Question

Aditya’s monthly salary is $$15\mathrm{\%}$$ more than Sanjay’s monthly salary. If Aditya’s monthly salary is Rs. $$17250$$, then what is Sanjay's annual salary?

Answer 1

Hint: As per the problem monthly salary of Sanjay is less than Aditya’s salary. So, if the salary of A is $$a\mathrm{\%}$$ more than the salary of B then B’s salary will be $${\displaystyle \frac{100}{100+a}}$$ of A’s salary. With the help of the formula we will find the monthly salary of Sanjay. With the monthly salary found we will multiply 12 to get the required annual salary.

Complete step-by-step answer:
It is given that; Aditya’s monthly salary is $$15\mathrm{\%}$$ more than Sanjay’s monthly salary.
Aditya’s monthly salary is Rs. $$17250$$.
We have to find Sanjay's monthly salary.
Let us consider, the monthly salary of Sanjay is $$x$$.
Since, Aditya’s salary is $$15\mathrm{\%}$$ more than Sanjay’s monthly salary.
So, the salary of Aditya is $$x+x\times 15\mathrm{\%}$$
Let us simplify the above salary of Aditya using the percentage formula, we get,
Aditya’s salary is $${\displaystyle \frac{115x}{100}}$$
According to the problem it is given that Aditya’s salary is Rs. $$17250$$
i.e. $${\displaystyle \frac{115x}{100}}=17250$$
Let us solve the above equation to get x, which is the salary of Sanjay we get,
$$x=17250\times {\displaystyle \frac{100}{115}}=15000$$
Hence we have found that the monthly salary for Sanjay is Rs.$$15000.$$
We should calculate the annual salary of Sanjay for that we have to multiply his monthly salary with 12.
The monthly salary of Sanjay is $15000\times 12=180000$
Hence the annual salary of Sanjay is $Rs180000$

Note: The problem can be solved by another process. We can solve it directly.
As Aditya’s monthly salary is $$15\mathrm{\%}$$ more than Sanjay’s monthly salary and Aditya’s monthly salary is Rs. $$17250$$.
So, Sanjay’s salary will be $$17250\times {\displaystyle \frac{100}{115}}$$
On solving the equation which is given in the above equation, we get, the monthly salary of Sanjay as $$=Rs.15000$$
Hence, monthly salary for Sanjay is Rs. $$15000.$$
Here percentage conversion plays a major role that is $x\mathrm{\%}=x\times 100\mathrm{\%}$