Question

In an examination, arpit scored 10 marks more than harsh. If arpit's score was 60% of the sum of their marks, by what percent is arpit's score more than harsh's

Answer 1

10 percent
Say me is it correct

Answer 2

In examination, Arpit's score is 50% more than Harsh's score

Solution:

Let harsh secured ‘x’ marks. It is given that Arpit scored 10 marks more than harsh. Thus Arpit secured (x +10) marks.

Again it is given that Arpits score is 60 % of the sum of Arpit and harsh’s marks,

According to question,

$\begin{array}{l}{x+10=60 \% \text { of }\{x+(x+10)\}} \\\\ {\Rightarrow x+10=\frac{60}{100} \times(2 x+10)}\end{array}$

$\Rightarrow x+10=\frac{120 x+600}{100}$

⇒100( x + 10) =  120x + 600

⇒ 100x + 1000 = 120x + 600

⇒ 1000 - 600 = 120x - 100x

⇒ 400 = 20x

⇒ x = 20

Thus Harsh score = 20 and arpits score = 20 + 10 = 30

We have to find by what percent is Arpit’s score more than Harsh.

$\text { Percentage }=\frac{\text { Arpits score-Harsh score }}{\text { Harsh score }} \times 100 \%$

$\begin{array}{l}{=\frac{30-20}{20} \times 100 \%} \\\\ {=\frac{10}{20} \times 100 \%} \\\\ {=10 \times 5 \%=50 \%}\end{array}$

Thus Arpits score is 50 % more than Harsh