# 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..

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

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.

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

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.

epollock | (Level 3) Valedictorian

Posted on

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%.

neela | High School Teacher | (Level 3) Valedictorian

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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.