Correct Answer - Option 3 : 112.5
Given: The marks of Dheeraj are increasing by 10 in every test from the previous test starting from the 1st.
Total no. of test is 8. The average number of marks in 3rd, 5th and 7th test was 120.
Formula: Average of n numbers a1, a2, ..., an = (a1 + a2 + ... + an)/n
Calculation:
Let the marks of Dheeraj in 1st test be x
Then in 2nd test = x + 10
3rd test = x + 20
4th test = x + 30
5th test = x + 40
6th test = x + 50
And so on.
From the question
The average number of marks in 3rd, 5th and 7th test = 120
x + 20 + x + 40 + x + 60 = 120 × 3
⇒ 3x = 360 – 120
⇒ 3x = 240
⇒ x = 80
So, the average number of marks in 1st, 2nd, 6th and 8th =
[x + (x + 10) + (x + 50) + (x + 70)]/4
⇒ (80 + 90 + 130 + 150)/4
⇒ 450/4 = 112.5