Question

In an examination Mohit obtained 20% more marks than sushant but is 10% less than Rajesh. If the marks obtained by sushant are 1080, find the percentage of marks obtained by Rajesh if the full marks are 2000.
A) $72\% $
B) $86.66\% $
C) $78.33\% $
D) $75\% $

Answer 1

Hint: Here we will use the percentage method.
For example: $A\% = \dfrac{A}{{100}}$
Finding 10% more than A: - for 10% more than A we first have to find out 10% of A then adding that value to A.
  $\dfrac{{10}}{{100}}A + A = \dfrac{{110}}{{100}}A$
Finding 10% less than A: - for 10% less than A we first have to find out 10% of A then subtracting that value from A.
  $A - \dfrac{{10}}{{100}}A = \dfrac{{90}}{{100}}A$

Complete step by step solution:
Let marks obtained by sushant = x
Mohit obtained 20% more marks than sushant

 = $20\% x + x$
 =$ \dfrac{{20}}{{100}}x + x = \dfrac{{120}}{{100}}x$

 Let marks obtained by rajesh= y
But, mohit’s marks are 10% less than rajesh

 = $y - 10\% y\\$
=$y - \dfrac{{10}}{{100}}y = \dfrac{{90}}{{100}}y$

Marks obtained by sushant = 1080 (given)
 $\therefore \dfrac{{120}}{{100}} \times 1080 = 1296$
Also mohit’s marks are 10% less than rajesh.

 =$ \dfrac{{90}}{{100}}y$
 = $\dfrac{{90}}{{100}}y $= 1296

Marks obtained by rajesh:-

$y = \dfrac{{1296 \times 100}}{{90}}\\$
$y = 1440$

Percentage of marks obtained by rajesh = $\dfrac{\text{Total marks obtained by rajesh}}{\text{Full marks}}$
Percentage $ = \dfrac{{1440}}{{2000}} \times 100 = 72\% $

Therefore option (A) is the correct option.

Note:
Percentage is a number or ratio that represents a fraction of 100.It is a number having no unit and dimentions.Be careful when converting from percentage and converting to percentage .when converting to percentage multiply by 100 and when converting from percentage divide by 100.Percentage approach is the easiest and the fastest approach that we can apply on such type of questions. This application of increasing or decreasing percentage can be used in analysing and comparing progress and performances.