Question

If one number is \[80\%\] of the other and the sum of their squares is \[656\], then the numbers are:
A. \[4,5\]
B. \[8,10\]
C. \[20,16\]
D. \[14,12\]

Answer 1

Hint: In this question, we need to find the two unknown numbers. Given that one number is \[80\%\] the other. And also given that the sum of their squares is \[656\]. First we need to assume the unknown numbers by two different variables. Then we need to proceed as the question says. Here we need to convert the percentage value in the form of a fraction of \[100\] .

Complete step by step answer:
Let us consider the one number as \[x\] and the other number as \[y\].
Given, one number is \[80\%\] of the other, that is , \[y\] is \[80\%\] of \[x\] .
 \[y = \left( \dfrac{80}{100} \right) \times x\]
By simplifying,
We get,
\[y = \left( 0.8 \right)x\]
Also given that the sum of their squares is \[656\] that is \[ square\ of\ x +\ square\ of\ y\] is \[656\]
⇒ \[x^{2} + y^{2} = 656\]
Now we can substitute the value of \[y\],
We get,
\[x^{2} + {(\left( 0.8 \right)x)}^{2} = 656\]
On simplifying,
We get,
\[x^{2} + {0.64x}^{2} = 656\]
By adding the variable terms,
We get,
\[1.64x^{2} = 656\]
⇒ \[x^{2} = \dfrac{656}{1.64}\]
By dividing,
We get,
\[x^{2} = 400\]
On taking square root on both sides,
We get,
\[x = \sqrt{400}\]
⇒ \[\ x = 20\]
Thus we get the one number as \[20\] . Now we need to find another number.
We can find the another number by substituting the known value in \[y = (0.8)\ x\]
Thus we have found the value of \[x\] as \[20\] .
By substituting ,
We get,
\[y = (0.8)\ \times 20\]
By multiplying,
We get,
\[y = 16.0\]
Thus we have found the another number as \[16\]
Therefore the numbers are \[20\] and \[16\] .

So, the correct answer is “Option C”.

Note:
An algebraic expression is nothing but it is built up with integers, constants, variables and mathematical operations (addition, subtraction, multiplication, division etc… ) In mathematics, a symbol (letter) which doesn’t have a value is called a variable. Similarly which has a fixed value is called constant . Percentage is defined as a number or a ratio expressed in the fraction of \[100\]. It is a dimensionless number and has no unit of measurement.