Question

Vijay’s salary was reduced by 50 percent. Again the reduced salary was increased by 50 percent. Then what will be the percent loss in salary?

Answer 1

Hint: Assume Vijay’s salary as variable and then apply the conditions given in the problem to get your problem solved and get the lost percentage.

Complete step-by-step answer:
Let the salary of Vijay be x.
It is given that salary was reduced by 50 percent so the 50 percent of x is:
$ \Rightarrow {\text{x }} \times \dfrac{{{\text{50}}}}{{{\text{100}}}}{\text{ = 0}}{\text{.5x}}$
The new salary of Vijay is:
$ \Rightarrow {\text{x - 0}}{\text{.5x = 0}}{\text{.5x}}$
Now it is said that the reduced salary was increased by 50 percent.
So, 50 percent of new salary is $ \Rightarrow {\text{0}}{\text{.5x }} \times {\text{ }}\dfrac{{50}}{{100}} = 0.25{\text{x}}$
The salary has been increased by 50 percent so the new salary is 0.5x + 0.25x = 0.75x.
So the final salary of Vijay is 0.75x.
So, the loss in salary from first to last can be written as the first salary – last salary
$ \Rightarrow {\text{x}} - {\text{0.75x }}= {\text{0.25x}}$
Therefore, the salary has decreased by 25 percent.
Therefore the percentage loss can be clearly seen as 25 percent since the difference between the first x and last salary (0.75x) is 0.25x.
Hence, his salary x is decreased by 25 percent.

Note: In this problem of percentage we have assumed the variable as salary the decreased it by 50 percent the increased salary obtained by 25 percent then we have calculated the loss percentage by subtracting the highest salary and the final salary. Then we got the loss percentage. Generally students forget to understand that increased salary will be 50 percent of reduced salary.