The average of five integers is 48. The average of the first four integers is 50% of the 5th integer. The 5th integer is:

Correct option is D

Given:

The average of five integers = 48.

The average of the first four integers is 50% of the 5th integer.

Formula Used:

Average of five integers:

Average =$$\frac{\text{Sum of integers}}{\text{Number of integers}}$$​

Solution:

Let the five integers be $$a_1, a_2, a_3, a_4, a_5.$$​​

From the given, we have two conditions:

The average of all five integers is 48:

​$$\frac{a_1 + a_2 + a_3 + a_4 + a_5}{5} = 48$$​​

This gives:

​$$a_1 + a_2 + a_3 + a_4 + a_5 = 48 \times 5 = 240$$       ...(1)​

The average of the first four integers is 50% of the 5th integer:

​$$\frac{a_1 + a_2 + a_3 + a_4}{4} = 0.5 \times a_5$$​​

​$$a_1 + a_2 + a_3 + a_4 = 0.5 \times a_5 \times 4 = 2 \times a_5$$​​

Substitute this into the first equation:

​$$a_1 + a_2 + a_3 + a_4 + a_5 = 240$$​

​$$2 \times a_5 + a_5 = 240$$​

​$$3 \times a_5 = 240$$​

​$$a_5 = \frac{240}{3} = 80$$​

Thus, the 5th integer is 80.