Question

The ratio of two positive numbers is 3:4. The sum of their squares is 400. What is the sum of the numbers?

A) 28 B) 22 C) 24 D) 26

Answer 1

✫ ANSWER ✫

• (A) 28 (✔)

GIVEN:

• The ratio of two positive numbers is 3:4.
• The sum of their squares is 400

TO FIND:

• What is the sum of the numbers ?

SOLUTION:

Let the two positive numbers be 'x' and 'y' respectively.

CASE:- ❶

➣ The ratio of two positive numbers is 3:4.

According to question:-

$\rm{\dashrightarrow x:y = 3:4 }$

$\rm{\dashrightarrow \dfrac{x}{y} = \dfrac{3}{4}}$

$\large\bf{\dashrightarrow 3y = 4x...1)}$

$\rm{\dashrightarrow y = \dfrac{4x}{3} }$

CASE:- ❷

➣ The sum of their squares is 400.

According to question:-

$\large\bf{\dashrightarrow x^2 + y^2 = 400...2) }$

Put the value of 'y' in equation 2)

$\rm{\dashrightarrow x^2 + \bigg( \dfrac{4x}{3} \bigg)^2 = 400 }$

$\rm{\dashrightarrow x^2 + \dfrac{16x^2}{9} = 400 }$

$\rm{\dashrightarrow \dfrac{9x^2 + 16x^2}{9} = 400 }$

$\rm{\dashrightarrow 25x^2 = 3600 }$

$\rm{\dashrightarrow x^2 = \cancel\dfrac{3600}{25}}$

$\rm{\dashrightarrow x^2 = 144 }$

$\bf{\dashrightarrow x = 12}$

Put the value of 'x' in equation 1)

$\rm{\dashrightarrow 3y = 4 \times 12 }$

$\rm{\dashrightarrow 3y = 48 }$

$\rm{\dashrightarrow y = \cancel\dfrac{48}{3}}$

$\bf{\dashrightarrow y = 16 }$

• x = 12
• y = 16

❑ Sum of the numbers = (x + y) = (12+16)= 28

❛ Hence, the sum of two numbers is 28 ❜

______________________

Answer 2

$a)28 \: is \: the \: answer \: \\ \huge \: thank \: you \:$