The number of days here is the unknown.

After some time, only 48 blue beads were left. This means all the red beads were taken out.

Since 4 red beads were taken out each day and 6 blue beads were taken out each day,

The ratio of red to blue beads taken out
= 4 : 6
= 2 : 3

This ratio stays the same regardless of how many days have passed.


So we can let the total number of red beads be 2 units.


When all the 2 units of red beads have been taken out, 3 units of blue beads have been taken out.

Then since there are twice as many blue as red beads,

Total number of blue beads = 2 units x 2 = 4 units.


Since 3 units of blue beads were taken out

Number of blue beads left
= 4 units - 3 units
= 1 unit


Since there are 48 blue beads left,

1 unit = 48 beads

Number of beads in the container at first

= 2 units + 4 units
= 6 units

= 6 × 48
= 288

What did not change :


① the total number of beads of each kind.
② the ratio of red beads to blue beads taken out

Thanks for your great help!

No problem