**Concept: The question tests on the application of Rates(Time and Work)**

**Solution:**

LCM of 9,3,4 = 36

=> Let the total work be of 36 units

=>Efficiency of X = 36/9 = 4 units/hr

Since it has worked alone for 3 hrs, the units of work completed by X alone = 4*3=12 units

Remaining units/Units completed by both X and Y = 36-12 = 24 units and this must have been completed in 4hrs by X and Y together.

=> Every hour 24/4

= 6 units are produced every hour.

Efficiency of X being 4 units/hr, Y must be producing 6-4

= 2units/hr (This is Y's efficiency)

=>36 units of work Y alone wll take 36/2

= 18 hrs.