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Ram completed a piece of work in 10 days. When the work was extended by 75%, Ram reduced his speed to (1/ A) times for the extended work. For the same extended work only, Ravi took (3.2B) days. If they worked together to finish the initial work (excluding extended work), they would take 480/47 days and 160/21 days if Ram worked at his slower and faster speeds respectively, during his entire work. Then A + B = ? (Take A & B upto two decimal places)

[Question in figure ] (https://i.stack.imgur.com/jMnIh.png)

Devesh Pandey
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1 Answers1

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At his normal pace, the ram does $1$ Job in $10$ Days. That is, it works at $0.1$ Jobs/Day. At its slower pace, it does $0.1 / A$ Jobs/Day.

On the other hand, Ravi completes $0.75$ Jobs in the space of $3.2B$ Days, so he works $0.75 / (3.2B) = 0.234375 / B$ Jobs/Day.

If Ravi and the Ram cooperate, the Ram working at his faster pace (assuming the jobs can be parallelised perfectly), then they complete jobs at $0.1 + 0.234375 / B$ Jobs/Day. So, to complete one Job, it will take $$\frac{1}{0.1 + 0.234375 / B} \text{ Days}.$$ Thus, we have \begin{align*} \frac{160}{21} = \frac{1}{0.1 + 0.234375 / B} &\iff \frac{21}{160} = 0.1 + \frac{0.234375}{B} \\ &\iff \frac{0.234375}{B} = \frac{21}{160} - \frac{1}{10} = \frac{5}{160} = \frac{1}{32} \\ &\iff B = 32 \cdot 0.234375 = 32 \cdot \frac{0.75}{3.2} = 7.5. \end{align*} Now, use the corresponding data where the Ram works at a slower pace to figure out $A$.

Theo Bendit
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