Question

Railneer is packaged in a water bottling plant, with the help of two machines $M_1$ and $M_2$. $M_1$ and $M_2$ produces 400 and 600 bottles per minute. One day's production can processed by $M_1$ operating alone for 9 hours, by $M_2$ operating alone for 6 hours or by both $M_1$ and $M_2$ operating simultaneously for 3 hours and 36 minutes. If one days production is processed by operating alone for $\frac{1}{3}$ of the time and $M_{1}and{M}_2$ simultaneously operating for $\frac{2}{3}$ of the time, then in how many hours total production of one day wiII be completed?

• A. 2
• B. 3
• C. 4.5
• D. 4.8

Answer 1

The correct option is C 4.5

One day's production = $400\times 9\times 60=2160000$ bottles per day Ratio of time utilised by $M_{1}and{M}_2=1:2$
Now, the production of bottles by $M_1$ in 1 minute = 400 and the production of bottles by $M_1$ and $M_2$ together in 2 minutes = 2000
Thus total 2400 bottles can be processed in 3 minutes
$\therefore$ 216000 bottles can be processed in $216000\times \frac{3}{2400}=4.5hours$