A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
📊 Work and Time Calculation 📊
A’s work rate = 1/4 (work done per hour)
B and C’s combined work rate = 1/3 (work done per hour)
A and C’s combined work rate = 1/2 (work done per hour)
Let’s find C’s work rate:
A and C’s combined work rate = A’s work rate + C’s work rate
1/2 = 1/4 + C’s work rate
C’s work rate = 1/2 – 1/4
= 1/4
Now, find B’s work rate:
B and C’s combined work rate = B’s work rate + C’s work rate
1/3 = B’s work rate + 1/4
B’s work rate = 1/3 – 1/4
= (4/12) – (3/12)
= 1/12
Time taken by B alone = 1 / B’s work rate
= 1 / (1/12)
= 12 hours
🎉 B alone will take 12 hours to do the work. 📊
