Question

The average marks scored by 5 students remain unchanged from 70 even when the marks scored by John and Anna are included. If John scored 10 marks more than Anna, find their scores.

• A. John = 85; Anna = 75
• B. John = 80; Anna = 70
• C. John = 75; Anna = 65
• D. John = 70; Anna = 60

Answer 1

The correct option is C John = 75; Anna = 65

We take:
$Joh{n}^{\prime }smarks=j$
$Ann{a}^{\prime }smarks=a$
$Sumofthemarksoftheother5students=S$

$⟹Average=\frac{j+a+S}{5+2}=\frac{j+a+S}{7}=70$

The average mark was 70 even when John's and Anna's marks were not considered.

$⟹Initialaverage=\frac{S}{5}=70$
$⟹S=5\times 70=350$

Substitutin this into the new average, we get:

$Average=\frac{j+a+350}{7}⟹\frac{j+a}{7}+50=70$
$⟹\frac{j+a}{7}=20$
$⟹j+a=\mathrm{140.......}\left(a\right)$

We also know that John has scored 10 more marks than Anna.

$⟹j–a=\mathrm{10........}\left(b\right)$

Adding equations (a) and (b), we get:

$(j+a)+(j–a)=140+10$
$⟹2j=150$
$⟹j=75$

Inserting this into equation (a), we find:

$j+a=140$
$⟹75+a=140$
$⟹a=140–75$
$⟹a=65$ ​​​​​​

Hence, the marks scored by John and Anna are:

John = 75; Anna = 65