Question

Study the pie chart given and answer the following questions:
The central angle of printing charge is x more than that of advertisement charge. What is the value of ‘x’?

A) $72^\circ $
B) $61.2^\circ $
C) $67.2^\circ $
D) $54.8^\circ $

Answer 1

Hint: In this question, we are given a pie chart which includes certain expenses. We have been asked the central angle x, when x denotes the difference between printing charge and advertisement charge. We are given the percentages of each charge. So first, we will find the central angle of printing charge and advertisement charge individually and then we will subtract them from each other to get the required difference.

Complete step-by-step solution:
We are given a pie chart showing the percentage of certain expenses. And we have been asked to tell the difference in the central angle of printing charge and advertisement charge.
We will start by finding the central angle of printing charge and advertisement charge individually first.
Central angle of printing charge - $\dfrac{{35}}{{100}} \times 360 = 126^\circ $
Central angle of advertisement charges - $\dfrac{{18}}{{100}} \times 360 = 64.8^\circ $
We have been given that the central angle of printing charge is x more than that of advertisement charge. Using this, we can make an equation –
$ \Rightarrow $Central angle of printing charge$ = x + $Central angle of advertisement charge.
Putting the values to find x,
$ \Rightarrow 126^\circ = x + 64.8^\circ $
On shifting we will get,
$ \Rightarrow 126^\circ - 64.8^\circ = x$
$ \Rightarrow x = 61.2^\circ $

Therefore, the central angle of printing charge is $61.2^\circ $ more than that of advertisement charge.

Note: We can also do it by the following way:
Find the difference in the percentage of printing charge and advertisement charge and then, find the central angle of that percentage. This is a shorter method.
Difference in the percentage = Percentage of printing charge – percentage of advertisement charge
Difference in the percentage = $35\% - 18\% = 17\% $
Now, we will find the central angle of 17%,
$ \Rightarrow \dfrac{{17}}{{100}} \times 360 = 61.2^\circ $
Hence, we can see that the answer remains the same.