Question

A man got a $ 10\% $ increase in his salary. If his new salary is Rs. $ 1,54,000 $ , find his original salary.

Answer 1

Hint: In the given problem, we will assume that the original salary of the man is Rs. $ x $ . We know that $ y\% $ of a number $ z $ can be written as $ \left( {\dfrac{y}{{100}}} \right) \times z $ . We will use this information and given data. So, we will get a linear equation in variable $ x $ . By solving that linear equation, we can find the original salary.

Complete step-by-step answer:
In this problem, we need to find the original salary of man. Let us assume that his original salary is Rs. $ x $ . It is given that a man got a $ 10\% $ increase in his salary (original salary). So, we can say that he got $ 10\% $ of $ x = \left( {\dfrac{{10}}{{100}}} \right) \times x = $ Rs. $ \dfrac{x}{{10}} $ increase in his original salary. It is also given that his new salary is Rs. $ 1,54,000 $ . So, now we have the following data:
Original salary $ = $ Rs. $ x $
Increase in original salary $ = $ Rs. $ \dfrac{x}{{10}} $
New salary $ = $ Rs. $ 1,54,000 $
Now note that the new salary is equal to the addition of original salary and increase in salary. So, by using this information and above data we can write
 $ 1,54,000 = x + \dfrac{x}{{10}} $
 $ \Rightarrow 1,54,000 = \dfrac{{10x + x}}{{10}} $
 $ \Rightarrow 1,54,000 \times 10 = 11x $
 $ \Rightarrow 11x = 15,40,000 \cdots \cdots \left( 1 \right) $
Equation $ \left( 1 \right) $ is called a linear equation in one variable $ x $ . Let us solve this equation to find $ x $ . For this, let us divide by $ 11 $ on both sides of equation $ \left( 1 \right) $ . So, we can write
 $ x = \dfrac{{15,40,000}}{{11}} $
 $ \Rightarrow x = 1,40,000 $
Hence, we can say that if a man got a $ 10\% $ increase in his salary and his new salary is Rs. $ 1,54,000 $ then his original salary is Rs. $ 1,40,000 $ .

Note: In this type of problem, we will assume that the required quantity is $ x $ . Then, by using given information we will try to construct a linear equation in one variable. Linear equations in one variable can be solved by using basic algebraic operations. Problems can be asked in such a way that if the original salary of a man is Rs. $ 1,40,000 $ and his new salary is Rs. $ 1,54,000 $ then find the percentage of increase in salary.