The marks scored by Rohit in two tests were 65 and 70. Find the minimu

1.	The marks scored by Rohit in two tests were 65 and 70. Find the minimum marks he should score in the third test to have an average of at least 65 marks.
Answer» Given as Marks scored by Rohit in two tests are 65 and 70. Suppose the marks in the third test be x. Therefore let us find minimum x for which the average of all three papers would be at least 65 marks. That is, The average marks in three papers ≥ 65 …(i) The average is given by: Average = (sum of all numbers)/(Total number of items) = (marks in 1^st two papers + marks in third test)/3 = (65 + 70 + x)/3 = (135 + x)/3 On 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 From this inequality means that Rohit should score at least 60 marks in his third test to have an average of at least 65 marks. Therefore, the minimum marks to get an average of 65 marks is 60. Hence, the minimum marks required in the third test is 60.

The marks scored by Rohit in two tests were 65 and 70. Find the minimum marks he should score in the third test to have an average of at least 65 marks.

Answer»

Given as

Marks scored by Rohit in two tests are 65 and 70.

Suppose the marks in the third test be x.

Therefore let us find minimum x for which the average of all three papers would be at least 65 marks.

That is,

The average marks in three papers ≥ 65 …(i)

The average is given by:

Average = (sum of all numbers)/(Total number of items)

= (marks in 1^st two papers + marks in third test)/3

= (65 + 70 + x)/3

= (135 + x)/3

On 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

From this inequality means that Rohit should score at least 60 marks in his third test to have an average of at least 65 marks.

Therefore, the minimum marks to get an average of 65 marks is 60.

Hence, the minimum marks required in the third test is 60.