Question

A satellite is composed of 30 modular units, each of which is equipped with a set of sensors, some of which have been upgraded. Each unit contains the same number of non-upgraded sensors. If the number of non-upgraded sensors on one unit is 1/5 the total number of upgraded sensors on the entire satellite, what fraction of the sensors on the satellite have been upgraded?

a) 5/6
b) 1/5
c) 1/6
d) 1/7
e) 1/24

Answer 1

1/7 (option d) of the sensors on the satellite have been upgraded

Explanation:

Each unit contains the same number of non-upgraded sensors

number of non-upgraded sensors for each module (nus)

total number of upgraded sensors on the satellite (tus)

satellite is composed of 30 modular units

total number of non-upgraded sensors on the satellite (tnus):

tnus=30*nus

total number of sensors on the satellite (ts):

ts=tnus+tus = 30*nus + tus (I)

The number of non-upgraded sensors on one unit is 1/5 the total number of upgraded sensors on the entire satellite

nus=(1/5)*tus

tus = 5 * nus (II)

Fraction of the sensors on the satellite have been upgraded (FU):

FU = tus/ts

Using I and II

FU= (5* nus)/(30*nus + tus)

FU = (5* nus)/(30*nus + 5 * nus)

FU = (5* nus)/(35*nus)

FU = 1/7

1/7 (option d) of the sensors on the satellite have been upgraded