Four numbers are in proportion. The sum of the squares of the four numbers is 50

Ques - Four numbers are in proportion. The sum of the squares of the four numbers is 50 and the sum of the mean is 5. The ratio of first two terms 1:3. What is the average of the four numbers?

(a) 2

(b) 3

(c) 5

(d) 6

Solution - 

Let,

Four numbers are in proportion = a : b :: c : d

The sum of the squares of the four numbers = 50

a²+ b² + c² + d²= 50

The ratio of first two terms = 1:3

a : b = 1 : 3

a = 1

b = 3

The sum of the mean = 5

b + c = 5

c = 5 - b

c = 5 - 3

c = 2

Now,

a : b = c : d

1 : 3 = 2 : d

1/3 = 2/d

d = 3*2

d = 6

Now,

The average of the four numbers = Sum of value / Total no. of value

The average of the four numbers = (1 + 3 + 2 + 6) / 4

The average of the four numbers = 12/4

The average of the four numbers = 3

Hence,

The correct answer is option (b) 3.