Question

Machines $A$ and $B$ produce $8,000$ clips in $4$ hr and $6$ hr respectively. If they work alternately for $1$ hr A starting first, then the $8,000$ clips will be produced in:

• A. $4.33$ hr
• B. $5.66$ hr
• C. $5.33$ hr
• D. $4.66$ hr

Answer 1

The correct option is D $4.66$ hr

(A+B)'s 2 hour's work$=(\frac{1}{4}+\frac{1}{6})=\frac{5}{12}$

(A+B)'s 4 hour's work$=\frac{5}{12}\times 2=\frac{5}{6}$

Remaining work$=1-\frac{5}{6}=\frac{1}{6}$

Now it is a's turn

$\because \frac{1}{4}$work by A in=1 hours

$\therefore \frac{1}{6}$ work done by A in $=4\times \frac{1}{6}=\frac{2}{3}hours$

$\therefore$ total time taken$=4\frac{2}{3}=4.66hours$