A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?
📊 Work and Time Calculation 📊
All three work together for 10 days, completing:
10 days × (1/16) = 10/16 = 5/8 of the work
Remaining work = 1 – 5/8 = 3/8 of the work
To find A’s work rate, let’s analyze the given information:
A and B’s combined work rate = 1/30 (work done per day)
B and C’s combined work rate = 1/24 (work done per day)
C and A’s combined work rate = 1/20 (work done per day)
Adding the equations, we get:
2(A + B + C)’s combined work rate = 1/30 + 1/24 + 1/20
= (4 + 5 + 6) / 120
= 15/120
= 1/8
(A + B + C)’s combined work rate = 1/16 (work done per day)
Now, let’s find A’s work rate:
A’s work rate + B’s work rate = 1/30
A’s work rate + C’s work rate = 1/20
Subtracting the equations, we get:
(C’s work rate – B’s work rate) = 1/20 – 1/30
= (3 – 2) / 60
= 1/60
Now, add the equations:
2A’s work rate + (B’s work rate + C’s work rate) = 1/30 + 1/20
2A’s work rate + 1/24 = 1/30 + 1/20
2A’s work rate = 1/30 + 1/20 – 1/24
= (4 + 6 – 5) / 120
= 5/120
= 1/24
A’s work rate = 1/48 (work done per day)
Time taken by A to complete the remaining work = Remaining work / A’s work rate
= (3/8) / (1/48)
= 3/8 × 48
= 18 days
🎉 A will take 18 days to finish the remaining work. 📊
