Question : A can do 75% of a job in 9 days and B can do half of the job in 8 days. If they work on it together then in how many days can they do half of the job?
Option 1: $\frac{40}{7}$
Option 2: $\frac{24}{7}$
Option 3: $\frac{7}{2}$
Option 4: $\frac{9}{2}$
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Correct Answer: $\frac{24}{7}$
Solution :
Given: A can do 75% of a job in 9 days and B can do half of the job in 8 days.
Let the total work be $a$ units.
So, work done by A in 1 day = $\frac{75a}{100}×\frac{1}{9}$ = $\frac{a}{12}$ units,
and work done by B in 1 day = $\frac{a}{2}×\frac{1}{8}$ = $\frac{a}{16}$ units.
Now work done by both in 1 day = $(\frac{a}{12}+\frac{a}{16})$ = $\frac{7a}{48}$ units.
Therefore, days required to do half of the work = $\frac{a}{2}÷\frac{7a}{48}$ = $\frac{a}{2}×\frac{48}{7a}$ = $\frac{24}{7}$ days
Hence, the correct answer is $\frac{24}{7}$.
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