A and B together can complete a piece of work in 10 2\7 days white B and C together can complete the same work in 13 1\3 days. B is 25% more efficient than C. In how many days will A and C together complete the same work ?

Explanation:

B is 25 % more efficient than C.

∴ Ratio of time taken by B and C

= 100 : 125 = 4 : 5

Time taken by B = 4x days

Time taken by C = 5x days

∴ 1\4x+1\5x = 3\40

=> 5+4\\20x = 3\40

=> 9\20x = 3\40

=> 3\x = 1\2

=> x = 6

Time taken by B = 24 days

Time taken by C = 30 days

If the time taken by A be y days,

then

1\y+1\24 = 7\72

=> 1\y = 7\72−1\24 = 7−3 \ 72

= 4\72 = 1\18

∴ y = 18

∴ (A + C)’s 1 day’s work

= 1\18+frac130 = 5+3 \ 90

= 8\90 = 4\45

∴Time taken by A and C together

= 45\4 = 11 1\4 days