Question
Roshan and Rahul received marks in their quarterly exam
in a ratio of 9:8. Additionally, the ratio of marks Roshan obtained in the quarterly exam to the marks he obtained in the half-yearly exam is 2:3. For Rahul, this ratio between the quarterly and half-yearly exams is 4:5. If the combined total of marks Roshan and Rahul earned in the half-yearly exam is 1410, determine the number of marks Rahul secured in the half-yearly exam.Solution
Let, marks obtained by Roshan and Rahul in quarterly exam be 9x and 8x, respectively. According to question, (9x) × (3/2) + (8x) × (5/4) = 1410 13.5x + 10x = 1410 23.5x = 1410 x = 1410/23.5 x = 60 So, marks obtained by Rahul in half-yearly exam = (8x) × (5/4) = 10 × 60 = 600
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