Question

The pie-chart given in figure represents the expenditure on different items in constructing a flat in Delhi. If the expenditure incurred on cement is Rs 112500, find the following:
Expenditure incurred on labour. ( in rupees)

Answer 1

Hint: The pie-chart is a diagram model question, it will consist of different items with a certain percentage, we have to find the quantity with the help of the percentage compared with the whole amount. In this diagram, the expenditure is provided in terms of degrees of the circle so firstly we have to convert the degrees into the percentage and can find the required output.

Complete step-by-step answer:
The total expenditure incurred on the cement is \[x = {\rm{Rs}}112500\]
The total that a circle consists of \[360^\circ \], but if we take the expenditure total for \[100\% \], then each degree will be taken as 0.27%.
Now, by observing the pie-chart, we know the labour is incurred \[100^\circ \], converting it into percentage we will get \[100^\circ \times 0.278\,\% = 27\,.8\% \]. Let us assume \[y = 27.8\% \].
The equation to find the expenditure incurred on labour is
Let us take z as the expenditure incurred on labour, then
\[\Rightarrow z = \dfrac{{x \times y}}{{100}}\]
Substituting the values in the equation, we will get
\[
\Rightarrow z = \dfrac{{x \times y}}{{100}}\\
 = \dfrac{{1125000 \times 27.8}}{{100}}\\
 = 312750\,{\rm{Rs}}
\]
Therefore, the expenditure incurred on labour is 303750 Rs


Note: In this solution, I converted the degrees to percentage and then I calculated the expenditure incurred but we can solve this question without converting the degree to percentage. Firstly, we have to find the amount of expenditure for each degree (it can be calculated by dividing the total expenditure by \[360^\circ \], we will get \[\dfrac{{112500}}{{360}} = 312.5\]Rs then we should multiply the\[100^\circ \]with 312.5 Rs then we will get \[312.5 \times 100 = 31250\]Rs)