Laser diodes and micro-controllers are among the components used to ma

Laser diodes and micro-controllers are among the components used to make a tracking system. During the past year, the cost of a laser diode (L) increased by x percent, and the cost of a micro-controller (M) decreased by y percent. If a tracking system is assembled using equal numbers of diodes and micro-controllers, and the cost of all other components remained the same during the past year, then the cost of a tracking system changed by what percent?

Tracking system cost (TS)= Cost of Laser Diode * No. of Laser Diode + Cost of MC * No. of MC
Before Price Change, \(TS_{old}\)= L * n + M * n ( Given equal no. of laser diode and MC)
After Price Change, \(TS_{new}\)= \(L(1+\frac{x}{100}) * n + M(1-\frac{y}{100}) * n \)

Let n=1
\(TS_{old}\)= L + M
\(TS_{new}\)= \(L(1+\frac{x}{100}) + M(1-\frac{y}{100}) \)

Change in Percent=\(\frac{TS_{new} - TS_{old}}{TS_{old}} *100\)
Change in Percent= \(L(1+x/100)*M(1-y/100) - L - M / (L + M) *100\)
Change in Percent =\(\frac{ Lx-My}{L+M}\)

1. The ratio of L to M is equal to the reciprocal of the ratio of x to y.

\(\frac{L}{M}=\frac{y}{x}\)
Lx=My
Change in Percent = 0
This statement is sufficient

2. The increase in the cost of a laser diode was the same as the decrease in the cost of a micro-controller.
\(L(1+\frac{x}{100}) = M(1-\frac{y}{100}) \)
\(L + \frac{Lx}{100} = M - \frac{My}{100}\)

This statement is insufficient.

Answer should be A

But the given choice is D

IS I am making some mistake? Bunuel please tell