A and B can do a work in 30 days; B and C in 24 days; C and A in 20 days. They all work together for 10 days and then B and C leave. How many more days will A take to finish the remaining work?

Problem restatement
Derive individual rates from pairwise rates; compute remaining work after 10 days with all three; then time for A alone to finish.

Given data

• a + b = 1÷30
• b + c = 1÷24
• c + a = 1÷20

Concept/Approach
Sum equations to get a + b + c. Then subtract to get A’s rate. Use work = rate × time.

Step-by-step calculation
2(a + b + c) = 1÷30 + 1÷24 + 1÷20 = 1÷8 ⇒ a + b + c = 1÷16Work in first 10 days = 10 × 1÷16 = 5÷8Remaining work = 1 − 5÷8 = 3÷8A’s rate = (a + b + c) − (b + c) = 1÷16 − 1÷24 = 1÷48Time for A alone = (3÷8) ÷ (1÷48) = (3÷8) × 48 = 18 days

Verification/Alternative
Direct substitution confirms the arithmetic.

Common pitfalls
Forgetting that only A continues after Day 10; the question asks for additional days after B and C leave.

Final Answer
18 days