Question

Ankit was given an increment of 10% on his salary is $ Rs.3575 $ , what was his salary before increment?

Answer 1

Hint: Percentage is a number or ratio that represents a fraction of 100. It is often denoted by the symbol ‘%’ such as $ 10\% $ of 50 will be = $ \dfrac{{10}}{{100}} \times 50 = 5 $ .
If the increment is x % of y then the new salary is given by $ y + x\,\% \,\,\,of\,y $ .

Complete step-by-step answer:
According to the question,
Salary of Ankit after increment of 10% = $ Rs.3575 $
Let the salary of Ankit before increment be $ Rs.x $
 $
\therefore x + 10\% x = 3575 \\
 \Rightarrow x + \dfrac{{10}}{{100}}x = 3575 \\
 \Rightarrow x + 0.1x = 3575 \\
 \Rightarrow 1.1x = 3575 \\
 \Rightarrow \dfrac{{11}}{{10}}x = 3575 \\
 \Rightarrow x = 3575 \times \dfrac{{10}}{{11}} \\
 \Rightarrow x = 3250 \\
 $
Hence the required salary of ankit before increment is = $ Rs.3250 $

Note: This question can also be solved by using the technique that if Ankit is getting 10 % of increment on his previous salary (suppose x Rs) then his new salary will be 110 % of his previous salary.
So, $ $
 $
 110\,\,\% \,\,of\,x = 3575 \\
 \Rightarrow \dfrac{{110}}{{100}} \times x = 3575 \\
 \Rightarrow \dfrac{{11}}{{10}} \times x = 3575 \\
 \Rightarrow x = \dfrac{{3575 \times 10}}{{11}} \\
 \Rightarrow x = 3250\,Rs. \\
 $