Question

There are six people at a bus stop. Each person is half the age of the next person in line. The mean age of the group is 21. How old is the youngest person?

Answer 1

Answer:

The youngest person is 2 years old

Step-by-step explanation:

There are six people at a bus stop.

We are told that:

The mean age of the group is 21.

The total number of people is 6 people

Hence:

The total sum of their ages is 21 × 6

= 126

Each person is half the age of the next person in line.

Let the age of the first person be = x

The age of the second person = x/2

The age of the third person = x/2 ÷ 2 = x/2 × 1/2 = x/4

The age of the fourth person = x/4 ÷ 2

x/4 × 1/2 = x/8

The age of the fifth person = x/8 ÷ 2

x/8 × 1/2 = x/16

The age of the sixth person = x/16 ÷ 2

x/16 × 1/2 = x/32

Hence:

x + x/ 2 + x/4 + x/8 + x/16 + x/32 = 126

Lowest Common Denominator is 32

32x + 16x + 8x + 4x + 2x + x/32 = 126

63x /32 = 126

Cross Multiply

63x = 126 × 32

63x = 4032

x = 4032 /63

x = 64 years

Hence, the age of the first person is 64 years.

The age of the youngest person which is the sixth person is :

x/32

= 64/32

= 2 years