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To pass an examination, a student must score 450 marks out of the maximum aggregate. Rahul scored 405 marks and failed by 3% of the total marks. What is the maximum aggregate marks?
1200
1500
1800
2000
1500
Convert 3% to 3/100, then compute 45 ÷ 0.03 as 45 × 100 ÷ 3 = 1500 in seconds
Passing marks = 450, Rahul's score = 405, deficit equals 3% of total marks
T=pD
Convert 3% to 3/100, then compute 45 ÷ 0.03 as 45 × 100 ÷ 3 = 1500 in seconds
Forgetting to change 3% into its decimal 0.03, leading to division by 3 instead of 0.03
Find deficit
The shortfall from the required passing marks is D=450−405=45 marks.
D=450−405=45
Express deficit as percentage of total
Given that this deficit is 3% of the total aggregate T, write D=0.03×T.
45=0.03×T
Solve for total aggregate
Rearrange to T=0.0345 which equals 1500 marks.
T=0.0345=1500
Verify passing condition
With T=1500, the passing mark 450 is 30% of T, and Rahul's 405 is 27%, confirming a 3% shortfall.
1500450×100=30%,1500405×100=27%
B is correct because the total aggregate marks compute to 1500.
Similar percentage‑deficit reasoning is used in profit‑loss and discount problems, where the loss amount equals a given percent of the original price.
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