Data Sufficiency

Hello,

Can you please help tell me if my approach here is correct for Stmnts. 1 and 2?

Machines X and Y produced identical bottles at different constant rates. Machines X. operating alone of 4 hours, filled part of a production lot; then Machine Y, operating alone for 3 hours, filled the rest of this lot.

How many hours would it have taken Machine X operating alone to fill the entire production lot?
1. Machine X produced 30 bottles per minute.
2. Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.

OA: B

1) Machine X produced 30 bottles per minute = 1800 bottles per hour. Hence, in 4 hours Machine X produces 1800 x 4 = 7200 bottles. However, we don't know how many bottles Machine Y produces in 3 hours. Hence, in-sufficient.


2)

Rate x Time = Work

X: r1 x 4 = 4r1
Y: r2 x 3 = 3r2

Given, 4r1 = 2(3r2)
=> 4r1 = 6r2
=> r1 = (6/4)r2
=> r1 = (3/2)r2

Rate x Time = Work
X: (3/2)r2 x 4 = 6r2
Y: r2 x 3 = 3r2

So,
X: (3/2)r2 x ? = 9r2

On solving, we get t = 6 hours. Hence, Sufficient.

Is this approach correct?

Thanks a lot.

Regards,
Sri