Machines M and N produce identical widgets but at different constant rates. Machine M takes 10 hours to produce 1000 widgets and Machines M and N together take 6 hours and 40 minutes to produce 2000 widgets. How much time does Machine N take to produce 3000 widgets?a)3 hoursb)5 hoursc)9 hoursd)10 hourse)15 hoursCorrect answer is option 'E'. Can you explain this answer?

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Machines M and N produce identical widgets but at different constant rates. Machine M takes 10 hours to produce 1000 widgets and Machines M and N together take 6 hours and 40 minutes to produce 2000 widgets. How much time does Machine N take to produce 3000 widgets?

a)
3 hours
b)
5 hours
c)
9 hours
d)
10 hours
e)
15 hours

Correct answer is option 'E'. Can you explain this answer?

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Test: Time And Work- 2

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Machines M and N produce identical widgets but at different constant r...

Given:

Let rate of machine N be n widgets per hour and let the rate of Machine M be m widgets per hour
m ≠ n
Number of widgets produced by M in 10 hours = 1000
Number of widgets produced by M and N together in 6 hours 40 minutes = 2000

To Find: Time taken by N to produce 3000 widgets

Approach:

So, to answer the question, we need to know the value of n

2. We are given the Combined output of M and N in 6 hours 40 minutes. From this piece of information, we can find the combined Rate of M and N

a. Combined Rate of M and N = m + n
b. So, n = (Combined Rate of M and N) – m
c. Therefore, we need to find not only the Combined Rate of M and N, but also the value of m

3. We’re given the output of M alone in 10 hours. From this piece of information, we can find the value of m.

Working out:

Finding the Combined Rate of M and N

Finding n
- n = (300 – 100) widgets per hour = 200 widgets per hour

Looking at the answer choices, we see that the correct answer is Option E

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