Question

here are four unknown numbers. The mean of the first two numbers is 4 and the mean of the first three is 9 The mean of all four number is 15, If one of the four number is 2 Find the other numbers

Answer 1

★Given:-

• There are four unknown numbers.
• The mean of the first two numbers is 4
• The mean of the first three is 9
• The mean of all four number is 15
• One of the four number is 2

★To find:-

• The other number.

★Solution:-

Let p,q,r,s be the four numbers.

According to question,

Given,The mean of the first two numbers is 4.Therefore,

➺(p + q)/2 = 4

➺p+q = 2×4

➺p+q = 8___(1)

The mean of the first three is 9.Therefore,

➺(p+q+r)/3 = 9

➺p+q+r = 9×3

➺p+q+r = 27___(2)

The mean of the all four numbers is 15.Therefore,

➺(p+q+r+s)/4 = 15

➺p+q+r+s = 15×4

➺p+q+r+s = 60___(3)

Given that one of the four numbers is 2.

Let p = 2.

Putting this in equation(1),

➺p + q = 8

➺2 + q = 8

➺q = 8 - 2

➺q = 6

From equation(1) we have,

• p+q = 8

Putting this values in equation(2),

➺p+q+r = 27

➺8 + r = 27

➺r = 27 - 8

➺r = 19

From equation(2) we have,

• p+q+r = 27

Putting this in equation(3),

➺p+q+r+s = 60

➺27 + s = 60

➺s = 60 - 27 = 33

➺s = 33

Therefore,

• p = 2
• q = 6
• r = 19
• s = 33

Hence, the other numbers are 6,19&33.

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