Question

Two students appeared in an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are
(a) 42, 30
(b) 42, 31
(c) 42, 32
(d) 42, 33

Answer 1

Hint: Here, we will assume the marks of both the students to be x and y. Then, we will make equations using the given conditions. We will use the concept of percentage here to calculate the values of x and y.

Complete step-by-step answer:

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, ‘%’. A percentage is a dimensionless number. The percentage value is calculated by multiplying the numeric value of the ratio or fraction by 100. Due to inconsistent wage, it is not always clear from the context what a percentage is relative to. When speaking of a x% rise or x% fall in a quantity, the usual interpretation is that this is relative to the initial value of that quantity.

Let us assume that the marks of the first student is x and marks secured by the second students is y.

Since, it is given that one of them secured 9 marks more than the other. Let us take x to be greater than y. So, we can write:

x = y + 9………..(1)

Now, his marks are 56% of the sum of their marks. Thus, we can write the following equation:

$x=\dfrac{56}{100}\times \left( x+y \right).........\left( 2 \right)$

From equation (1), we can write:

y = x-9

On putting y = x-9 in equation (2), we get:

$\begin{align}

  & x=\dfrac{56}{100}\times \left( x+x-9 \right) \\

 & \Rightarrow x=\dfrac{56}{100}\times \left( 2x-9 \right) \\

 & \Rightarrow 100x=56\times 2x-56\times 9 \\

 & \Rightarrow 100x-112x=-504 \\

 & \Rightarrow -12x=-504 \\

 & \Rightarrow x=\dfrac{504}{12} \\

 & \Rightarrow x=42 \\

\end{align}$

Therefore, y = 42-9=33.

So, the value of x is 42 and that of y is 33.

Hence, option (d) is the correct answer.

Note: Students should note here that it is not necessary to consider x to be greater than y, that is marks of any of the students can be considered to be greater than the other. The calculations must be done properly to avoid mistakes.