14`
C, D and A can reap the field in = 18 days
C, D and A’s `1` day work = `1/18`
D, A and B can reap the field in = `21` days
D, A and B’s 1 day work = `1/24 `
Now adding (A+B+C+D), `3[A+B+C+D] `= `4/63 + 1/14 + 1/18 + 1/21`
= `(8+9+7+6)/126`
= `30/126 `
=` 5/21`
`(A+B+C+D) = 5/(21xx3) `
=` 5/63`
`therefore` A, B, C and D together can reap the field in = `1/(5/63) = 63/5 = 12 3/5 days`.