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10 Sep 2021, 21:27
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in one hour 1st machine will do 1/8 of work and 2nd machine will do 2/8 of work. When we add we get 3/8 both machine will do work in one hour, now we get that 8/3 will be the time taken for work done.
Now, time*rate = work; so we get
[Time]8/3*1/4[rate of machine 2] so we get 2/3 of the work done.
Now, time*rate = work; so we get
[Time]8/3*1/4[rate of machine 2] so we get 2/3 of the work done.
19 Sep 2022, 21:03
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Together rate is 3k/8
Question is asking us what % of work is done by the faster machine (which is Machine two)
Frame it this way, k/4 is what % of 3k/8?
Answer is 2/3 or 66.67.
D
Question is asking us what % of work is done by the faster machine (which is Machine two)
Frame it this way, k/4 is what % of 3k/8?
Answer is 2/3 or 66.67.
D
28 Feb 2025, 03:01
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Given:
- Working alone at its own constant rate, a machine seals k cartons in 8 hours. (say, Machine A)
- Working alone at its own constant rate, a second machine seals k cartons in 4 hours. (say, Machine B)
- The two machines, each working at its own rate and for the same time, together sealed some cartons.
To find: What percentage of the cartons were sealed by the machine working at the faster rate?
Solution:
We are interested in the machine that works at the faster rate. First, let’s find out which one this machine is.
- Machine A: k cartons in 8 hours
- Machine B: k cartons in 4 hours
Since machine B seals k cartons in less time than A, we can be sure that machine B is faster.
So, we need to find what percentage of the cartons A and B sealed together did B seal.
- We know that for a given Total Amount of Work, the Number of Workers is inversely proportional to the total Time spent doing that work.
- That is, for fixed Total Time, Rate of Work (R) ∝ Work (W).
- Hence, \(\frac{Rate-B}{Rate-A}\) = \(\frac{Work-B}{Work-A}\)
- Since Machine B takes half the time that machine A takes in doing the same work, \(\frac{Rate-B}{Rate-A}\) = \(\frac{2}{1}\).
- So, \(\frac{2}{1}\) = \(\frac{Work-B}{Work-A}\)
- If Total work = 3 units, then Work-B = 2 units and Work-A = 1 unit.
- Hence, Required percentage =\( \frac{2}{3}\) × 100 = \(66 \frac{2}{3}\%\)
Correct Answer: D
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