The mean time for running a race by a group of 20 people was 54 seconds. The times for a second group of people were added and the value of the mean went up to 56 seconds. Which formula represents the relationship between the number of people in the second group, P, and the mean time of the second group, T?

Answer:

12) C

Total time taken by first group = 54 x 20 = 1080s
We know number of people in second group = ‘P’
Mean time of second group = ‘T’
Total number of people = 20 + P
Total time taken by second group = T x P
Total time taken by both groups = 1080 + (T x P)

In order to get total mean time (56), we need to divide total amount of time by total number of people.

56 = (1080 + TP) ÷ (20 + P)
56 (20 + P) = 1080 + TP
1120 + 56P = 1080 + TP
1120 – 1080 = TP – 56P
40 = P (T – 56)
P = 40 / (T – 56)

Hence, the answer is C.