Meena scores 40% in an examination and after review, even though her score is…
2023
Meena scores 40% in an examination and after review, even though her score is increased by 50%, she fails by 35 marks. If her post-review score is increased by 20%, she will have 7 marks more than the passing score. The percentage score needed for passing the examination is
Answer: D. 70 — When a score is increased successively and its position relative to a fixed passing mark is tracked in marks (not percentage) at each stage, the resulting…
- A.
75
- B.
80
- C.
60
- D.
70
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Correct answer: D
When a score is increased successively and its position relative to a fixed passing mark is tracked in marks (not percentage) at each stage, the resulting mark differences translate directly into a percentage-point gap on the total marks -- so two such snapshots pin down both the total marks and the passing mark.
Let the total marks be M and the passing marks be P.
Meena's post-review score, after a 50% increase on her original 40%, is 40% x 1.5 = 60% of M.
At this 60% score she is 35 marks short of passing: 0.60M = P - 35 ... (i)
A further 20% increase on this post-review score gives 60% x 1.2 = 72% of M.
At this 72% score she is 7 marks above passing: 0.72M = P + 7 ... (ii)
Subtracting (i) from (ii): 0.12M = 42, so the total marks M = 350.
Substituting back in (i): P = 0.60 x 350 + 35 = 245.
Passing percentage = (245 / 350) x 100 = 70%.
Cross-check against equation (ii): 0.72 x 350 = 252, and P + 7 = 245 + 7 = 252 -- both sides match, confirming the passing percentage is 70%.