Question

The mean of five numbers is 10. Two of the five numbers are 10 and 13. The remaining
three numbers are in the ratio of 2:3: 4. Find the numbers.
Coo
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Answer 1

Answer :

The remaining three numbers are 6 , 9 and 12

Step-by-step explanation :

Given,

• The mean of five numbers is 10
• Two of the five numbers are 10 and 13
• The remaining  three numbers are in the ratio of 2 : 3 : 4

To find,

• the numbers

Solution,

The remaining  three numbers are in the ratio of 2 : 3 : 4

   Let the three remaining numbers be

• 2x
• 3x
• 4x

➟ Sum of observations = Sum of the numbers

         = 10 + 13 + 2x + 3x + 4x

         = 23 + 9x

➟ Number of observations = 5

➟ Mean of the five numbers = 10

we know,

      $\boxed{\sf Mean=\frac{Sum \ of \ observations}{No.of \ observations}}$

         $\sf 10=\frac{23+9x}{5} \\\\ 23+9x = 10 \times 5 \\\\ 23+9x=50 \\\\ 9x=50-23 \\\\ 9x=27 \\\\\\ x=\dfrac{27}{9} \\\\\\ x=\dfrac{9 \times 3}{9} \\\\ x=3$

➪ 2x = 2(3) = 6

➪ 3x = 3(3) = 9

➪ 4x = 4(3) = 12

The remaining three numbers are 6 , 9 and 12

∴ The five numbers are 6 , 9 , 10 , 12 and 13