Mike, Tom, and Walt are working as sales agents for an insurance company. Previous month relationship between their commissions was \(\frac{MT}{6}=W\), where \(M\), \(T\), and \(W\) are the commissions received by Mike, Tom, and Walt respectively. If this month, Mike's commission is 60% more than previous month and Tom's commission is 50% less than previous month, then how much should Walt's commission change compared to the previous month to ensure that the relationship between their commissions remains the same?

A. Decrease by 12.5%
B. Decrease by 20%
C. Decrease by 22.5%
D. Increase by 12.5%
E. Increase by 15%

M06-36

1.6M X 0.5 T = 0.8MT=0.8 W/6 ==> hence W shud decrease sales by 20% so that the relation remains intact

I believe this is the same question that has already been answered. But here's my take:

MT = W/6 => 6MT = W (1)

1.6M * 0.5T = Wx/6
0.8MT = Wx/6
4.8MT = Wx (2)

Comparing (1) and (2):

(1) 6MT = W
(2) 4.8MT = Wx

Since 4.8 is 4/5 of 6, x would need to be 4/5 for the equation to hold. Therefore, W needs to decrease by 20%, or answer choice B, for the equation to remain intact.

It is given that: MT = W/6....eq(1)

Now, M 's sales increased by 60 percent, whereas that of T decreased by 50 %.

Thus, Mnew= 1.6M, and Tnew = 0.5T. So, now lets assume that we increase or decrease W by X%. As the equation is still valid, we can represent it as:

1.6M * 0.5T = [ W (1 + X/100) ] / 6 ....where X is the percent increase or decrease

We can further simplify this as,
0.8MT = [W (1 + X/100) ] / 6 ]
From eq 1, however, W = 6MT
So,
0.8MT = [W (1 + X/100) ] / 6 ] => 0.8MT = [6MT (1+ X/100)] / 6
Further simplifying,

0.8MT/6MT * 6 = (1 + X/100) => (1 + X/100) = 0.8 => X/100 = -0.2 => X = -20 => Answer Choice B

Thus, we need to reduce W by 20% in order to maintain the equation. I have listed all the steps to clarify, otherwise the problem could be solved much faster.

Simplifying the condition:

mt = 6w

6 is a constant; for the sake of the required calculation, it can be ignored.

mt = w ............... (1)

60% increase in m, 50% decrease in t

\(\frac{160}{100} m * \frac{50}{100} t = w\)

\(mt = \frac{100}{80} w\) .................. (2)

By comparing (1) & (2), increase in\(w = \frac{100}{80} - 1 = \frac{20}{80}\)

Required decrease = 20%

Answer = B
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