Question

9. Two numbers are in the ratio 3: 5. If the sum of the numbers is 144, then the
number is
(b) 54
(c) 72
(d) 90
​

Answer 1

Given

Two numbers are in the ratio 3:5

Sum of the numbers is 144

____________________________

To Find

The two numbers

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Solution

Let the two numbers be 3x and 5x (This is because the numbers are in the ratio of 3:5)

We know that the sum of the two numbers gives us 144. We will solve this equation to find the two numbers ⇒ 3x + 5x = 144

Let's solve your equation step-by-step.

3x + 5x = 144

Step 1: Simplify the equation.

⇒ 3x + 5x = 144

⇒ 8x = 144

Step 2: Divide 8 from both sides of the equation.

⇒ 8x ÷ 8 = 144 ÷ 8

⇒ x = 18

∴ One of the number is ⇒ 3x = 3(18) = 54

∴ The other number is ⇒ 5x ⇒ 5(18) = 90

∴ The two numbers are 54 and 90.

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Answer 2

$\Large{\underline{\bf{\color{indigo} GiVeN,}}}$

• Two numbers are in ratio 3:5.

$\bf\red{Let,}$

$\longmapsto\:\:\bf\blue{First\:number\:is\:3x}.$

$\longmapsto\:\:\bf\purple{Second\:number\:is\:5x}.$

• The sum of these numbers are 144.

$\bf\pink{According\:to\:the\:question,}$

$:\implies\:\:\bf{3x\:+\:5x\:=\:144}$

$:\implies\:\:\bf{8x\:=\:144}$

$:\implies\:\:\bf{x\:=\:\dfrac{144}{8}}$

$:\implies\:\:\bf\orange{x\:=\:18}$

━─━─━─━─━─━─━─━─━─━─━─━─━─━─━

$\bf\green{Hence,}$

$\longrightarrow\:\:\bf{First\:number\:=\:3\times{18}}$

$\longrightarrow\:\:\bf\blue{First\:number\:=\:54}$

$\Large\bf\red{And,}$

$\longrightarrow\:\:\bf{Second\:number\:=\:5\times{18}}$

$\longrightarrow\:\:\bf\purple{Second\:number\:=\:90}$

$\Large\bold\therefore$ The two numbers are 54 & 90.