Question -
Answer -
Given:
Marks scored by Rohit in two tests are 65 and 70.
Let marks in the third test be x.
So let us find minimum x for which the average of all three papers would be at least 65 marks.
That is,
Average marks in three papers ≥ 65 …(i)
Average is given by:
Average = (sum of all numbers)/(Total number of items)
= (marks in 1st two papers + marks in third test)/3
= (65 + 70 + x)/3
= (135 + x)/3
Substituting this value of average in the inequality (i), we get
(135 + x)/3 ≥ 65
(135 + x) ≥ 65 × 3
(135 + x) ≥ 195
x ≥ 195 – 135
x ≥ 60
This inequality means that Rohit should score at least 60 marks in his third test to have an average of at least 65 marks.
So, the minimum marks to get an average of 65 marks is 60.
∴ The minimum marks required in the third test is 60.