Average marks of Sameer decreased by 1, when he replaced subject in which he has scored 40 ,marks by

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The average marks of Sameer decreased by $1,$ when he replaced the subject in which he has scored $40 \,marks$ by the other two subjects in which he has just scored $23$ and $ 25$ marks respectively. Later he has also included $57$ marks of Computer Science, then the average marks increased by $2.$ How many subjects were there initially?

A

$6$

B

$12$

C

$15$

D

$9$

Solution

Let the number of subjects be $n$ and average marks be $x,$ the total marks $= nx$ $\operatorname{Again}(n+1)(x-1)=(n x-40)+(23+25) \quad x-n=9$

Further $(n+2)(x+1)=(n x-40)+(23+25)+57$

$n x+2 x+n+2=n x+65 \quad 2 x+n=63$

Solving equation I and II we get $n=15 \Rightarrow x=24$

Standard 13

Quantitative Aptitude

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