A can do a piece of work in 14 days while B can do it in 21 days. They began together and worked at it for 6 days. Then, A fell ill and B had to complete the remaining work alone. In how many days was the work completed?
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A 1day work = 1/14
B 1day work = 1/21
(a+b) one day work = 1/14 + 1/21 = 5/42
both worked for six days = 5/42 * 6 = 5/7
b had completed the remaining work = 1-5/7 = 2/7
b had completed the work = 2/7 ÷ 1/21
= 2/7 * 21/1 = 6
total time taken =6+6 = 12
B 1day work = 1/21
(a+b) one day work = 1/14 + 1/21 = 5/42
both worked for six days = 5/42 * 6 = 5/7
b had completed the remaining work = 1-5/7 = 2/7
b had completed the work = 2/7 ÷ 1/21
= 2/7 * 21/1 = 6
total time taken =6+6 = 12
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