Rate and Time question (Help needed)

In a store room, one group of staff members fill the store with boxes and the other group of staff take the boxes from the store and supply them to the market. The boxes are stored at the rate of 5 boxes per hour whereas they are supplied at the rate of 3 boxes per hour. If the room is 1/4 filled with 60 boxes, in how many hours it will be 2/3 filled?​

A.) 20 hours
B.) 30 hours
C.) 50 hours
D.) 80 hours
E.) 120 hours

(Answer given is C but I highly doubt it. So, any help is appreciated.)

Here’s how I solved it [Please correct me if any mistakes :slight_smile:] -

Rate of storing = 5 boxes per hr
Rate of supplying = 3 boxes per hr
No. of boxes in the room at 1 hr = 5 - 3 = 2 boxes

Rate = 2 boxes per hr

\frac{1}4 of the room = 60 boxes
Total capacity of the room = 60 x 4 = 240 boxes

So, \frac{2}3 of the room = 240 x \frac{2}3 = 160 boxes

We should fill the room with 160 boxes. But 60 boxes are already present.

Boxes left to be filled = 160 - 60 = 100

At the rate of 2 boxes per hr, 100 boxes would take 100/2 = 50 hours.

Ans: C

1 Like

Thank you. Now I know where I went wrong. So, 1/4 is included in 2/3? @Karishma .

Yes. In case you ignore the fact that 60 boxes are present already, the answer would have been D 80hrs.
160/2 = 80hrs.

1 Like

Got it. Thanks

1 Like