# Math ProblemBy scoring 72% marks, a student obtained 24 marks less than the three-fourth of the maximum marks. What are the maximum marks? Give me guidence to proceed with this problem..

### 7 Answers | Add Yours

Put x = maximum marks.

72% of x = 72x/100

72x/100 = 3x/4 - 24

You should bring the fractions to a common denominator:

72x/100 - 3*25x/4*25 = - 24

-3x/100 = -24 100 => x = 8*100 => x = 800

**The maximum marks -> x = 800.**

When the student scored 72%, (100 - 72)/100 = 28% of the marks were not scored.

28% is 3% more than the 25% of the maximum. According to the information provided in the problem, this 3% of the maximum is equal to 24.

The maximum marks are 24/0.03 = 24*100/3 = 800

**The maximum marks = 800**

To solve this problem systematically you can start by representing the maximum marks by a symbol, say 'M', and then constructing an equation to present the data given in the question.

Thus, 72% marks are equal to (M x 72)/100 = 72M/100

Similarly three-fourth of maximum marks, that is 75% marks are equal to 75M/100.

It is given that 72% marks are less than three-fourth of maximum marks by 24 marks.

Therefore 75M/100 - 72/100 = 24

or 3M/100 = 24

or 3M = 24 x 100 = 2400

Therefore M = 800

Therefore maximum marks are 800.

The difference between 75% and 72%marks. The difference will give you the result for 24 marks, then find for 1 mark then multiply by 100%.

If the maximum marks is M out of which you scored 72%, then your score = 72% of M = 0.72M

On the other hand this score ,

0.72M = (3/4)M-24=0.75M-24.

Thus the magic maximum , M is hidden in the equation:

0.72M=0.75M-24=>

24=0.75M-0.72M

24=(0.75-0.72)M=> This is equivalent to the difference of 75% and &2%=3% of M is equal to 24 actual. Then what value is 100% which is M, the maximum.

24=0.03M. Divide by 0.03 both sides:

800=M. Or **800 is the maximum marks.**

Tally: 72% of 800 = 576.

(3/4)th of 800 less 24 =600-24 =576.

Thank you..Yes it helped.

Start by figuring out the difference between three-fourth marks and 72% marks. These two values are measuring the same thing, they are just different numbers. Then when you do that, you will know how many percentage of marks must equal 24 marks. Then you calculate how many marks per 1 percentage of marks. Multiply by 100, the maximum marks, and you should have your final answer. I hope that helps!