Y can do a work in 2/3 the time it takes x, z can do same work in 3/4 time it takes y. when all three are typing the same time what is the fraction of total work does y do ?

Time Taken by Y = (2 * 100) / 3
= 66.66 unit.

Time taken by Z = (3 * 66.66) / 4
= 50 unit.

Ratio of time of X, Y and Z = 100 : 66.66 : 50

Fraction of work Y do = 66.66 / (100 + 66.66 + 50)
= 0.307
= 4/13.