Question

a group of pupils calculated their average score for a math test. if 1 of them scored 9 marks more, their average score will b 81.if 1 of them scored 3 marks less, their average score will be 78. how mani pupil there in the group.

Answer 1

Answer:  The required number of pupils in the group is 4.

Step-by-step explanation:  Given that a group of pupils calculated their average score for a math test.

If one of them scored 9 marks more, their average score will b 81 and one of them scored 3 marks less, their average score will be 78.

We are to find the number of pupils in the group.

Let n denotes the number of peoples in the group and S denotes the sum of the marks scored by all the pupils in the group.

Then, according to the given information, we have

$\dfrac{S+9}{n}=81\\\\\Rightarrow S+9=81n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

and

$\dfrac{S-3}{n}=78\\\\\Rightarrow S-3=78n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Subtracting equation (ii) from equation (i), we get

$(S+9)-(S-3)=81n-78n\\\\\Rightarrow 12=3n\\\\\Rightarrow n=\dfrac{12}{3}\\\\\Rightarrow n=4.$

Thus, the required number of pupils in the group is 4.