The average of some numbers is 54.6. If 75% of the numbers are increased by 5.6 each, and the rest are decreased by 8.4 each, then what is the average of the numbers so obtained?

56.7

Lets assume there are 4 numbers, each of value 54.6

Average of 4 numbers = 54.6

Sum = 54.6 x 4 = 218.4

75% of the numbers of total numbers increased by 5.6 each

⇒ \(\frac{3}{4}\) x 4 = 3 (54.6 + 5.6)

25% of the numbers of total numbers decreased by 8.4 each

⇒ \(\frac{1}{4}\) x 4 = 54.6 - 8.4

New average of 4 numbers = 3(54.6 + 5.6) + ( 54.6 - 8.4) = 3x 60.2 + 46.2 = 226.8

New average of 4 numbers = \(\frac{226.8}{4}\) = 56.7