Mike, Tom, and Walt are working as sales agents for an insurance compa

Mike, Tom, and Walt are working as sales agents for an insurance company, and the commissions they receive can be expressed by the following formula: MT=W/6 . If Mike sells 60% more this month and Tom decreases his sales by 50%, how should Walt's performance change to ensure that the above relationship is true ?

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.

Please tell me the official answer

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.

Lost
shouldnt any change in MT be 6 times that of W?

\(MT/6=W\)

\(0.8MT=6W\)

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

(8/5)(1/2)*(MT/6)=x*W <-> x=(4/5)

->20% decrease

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