Question

From the salary of an officer, $10\% $ is deducted as the house rent, $20\% $ of the rest he spends on the conveyance, $20\% $ of the rest he pays as the income tax and $10\% $ of the balance he spends at the clothes. Then, he is left with ${\text{Rs}}{\text{.15,552}}$. Find his total salary.
A. ${\text{Rs}}{\text{.25,000}}$
B. ${\text{Rs}}{\text{.30,000}}$
C. ${\text{Rs}}{\text{.35,000}}$
D. ${\text{Rs}}{\text{.40,000}}$

Answer 1

Hint:Let us assume that the total salary be $x$.After all the deductions, he is left with ${\text{Rs}}{\text{.15,552}}$.Money left after the house rent deduction$ = x - 10\% {\text{ of }}x$.And now let money left after the house rent deduction$ = {x_1}$.Money left after the conveyance deduction $ = {x_1} - 20\% {\text{ of }}{x_1}$.Agin consider money now left be $ = {x_2}$.Money left after paying the income tax $ = {x_2} - 20\% {\text{ of }}{x_2}$.Let us say that the money left after tax be $ = {x_3}$.Then the money left after buying clothes $ = {x_3} - 10\% {\text{ of }}{x_3}$.After simplifying equate it to the $Rs.15552$ to get required answer.

Complete step-by-step answer:
In this question, we are given that from the salary of an officer, $10\% $ is deducted as the house rent, $20\% $ of the rest he spends on the conveyance, $20\% $ of the rest he pays as the income tax and $10\% $ of the balance he spends at the clothes. Then, he is left with ${\text{Rs}}{\text{.15,552}}$.
Now let us consider that the total salary received by the officer be $x$
Now $10\% $ of the total salary is deducted at the house rent.
So initially the salary assumed is $x$
Amount that got deducted$ = 10\% {\text{ of }}x$
Money left after the house rent deduction $ = x - 10\% {\text{ of }}x{\text{ = }}x - \dfrac{{10x}}{{100}} = \dfrac{{9x}}{{10}}$
Now $20\% $ of the rest he spends on the conveyance
So the money spent on the conveyance $ = 20\% {\text{ of }}\dfrac{{9x}}{{10}}$$ = \dfrac{{20}}{{100}} \times \dfrac{{9x}}{{10}} = \dfrac{{18x}}{{100}}$
 Money left after the conveyance deduction $ = \dfrac{{9x}}{{10}} - 20\% {\text{ of }}\dfrac{{9x}}{{10}} = \dfrac{{9x}}{{10}} - \dfrac{{20}}{{100}} \times \dfrac{{9x}}{{10}} = \dfrac{{36x}}{{50}}$
Now $20\% $ of the rest he spends on the income tax
Money left after paying the income tax$\dfrac{{36x}}{{50}} - 20\% {\text{ of }}\dfrac{{36x}}{{50}} = \dfrac{{36x}}{{50}} - \dfrac{{36x}}{{50}} \times \dfrac{{20x}}{{100}} = \dfrac{{144x}}{{250}}$
Now he spends $10\% $ of the remaining balance on the clothes
So after buying clothes now the remaining balance$ = \dfrac{{144x}}{{250}} - \dfrac{{144x}}{{250}} \times \dfrac{{10x}}{{100}} = \dfrac{{144x}}{{250}} \times \dfrac{9}{{10}}$
This above value is given to be ${\text{Rs}}{\text{.15,552}}$
So equating the value left at last with ${\text{Rs}}{\text{.15,552}}$
$\dfrac{{144x}}{{250}} \times \dfrac{9}{{10}}$$ = {\text{Rs}}{\text{.15,552}}$
$x = \dfrac{{15552 \times 10 \times 250}}{{9 \times 144}}$
On solving we get that $x = 12 \times 2500 = 30000$
Hence salary of an officer is ${\text{Rs}}{\text{.30,000}}$

So, the correct answer is “Option B”.

Note:If we are finding the percentage of any number then that must be smaller or equal to that given number. For example if we are given the number $250$, then we need to find its $50\% $ then it will be $ = 50\% {\text{ of 250}}$$ = \dfrac{{50}}{{100}}(250) = 125$ ,which is smaller than $250$, then we can say that $x\% {\text{ of }}N \leqslant N$ where $N,x$ be any number.