Question

The average runs scored by 3 players is 160 per match. Their runs are in a ratio 4:6:2. What will be the average if the player who scored the minimum runs hits a century in the next match and the other two play with the same runs?

• A. 160.50
• B. 166.66
• C. 162.50
• D. 164.50

Hint:

If only one player's score changes, the new average is: \(\text{Old Average} + \frac{\text{Score Change}}{\text{Number of Players}}\).
Score change = \(100 - 80 = 20\).
New Avg = \(160 + (20/3) = 160 + 6.66 = 166.66\).

Answer 1

The Correct Option is B

Concept: Total runs = \(Average \times \text{Number of players}\). Century = 100 runs.
Step 1: Find the individual runs.
Total runs = \(160 \times 3 = 480\).
Ratio = 4 : 6 : 2. Sum of parts = 12.
1 part = \(480 / 12 = 40\).
Runs: 160, 240, 80. (Minimum = 80).

Step 2: Calculate the new total runs.
New runs for minimum player = 100.
New Total = \(160 + 240 + 100 = 500\).

Step 3: Find the new average.
New Average = \(500 / 3 = 166.66\).