Question : Student A got 25 marks more than student B and the marks of A were equal to 60% of the sum of their marks. What are the marks obtained by A and B respectively?
Option 1: 75 and 100
Option 2: 75 and 50
Option 3: 45 and 120
Option 4: 55 and 80
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Correct Answer: 75 and 50
Solution :
Let the marks of student A as p and the marks of student B as q.
From the problem, we have two equations:
Since A got 25 marks more than B
⇒ p = q + 25 ...(1)
Since the marks of A were equal to 60% of the sum of their marks
⇒ p = 0.6 × (p + q) ...(2)
Substituting equation 1 into equation 2, we get:
⇒ q + 25 = 0.6 × (q + 25 + q)
⇒ q + 25 = 1.2q + 15
⇒ 0.2q = 10
⇒ q = 50
$\therefore$ p = 50 + 25 = 75
Hence, the correct answer is 75 and 50.
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