The average score of 10 contestants in a competition is ‘y’ points. Two new contestants entered the competition with a total combined score of 60 points, causing the overall average score to decrease by $\frac{y}{12}$ points. If the score of the higher-scoring new contestant is $y-20$ points, what is the difference between the scores of the two new contestants?

The correct option is 20 points.

Step 1: Express the initial total score of the contestants.

The initial number of contestants is 10 and their average score is y points.

Initial total score = 10 × y = 10y

Step 2: Find the new overall average score and total score.

Two new contestants enter with a combined score of 60 points, making the total number of contestants 10 + 2 = 12.

The overall average score decreases by
$\frac{y}{12}$
points.

New average score:
$y-\frac{y}{12}=\frac{11y}{12}$

New total score of 12 contestants:
$12\times \frac{11y}{12}=11y$

Step 3: Calculate the value of y.

The total score of all 12 contestants is also equal to the initial total score plus the combined score of the two new contestants (60 points):

$10y+60=11y$

Subtracting 10y from both sides:
$11y-10y=60$
$y=60$

Step 4: Determine the individual scores of the two new contestants.

The score of the higher-scoring new contestant is:
$y-20=60-20=40$
points.

Since the combined score of the two new contestants is 60 points, the score of the lower-scoring contestant is:
$60-40=20$
points.

Step 5: Calculate the difference between their scores.

Difference = Higher score - Lower score
$40-20=20$
points.

Therefore, the difference between the scores of the two new contestants is 20 points.