Ramya scored 65% of the marks in an examination and scored 75 marks more than the passing marks and Reena scored 38% marks and failed by 6 marks. If the total marks scored by Ramya, Reena and Raja together is 459, then find the percentage of the marks scored by Raja.
Question
Ramya scored 65% of the marks in an examination and scored 75 marks more than the passing marks and Reena scored 38% marks and failed by 6 marks. If the total marks scored by Ramya, Reena and Raja together is 459, then find the percentage of the marks scored by Raja.
Solution
To solve this problem, we need to follow these steps:
Step 1: Let's assume the total marks in the examination are x.
Step 2: According to the problem, Ramya scored 65% of the total marks and this was 75 marks more than the passing marks. So, the passing marks are 65% of x - 75.
Step 3: Reena scored 38% of the total marks and this was 6 marks less than the passing marks. So, the passing marks are also 38% of x + 6.
Step 4: Since the passing marks are the same for both Ramya and Reena, we can set the two equations equal to each other and solve for x.
So, 65% of x - 75 = 38% of x + 6.
Step 5: Solving this equation will give us the total marks in the examination.
Step 6: Once we have the total marks, we can subtract the marks scored by Ramya and Reena from the total marks to find the marks scored by Raja.
Step 7: Finally, we can calculate the percentage of the marks scored by Raja by dividing the marks scored by Raja by the total marks and multiplying by 100.
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