A can do a job in 20 days. A works alone for 4 days, then B joins and together they finish the rest in 6 days. How long would B take alone?
SHORT ANSWER
12 days. A works all 10 days and does 10/20 = half the job. B does the other half in 6 days, so B alone would need 12 days.
Explain it simply
Track each person's own working days separately. A was there from start to finish, 4 + 6 = 10 days. B was there only for the last 6 days. Work done by each person is their rate times their own days. The two pieces add up to one whole job.
Example
Question: A alone takes 20 days. A works 4 days alone, then A + B finish in 6 more days. B alone?
- A works 4 + 6 = 10 days in total. A's work = 10/20 = 1/2.
- B's work = 1 - 1/2 = 1/2, done in 6 days.
- B alone = 6 x 2 = 12 days.
Check with units: total 60 units. A does 3 a day, B does 5 a day. A's 4 days alone = 12 units. Then 6 days together at 8 a day = 48 units. Total 60.
js
const total = 60, a = total / 20;
const bWork = total - a * 10;
console.log(6 * (total / bWork)); // Output: 12
console.log(a * 4 + (a + 5) * 6); // Output: 60What to say in the interview
"I count each person's own days. A works all 10 days and finishes half. B does the other half in 6 days, so B alone takes 12."
Common mistakes
- Counting only 4 days for A.
- Assuming B's 6 days produced the remaining work alone.