Question

Out of her total monthly salary, Tanvy spends 30% on house rent and 60% of the rest on household expenditure. If she saves ₹ 10500, what is her total monthly salary?

Answer 1

Hint: Use properties of percentage. Use the logic that savings is the rest of salary after deducting expenditure from the total salary.

Complete Step by Step Solution:
Let the total monthly salary of Tanvy be $x$.
She spends 30% on house rent.
Let her house rent be $y$.
$ \Rightarrow y = \dfrac{{30}}{{100}} \times x$
$ \Rightarrow y = \dfrac{{3x}}{{10}}$.
Then the rest amount that she will have, will be $\left( {x - \dfrac{{3x}}{{10}}} \right)$
She spends $60\% $of it on household expenditure.
Let her household expenditure be $z$.
Then, $z = 60\% $ of $\left( {x - \dfrac{{3x}}{{10}}} \right)$
The rest of the amount would be her saving
Thus, her savings = $40\% $of $\left( {x - \dfrac{{3x}}{{10}}} \right)$.
$ = \dfrac{{40}}{{100}} \times \left( {x - \dfrac{{3x}}{{10}}} \right)$
$ = \dfrac{2}{5}\left( {\dfrac{{10x - 3x}}{{10}}} \right)$
$ = \dfrac{2}{5} \times \dfrac{{7x}}{{10}}$
$ = \dfrac{{7x}}{{25}}$
It is given that her savings is ₹ $10500$.
$ \Rightarrow \dfrac{{7x}}{{25}} = 10500$
$ \Rightarrow 7x = 10500 \times 25$
$ \Rightarrow x = \dfrac{{10500 \times 25}}{7}$
$ \Rightarrow x = 1500 \times 25$
$ \Rightarrow x = $₹ $37500$
Thus, the total monthly salary of Tanvy is ₹$37500$

Note: Alternative method:
Total salary, $x = 10500 + \dfrac{{3x}}{{10}} + \dfrac{6}{{10}}\left( {x - \dfrac{{3x}}{{10}}} \right)$
$ \Rightarrow x = 10500 + \dfrac{{3x}}{{10}} + \dfrac{{6x}}{{10}} - \dfrac{{18x}}{{100}}$
$ \Rightarrow x = 10500 + \dfrac{{9x}}{{10}} - \dfrac{{18x}}{{100}}$
$ \Rightarrow x = 10500 + \dfrac{{90x - 18x}}{{100}}$
$ \Rightarrow 100x - 90x + 18x = 1050000$
$ \Rightarrow 28x = 1050000$
$ \Rightarrow x = $₹$37500$.