**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.**