X can finish a job in 20 days; Y can finish it in 12 days. X works alone for 4 days, then Y joins and both work together till completion. How long does the entire job take?

Problem restatement
Compute the total duration when a faster worker joins after a head start by another worker.

Given data

• X's time = 20 days → rate x = 1/20 job/day.
• Y's time = 12 days → rate y = 1/12 job/day.
• X works alone for first 4 days.

Concept/Approach
Use work done = rate × time. After the initial phase, compute the remaining work and divide by the combined rate.

Step-by-step calculation
Work done by X in 4 days = 4 × (1/20) = 1/5 Remaining work = 1 − 1/5 = 4/5 Combined rate (X + Y) = 1/20 + 1/12 = (3 + 5)/60 = 8/60 = 2/15 per day Time for remaining = (4/5) ÷ (2/15) = (4/5) × (15/2) = 6 days Total duration = 4 + 6 = 10 days

Verification/Alternative
Check total work: X alone contributed 1/5; together for 6 days contributed 6 × (2/15) = 12/15 = 4/5. Sum = 1 (complete).

Common pitfalls

• Adding times instead of computing remaining work with rates.

Final Answer
10 days