The average of a few numbers is 48. If 75% of the numbers are increased by 4 each and the rest are decreased by 6 each, then what is the average of the numbers, so obtained?

Let the total numbers be 100 and their average is 48.

• 75% of the number's average is increased by 4 (given)

i.e; Average of 75 numbers is 52 now. 

As we know, 

$$average\ =\ \frac{sum\ of\ observation\ }{number\ of\ observation}$$

Sum of 75 numbers now, = $$75\times\ 52=3900$$

• 25% of the number's average is decreased by 6 (given)

i.e; Average of 25 numbers is 42 now

Sum of 25 numbers = $$25\times\ 42=1050$$

Now,

Average of total numbers = $$\frac{\left(sum\ of\ 25\ numbers\ +\ sum\ of\ 75\ numbers\right)}{Total\ number}$$

= $$\frac{3900+1050}{75+25}$$

= $$\frac{4950}{100}=49.5$$

Hence, Option C is correct.