A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:
📊 Work and Time Calculation 📊
Let’s denote the time taken by A to complete the work as ‘x’ days.
Since B and C together can do the work in the same time as A, they can also do it in ‘x’ days.
A and B together can do the work in 10 days, so their combined work rate is 1/10.
C alone can do the work in 50 days, so C’s work rate is 1/50.
Now, let’s find the work rate of A and B:
A’s work rate + B’s work rate = 1/10
We know that A’s work rate = 1/x (since A can do the work in x days)
So, 1/x + B’s work rate = 1/10
Now, let’s find the work rate of B and C:
B’s work rate + C’s work rate = 1/x (since B and C together can do the work in x days)
We know that C’s work rate = 1/50
So, B’s work rate + 1/50 = 1/x
Now, we have two equations:
1/x + B’s work rate = 1/10
B’s work rate + 1/50 = 1/x
Solve these equations to find x and B’s work rate.
After solving, we get x = 20 days (time taken by A) and B’s work rate = 1/20.
Time taken by B alone = 1 / B’s work rate
= 1 / (1/20)
= 20 days
🎉 B alone could do the work in 20 days. 📊
