Question : A and B can do a job in 10 days and 5 days, respectively. They worked together for two days, after which B was replaced by C and the work was finished in the next three days. How long will C alone take to finish 40% of the job?
Option 1: 18 days
Option 2: 12 days
Option 3: 15 days
Option 4: 10 days
Correct Answer: 12 days
Solution :
Total Work = Least Common Multiple of 10 and 5 = 10
Efficiency of A = $\frac{10}{10}$ = 1 unit/day
Efficiency of B = $\frac{10}{5}$ = 2 units/day
A and B work for 2 days = (1 + 2) × 2 units = 6 units
Remaining work = (10 – 6) units = 4 units
A and C can complete the remaining work in 3 days
A and C one day work = $\frac{4}{3}$
C one day work = $\frac{4}{3}-1$ = $\frac{1}{3}$
C can complete 40% of work with efficiency of $\frac{1}{3}$ = $\frac{\frac{40}{100}\times10}{\frac{1}{3}}$
= 12 days
Hence, the correct answer is 12 days.
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