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Question:

Three machines, A, B and C can be used to produce a product. Machine A will take 60 hours to produce a million units. Machine B is twice as fast as Machine A. Machine C will take the same amount of time to produce a million units as A and B running together. How much time will be required to produce a million units if all the three machines are used simultaneously? (in hous)

Explanation:

B being twice as fast as A, will take half of time of A to produce a million units i.e. = 30 hrs.

Since, Machine C takes the same amount of time as A & B running together,

∴ $\frac{1}{C}$ = $\frac{1}{A}$ + $\frac{1}{B}$ or

$\frac{1}{A}$ + $\frac{1}{B}$ + $\frac{1}{C}$ = $\frac{2}{A}$ + $\frac{2}{B}$

⇒ $\frac{1}{A}$ + $\frac{1}{B}$ + $\frac{1}{C}$ = $2 (\frac{1}{A} + \frac{1}{B})$ = $2 (\frac{1}{60} + \frac{1}{30})$ = $\frac{1}{10}$

Hence, it will take 10 hours for all three of them to produce 1 million units.

Hence, option (b).

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