Question

Study the following pie-chart carefully and answer the questions that follow:

Total estimated cost is Rs1,20,000.
During the process of renovation, the family actually incurred miscellaneous expenditure of Rs10,200. The miscellaneous expenditure incurred by the family is what percentage of the total estimated cost?
(a) 9.5%
(b) 9%
(c) 8.5%
(d) 10.5%
(e) None of these

Answer 1

Hint: Let us assume the required percentage as x. Then, we can write the given condition mathematically as $x\mathrm{\%}\times 120000=10200$ . We have to convert x% into its number form by dividing x by 100 and solve for x.

Complete step-by-step solution:
We have to find what percentage of the total estimated cost is the miscellaneous expenditure incurred by the family. Let this percentage be x. We are given that the miscellaneous expenditure is Rs10,200 and total estimated cost is Rs1,20,000. Then, we can find the required percentage as follows:
$\Rightarrow x\mathrm{\%}\times 120000=10200$
Let us convert x% into its number form by dividing x by 100.
$\Rightarrow {\displaystyle \frac{x}{100}}\times 120000=10200$
Let us cancel the zeroes from the numerator and the denominator.
$\Rightarrow {\displaystyle \frac{x}{1\text{cancel}0\text{cancel}0}}\times 1200\text{cancel}0\text{cancel}0=10200$
We will get
$\Rightarrow 1200x=10200$
Let us move the coefficient of x to the RHS.
$\Rightarrow x={\displaystyle \frac{10200}{1200}}$
Let us cancel the zeroes from the numerator and the denominator.
$\Rightarrow x={\displaystyle \frac{102\text{cancel}0\text{cancel}0}{12\text{cancel}0\text{cancel}0}}$
We will get the result of the above simplification as
$\Rightarrow x={\displaystyle \frac{102}{12}}$
Now, let us divide 102 by 12.
$\Rightarrow x=8.5$
Therefore, the required percentage is 8.5%.
Hence, the correct option is C.

Note: Students must read the question carefully as they have a chance of writing the mathematical equation as $x\mathrm{\%}\times 10200=120000$ . They must be thorough with the formulas of percentage. To convert a number into percentage, we will multiply that number by 100. Students must learn to solve algebraic equations.