A can do a piece of work in 16 days. B can do the same work in 24 days. A started the work alone. After how many days should B join him, so that the work is finished in 10 days?

Given:

A can do the work in 16 days (A's work rate = 1/16)

B can do the work in 24 days (B's work rate = 1/24)

A starts the work alone.

Let "x" be the number of days A works alone before B joins.

In "x" days, A completes a fraction of the work equal to (x/16).

When B joins, they work together for (10 - x) days to complete the remaining work.

The combined work rate of A and B is (1/16 + 1/24) = (3/48 + 2/48) = 5/48.

Now, we can set up the equation based on the work done:

(x/16) + (5/48) × (10 - x) = 1 (the entire work is 1)

Let's solve for "x":

(x/16) + (5/48) × (10 - x) = 1

3x + 5(10 - x) = 48

3x + 50 - 5x = 48

-2x + 50 = 48

-2x = 48 - 50

-2x = -2

x = (-2)/(-2)

x = 1

So, A works alone for 1 day before B joins to finish the work in 10 days.