Single correct option
A is thrice as efficient as B, and working together they can complete a job in 12 days. B starts the job alone and works for 8 days, after which A joins him and they finish the remaining work together. In how many days, from the start, is the job completed?
- A. 16
- B. 18
- C. 20
- D. 22
Show answer and solution
Answer: (B) 18
Let B's rate = r, so A's rate = 3r. Together: 4r = 1/12 ⇒ r = 1/48.
So B alone would take 48 days, and A alone would take 16 days.
In the first 8 days, B alone does 8 × (1/48) = 1/6 of the job, leaving 5/6.
Once A joins, their combined rate is again 4r = 1/12 per day, so the remaining 5/6 takes (5/6) ÷ (1/12) = 10 days.
Total time = 8 + 10 = 18 days.
Tip: the combined rate after A joins is the same 'together' rate given at the start — no need to recompute it.
So B alone would take 48 days, and A alone would take 16 days.
In the first 8 days, B alone does 8 × (1/48) = 1/6 of the job, leaving 5/6.
Once A joins, their combined rate is again 4r = 1/12 per day, so the remaining 5/6 takes (5/6) ÷ (1/12) = 10 days.
Total time = 8 + 10 = 18 days.
Tip: the combined rate after A joins is the same 'together' rate given at the start — no need to recompute it.
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