One student secured 14 marks more than the other and his marks was 60% of the…
2023
One student secured 14 marks more than the other and his marks was 60% of the sum of their marks . Find the marks obtained by them ?
- A.
38 and 24
- B.
54 and 40
- C.
42 and 28
- D.
40 and 26
Attempted by 10 students.
Show answer & explanation
Correct answer: C
Answer: 42 and 28
Let the higher mark be x and the lower mark be y.
Given: x - y = 14 and x = 0.6(x + y).
Substitute x = y + 14 into the second equation: y + 14 = 0.6(2y + 14) = 1.2y + 8.4.
Solve: y + 14 = 1.2y + 8.4 → 14 - 8.4 = 1.2y - y → 5.6 = 0.2y → y = 28.
Then x = y + 14 = 42. Therefore the marks are 42 and 28.
Quick check using percentages: The higher mark is 60% and the lower is 40% of the total, so their difference is 20% of the total. If 20% of the total = 14, total = 14 ÷ 0.20 = 70. Then 60% of 70 = 42 and 40% = 28, confirming the result.