Question : A can do a piece of work alone in 15 days, while B complete the same piece of work alone in 12 days. If they work on it together for 5 days, then the fraction of the work that will be left is:
Option 1: $\frac{3}{4}$
Option 2: $\frac{5}{8}$
Option 3: $\frac{1}{4}$
Option 4: $\frac{5}{7}$
Correct Answer: $\frac{1}{4}$
Solution :
Given,
A can do a piece of work = 15 days
B can do a piece of work = 12 days
A and B both work together = 5 days
Left work = total work – completed work
Let, Total Work = LCM of 15, 12 and 5 = 60
Total efficiency of A and B = $\frac{60}{15}+\frac{60}{12}$ = 4 + 5 = 9
Both A and B together work for 5 days
So, work completed in 5 days by A and B = 9 × 5 = 45
⇒ Remaining work = 60 – 45 = 15
⇒ The fraction of work left = $\frac{15}{60}$ = $\frac{1}{4}$
Hence, the correct answer is $\frac14$.
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