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Quantitative Aptitude :: Time and Work Problems And Answers

59. A can do a piece of work in 14 days which B alone can do in 21 days. They begin together but 3 days before the completion of the work, A leaves off. The total number of days for the work to be completed is 
A. 6 3/5 days  B. 8 ½ days
C. 10 1/5 days  D. 13 ½ days
Answer & Explanation

Answer: Option C

Explanation:
B’s 1 day’s work = 1/21
B’s 3 day’s work = 1/21 ×3 = 1/7 
The remaining work finished by both of them = 1 – 1/7 = 6/7 
Both together can finish it in 14 × 21/35 days = 42/5 days 
Their, 1 day’s work = 5/42 
Therefore, the No. of days taken by them together to finish 6/7 work 
                                                  = 6/7/5/42 = 6/7 × 42/5 =  36/5 = 7 1/5 days 
Therefore, the total No. of days for the work to be completed = 3 + 7 1/5 = 10 1/5 days.
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