Question : A can complete $\frac{2}{3}$ of a work in 4 days and B can complete $\frac{3}{5}$ of the work in 6 days. In how many days can both A and B together complete the work?
Option 1: $3$
Option 2: $2$
Option 3: $3\frac{3}{4}$
Option 4: $2\frac{7}{8}$
Correct Answer: $3\frac{3}{4}$
Solution :
Time taken by A alone to complete $\frac{2}{3}$ of a work = 4 days
Time taken by A alone to complete the work = $4 × \frac{3}{2}$ days = 6 days
⇒ Part of work done by A alone in a day = $\frac{1}{6}$
Time taken by B alone to complete $\frac{3}{5}$ of the work = 6 days
Time taken by B alone to complete the work = $6 ×\frac{5}{3}$ = 10 days
⇒ Part of work done by B alone in a day = $\frac{1}{10}$
Let the time taken by A and B together to complete the work = $x$
⇒ Part of work done by A and B in a day = $\frac{1}{x}$
⇒ $\frac{1}{6}$ + $\frac{1}{10}$ = $\frac{1}{x}$
⇒ $\frac{5+3}{30}$ = $\frac{1}{x}$
⇒ $x$ = $\frac{30}{8}$ = $\frac{15}{4}$ = $3 \frac{3}{4}$ days
Hence, the correct answer is $3\frac{3}{4}$.
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Get Updates Brochure
Your Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.
