Question

A student secured 80% of the total marks and got 720 marks. Find the marks got by the student securing 90% of the total marks.
[a] 770
[b] 810
[c] 900
[d] 990

Answer 1

Hint: Assume that the total marks are x. Hence find the marks secured by the student securing 80% of the marks in terms of x. Equate this expression to 720 and hence form an equation in x. Solve for x and hence find the total. Hence find the marks secured by the student securing 90% of the total marks.

Complete step-by-step answer:
Let the total marks of the examination be x.
Hence the marks secured by the student securing 80% of the total marks $=\dfrac{80}{100}\times x=0.8x$
But given that the marks secured by the student securing 80% of the total marks = 720
Hence, we have
$0.8x=720$
Dividing both sides by 0.8, we get
$x=\dfrac{720}{0.8}=\dfrac{7200}{8}=900$
Hence the total marks are 900.
Hence the marks secured by the student securing 90% of the total marks $=\dfrac{90}{100}\times 900=810$
Hence the marks secured by the student = 810
Hence option [b] is correct.

Note: Alternative solution:
Let the marks secured by the student securing 90% of the total marks be P
The marks secured by the student and the percentage of the total marks secured from the total marks should be in proportion.
Hence, we have
P:90::720:80
Here extremes are P and 80, and the means are 90 and 720
Since the product of extremes is equal to the product of means, we get
Hence, we have
$P\times 80=720\times 90$
Dividing both sides by 80, we get
$P=\dfrac{720}{80}\times 90=810$
Hence the marks secured by the student = 810, which is the same as obtained above
Hence option [b] is correct.