Each of A, B, C and D need a umique
time to do a certain work. A can do the work in x days and B can
do the work in 2x days. A started the work and do it for `22 2/9` days
then he is replaced by B and B completed remaining work in same
time as C and D together can complete the whole work.
The ratio of the efficiency of C and D is `4: 5`. If C and D work for
alternative days starting form C then they can do the total work
in `44 1/2` days.

Options

A. `66 2/3`
B. `33 1/3`
C. `16 2/3`
D. `14 2/7`

Answer

(b)

Explanation

Let the C do in one day = 4y work
Let the D do in one day = 5y work
2 day work of ` C + D = 9y`
In 44 days they will complete `9yxx22 = 198 y`
In another 1/2 days 2y work will be done
C will take ` (200y)/4y" "days = 50`days
D will take ` = 40` days
C and D will complete work together in
`=(50xx40)/90 = 200/9`
According to condition
`200/(9x) + 200/(9xx 2x) = 1`
`(400 + 200)/18x = `
`rArr x = 33 1/3`