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There are 4 machines with the same work rate. If it took kk

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There are 4 machines with the same work rate. If it took kk

by BTGmoderatorAT » Thu Mar 01, 2018 6:51 am
There are 4 machines with the same work rate. If it took kk hours for 3 machines to work and did k−2k−2 hours for 4 machines when working together, what is the value of kk?

A. 4
B. 5
C. 6
D. 7
E. 8

Is there a strategic approach to this question? Can any experts help?
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TTT

by deloitte247 » Sat Mar 03, 2018 1:18 pm
The workrate of a mixture has inverse proportion
$$i.eAmount\ of\ workdone\ (W)=\frac{1}{time\ taken\ \left(T\right)}$$
$$or\ \frac{W1}{W2}=\frac{T2}{T1}$$
Let the amount of workdone by a machine be x.
Therefore, three machines do 3x work in the same time and four machines do 4x work.
$$=>\frac{3x}{4x}=\frac{k-2}{k}$$
$$or\ \frac{3}{4}=\frac{k-2}{k}$$
$$Cross\ multiply$$
$$we\ have,\ 4k-8=3k$$
$$k=8$$
Hence the correct option is e
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