Question

the qualifying marks in an examination is 40%.Ali gets 58 marks and is disqualified by 22 marks. Find the minimum marks of the examination​

Answer 1

$\large\underline{\bold{Given \:Question - }}$

• The qualifying marks in an examination is 40%. Ali gets 58 mark and is dis-qualified by 22 marks. Find the minimum mark of the examination.

$\large\underline{\bold{Solution-}}$

Basic Concept Used :-

Writing Systems of Linear Equation from Word Problems

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.

Let's solve the problem now!!

Given :-

• The qualifying marks in an examination is 40%.

• Ali gets 58 marks and is disqualified by 22 marks.

To Find :-

• The minimum marks of the examination.

Now,

• Let the minimum marks of the examination be 'x'.

So,

$\sf \: Minimum \: passed \: marks \: = 40\% \: of \: x$

$\sf \: Minimum \: passed \: marks \: = \dfrac{40}{100} \times x = \dfrac{2}{5} x$

Now,

• Ali got = 58 marks

• Ali fail by = 22 marks

So,

• Qualifying marks in exam = 58 + 22 = 80

So, we get,

$\sf \: \dfrac{2x}{5} = 80$

$\sf \: x = 80 \times \dfrac{5}{2}$

$\: \boxed{ \bf{ \therefore \: x \: = \: 200}}$

$\boxed{ \bf \: Hence, \: minimum \: marks \: of \: the \: exam \: = 200}$

Additional Information

1. Percentage Formula :-

$\boxed{ \bf \: \% \: age \: = \: \dfrac{value}{total \: value} \times 100 \: \%}$

2. Percentage change Formula :-

$\sf \:\% \: age \: Change=\dfrac{New\;Value-Old\;Value}{Old\;Value}\times 100\%$

• If the result is positive, then it is an increase.

• If the result is negative, then it is a decrease.