Question

two nos are in ratio 10:6 .if the sum of the nos is 572. find the no​

Answer 1

Required Answer:

$\star \underbrace{\sf{Given:-}}$

• A ratio of two numbers = 10 : 6
• Sum of two numbers = 572

$\star \underbrace{\sf{What \: To \: Find :-}}$

• We have to find those two numbers.

$\star \underbrace{\sf{How \: To \: Find :-}}$

To find the two numbers we have to,

• Take x as the common multiple in the ratio = 10 : 6 = 10x : 6x
• Frame an equation according to the question.
• Solve the equation and find x.
• Substitute the value and find the two numbers.

$\star \underbrace{\sf{Solution:-}}$

$\sf{\rightarrow{ Framing \: the \: equation}}$

According to the question,

⇒ The sum of two numbers (10x and 6x) is 572.

Hence the equation will be,

⇒ 10x + 6x = 572

$\sf{\rightarrow{Solving \: the \: equation}}$

The equation,

⇒ 10x + 6x = 572

Add 10x and 6x,

⇒ 16x = 572

Take 16 to RHS,

⇒ $\sf{x = \dfrac{572}{16}}$

Divide 572 by 16,

⇒ $\sf{x = \dfrac{143}{4}}$

Convert it into a decimal,

⇒ x = 35.75

Substitute the value,

• 10x = 10 × 35.75 = 357.5
• 6x = 6 × 35.75 = 214.5

$\bf{\therefore \: Hence, the \: two \: numbers \: are \: 357.5 \: and \: 214.5.}$

$\star \underbrace{\sf{Verification:-}}$

Here the equation,

⇒ 10x + 6x = 572

Substitute the value of x,

⇒ (10 × 35.75) + (6 × 35.75) = 572

Multiply 10 by 35.75,

⇒ 357.5 + (6 × 35.75) = 572

Multiply 6 by 35.75,

⇒ 357.5 + 214.5 = 572

Add the numbers,

⇒ 572 = 572

$\bf{\therefore \: LHS = RHS}$

$\bf{\therefore \: Hence, verified.}$