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Vandita scored an overall average of 80% marks in five subjects taken together, viz. Hindi, Science, Maths, English and Sanskrit, wherein the maximum marks of each subject were 105. How many marks did Vandita score in Science if she scored 89 marks in Hindi, 92 marks in Sanskrit, 98 marks in Maths and 81 marks in English?
70
75
60
65
60
Calculate the difference of each subject from 80% of 105 (i.e., 84). Net deviation must be 0: (89-84) + (92-84) + (98-84) + (81-84) + (x-84) = 0. So, 5 + 8 + 14 - 3 + (x-84) = 0 => 24 + x - 84 = 0 => x = 60.
Average of 5 subjects is 80%, maximum marks per subject is 105. Marks: Hindi 89, Sanskrit 92, Maths 98, English 81.
Total=Average×n,Science=Total−(Hindi+Sanskrit+Maths+English)
Calculate the difference of each subject from 80% of 105 (i.e., 84). Net deviation must be 0: (89-84) + (92-84) + (98-84) + (81-84) + (x-84) = 0. So, 5 + 8 + 14 - 3 + (x-84) = 0 => 24 + x - 84 = 0 => x = 60.
Students often calculate 80% of the total 525 as 420 and subtract the sum of known marks incorrectly or forget that the average applies to all five subjects equally.
Calculate total marks required
Since the average for 5 subjects is 80% and the maximum for each subject is 105, the total marks obtained by Vandita is calculated as 5×(0.80×105).
Total=5×84=420
Sum the marks of the known subjects
Add the marks obtained in Hindi, Sanskrit, Maths, and English: 89+92+98+81.
Sum=360
Find the Science marks
Subtract the sum of the four subjects from the total marks obtained: 420−360.
Science=60
C is correct because the total marks obtained is 420 and the sum of the other four subjects is 360, leaving 60 marks for Science.
This concept of 'summing to mean' is highly useful in data interpretation and statistics questions where you have to balance positive and negative deviations from the mean.
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