Question

Two students appeared at an examination. One of them secured 15 marks more than the other and his marks were 55% of the sum of their marks. The marks obtained by them are:
1. 73.5, 88.5
2. 40, 60
3. 67.5, 82.5
4. 53, 68

Answer 1

Correct Answer - Option 3 : 67.5, 82.5

Given:

Among two students one of them secured 15 marks more than the other and his marks were 55% of the sum of their marks.

Concept Used:

Concept of the linear equation of one variable.

Calculation:

Let, one of them scored x

Then the score of the other student is (x + 15)

Sum of their marks = (x + x + 15) = (2x + 15)

Accordingly,

(x + 15) = (55/100) × (2x + 15)

⇒ 20 × (x + 15) = 11 × (2x + 15)

⇒ 20x + 300 = 22x + 165

⇒ (22x - 20x) = (300 - 165)

⇒ 2x = 135

⇒ x = 67.5

The number secured by the other student is (67.5 + 15) = 82.5

∴ The marks obtained by them are 67.5 and 82.5.