Question: A machine puts c caps on the bottles in m minutes. How many hours it take to put caps on b bottles?

1. \(\frac{60bm}{c}\)
2. \(\frac{bm}{60c}\)
3. \(\frac{bc}{60m}\)
4. \(\frac{60b}{cm}\)
5. \(\frac{b}{60cm}\)

“A machine puts c caps on the bottles in m minutes. How many hours it take to put caps on b bottles?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution (1):

A machine puts c caps on bottles in m minutes

The rate of the machine is \(rate=\frac{job}{time}=\frac{cap}{minute}=\frac{c}{m}=\frac{bm}{60c} hours\)

Correct Answer: B

Approach Solution (2):

Either we can fix it with help of a small formula that is:
\(\frac{M1*D1*H1}{W1}=\frac{M2*D2*H2}{W2}\)

Where M, D and H stands for Men, Days and Hours invested for each of the 2 works respectively.

So here it goes:

M1 = 1 (as we are not given the value)

D1 = \(\frac{m}{60}\) (in hours)
H1 = 1 (as we are not given the value) and
W1 = C

And

M2 = 1 ( as we are not given the value)
D2 = x (in hours) (to be found out)
H2 = 1 (as we are not given the value) and
W2 = b (as given)

So, \(\frac{\frac{1*m*1}{60}}c=\frac{1*m*1}{b}\)

\(\frac{m}{\frac {60} c}=\frac{x}{b}\)

Therefore, \(x=\frac{bm}{60c}\)

Correct Answer: B

Approach Solution (3):

A machine puts c caps on the bottles in m minutes

So, the machine puts 1 cap in \(\frac{m}{c}\) minutes

To put caps on b bottles, the machine will take bm/c minutes

In order to calculate the no. of hours taken, divide the product by 60

Correct Answer: B

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