10. The mean of ten exam scores is 20. When two more scores are added, the mean
becomes 30. What is the mean of the two scores added?
a. 20
b. 30
c. 60
d. 80

Mean of Two Added Scores: Exam Problem Solved (Original Mean 20 to New Mean 30)

Question: The mean of ten exam scores is 20. When two more scores are added, the mean becomes 30. What is the mean of the two scores added?
a. 20 | b. 30 | c. 60 | d. 80

Solution Explanation

The mean of ten exam scores is 20, so their total sum is 10 × 20 = 200[web:2]. Adding two scores makes twelve scores with a new mean of 30, so the new total sum is 12 × 30 = 360. The two added scores contribute 360 – 200 = 160, giving their mean as 160 / 2 = 80.

Option Analysis

• a. 20: This equals the original mean. If added, the new mean stays 20, not rising to 30.
• b. 30: Matches the new mean. Adding scores at 30 each yields a new mean of (200 + 60)/12 ≈ 22, insufficient for 30.
• c. 60: Sum of 120 yields new mean (200 + 120)/12 ≈ 26.7, still below 30.
• d. 80: Correct, as sum of 160 gives new mean exactly 30.

Step-by-Step Calculation

Original sum: 10 × 20 = 200. New sum: 12 × 30 = 360. Added sum: 360 – 200 = 160. Mean of added scores: 160 / 2 = 80.

Why Options Fail

Key Takeaway for Competitive Exams

Mastering mean of two added scores calculation boosts performance in statistics sections of CSIR NET, quantitative aptitude exams. The formula is: Mean_added = [(n_new × mean_new) – (n_old × mean_old)] / scores_added.