In an examination, a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination?
A
8
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B
9
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C
10
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D
11
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Solution
The correct option is D11 Let the number of papers in the examination be x
Let the geography paper marks be x1 and
the history paper marks be x2
Given that the total average marks is 63
Therefore, 63=x1+x2+sum of the remaining papersx
x1+x2+sum of the remaining papers=63x -----(1)
Given that the geography paper marks is increased by 20 and the history marks by 2 then average becomes 65
Therefore, 65=x1+20+x2+2+sum of the remaining papersx
⟹x1+x2+sum of the remaining papers+22=65x
⟹63x+22=65x (from (1))
⟹2x=22
⟹x=11
Therefore, the number of papers in the examination is 11