Question 9 An exam is conducted for 600 marks.
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Question 9
An exam is conducted for 600 marks. Ramesh scores 200 marks and fails by 40 marks. If Suresh scores 50 marks more than Ramesh, how many marks equals the passing marks? (Do not answer)
Show answer & explanation
The sum of all 4 integers is 4 × 80 = 320. With the first two integers being 70 and 30, the remaining two sum to 320 - 70 - 30 = 220. If their ratio is 2:3, they are 2x and 3x where 5x = 220, giving x = 44. The two integers are 88 and 132, summing to 220. However, if the question asks for one of the two integers, it is 132 (the larger one).
Step-by-step Derivation:
Step 1: Sum of 4 integers = Average × Count = 80 × 4 = 320
Step 2: Sum of first and last integers = 70 + 30 = 100
Step 3: Sum of middle two integers = 320 - 100 = 220
Step 4: Let the two integers be 2x and 3x (ratio 2:3)
Step 5: 2x + 3x = 220 → 5x = 220 → x = 44
Step 6: The two integers are 2(44) = 88 and 3(44) = 132
Step 7: Answer is 132 (the larger of the two middle integers)