Question

Average marks of 17 girls in a class are p. When their marks are arranged in ascending order it was found to be arithmetic progression

Answer 1

Answer:

Y < X

Step-by-step explanation:

I guess the question is somewhat like this:

Average marks of 17 girls in a class is X. When their marks are arranged in ascending order it was found to be in Arithmetic Progression. The class teacher found that rank the students who ranked 15th, 11th, 9th and 7th had copied the exam and hence they are suspended. Now the average of the remaining class is Y. Then

1. X =Y

2. X >Y

3. X<Y

4. X = 2Y

Solution

Let the mark of 1st girl be a and if the common difference of the AP is d then the marks of the girls will be

$a, a+d, a+2d, ...., a+16d$

Total marks

$=\frac{17}{2}[a+a+16d]$

$=17[a+8d]$

Also the total marks = 17X

Thus,

$17X=17[a+8d]$

$\implies X=a+8d$

15th term of the AP = a+14d

11th term of the AP = a+10d

9th term of the AP = a+8d

8th term of the AP = a+7d

7th term of the AP = a+6d

Sum of the above = 5a+45d

                              = 5a + 40d + 5d

                              = 5(a+8d) + 5d

                              = 5X + 5d

New Average

$Y=\frac{17X-(5X+5d)}{12}$

$Y=\frac{12X-5d}{12}$

$Y=X-\frac{5d}{12}$

Therefore, we can say that

$Y<X$

Hope this helps.