16. If three numbers are in the ratio of 1:3:5 and half
the sum is 9, then the ratio of cubes of the numbers
is:
Answers
Given,
Three numbers are in the ratio of 1:3:5.
The half value of the sum of the three numbers = 9
To find,
The ratio of the cubes of the numbers.
Solution,
We can simply solve this mathematical problem using the following process:
According to the question,
The three numbers are in the ratio of 1:3:5
=> let us assume that the three numbers are x, 3x, and 5x, respectively.
Now, according to the question;
The half value of the sum of the three numbers = 9
=> 1/2 × (sum of the three numbers) = 9
=> sum of the three numbers = 9×2
=> sum of the three numbers = 18
=> x + 3x + 5x = 18
=> 9x = 18
=> x = 18/9
=> x = 2
So, the first number is x = 2
The second number = 3x = 3×2 = 6
The third number = 5x = 5×2 = 10
So, the ratio of the cubes of the numbers
= (x)^3:(3x)^3:(5x)^3
= (2)^3:(6)^3:(10)^3
= 8:216:1000
= 1:27:125
Hence, the ratio of the cubes of the numbers is equal to 1:27:125.