Question : A can finish a work in 7 days. B can finish the same work in 9 days. The number of days required to finish the same work by both of them together is:
Option 1: $1\frac{15}{16}$
Option 2: $2\frac{15}{16}$
Option 3: $3\frac{15}{16}$
Option 4: $4\frac{15}{16}$
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Correct Answer: $3\frac{15}{16}$
Solution :
Given: A can finish a work in 7 days. B can finish the same work in 9 days.
LCM of 7 and 9 = 63
Let total work = 63 units
Now A's efficiency $=\frac{63}{7}=9$ units
B's efficiency $=\frac{63}{9}=7$ units
Total efficiency = (9 + 7) = 16 units
So, The number of days required to finish the same work by both of them together is
= $\frac{\text{Total Work}}{\text{Total Efficiency}}=\frac{63}{16}=3\frac{15}{16}$ days
Hence, the correct answer is $3\frac{15}{16}$.
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