Question

Two numbers are in the ratio 1:5. When 9 is subtracted from each number they will be in the ratio 1 : 9. Which are the numbers?​

Answer 1

Answer:

18,90

Step-by-step explanation:

let the no.s be x,5x

ATC

x-9/5x-9 =1/9

on cross multiplying

9x-81=5x-9

4x = 72

x=18

5x= 90

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

Two numbers are in the ratio 1:5.

Let assume that

• First number be x

• Second number be 5x

According to statement

When 9 is subtracted from each number they will be in the ratio 1 : 9.

Now numbers become,

• First number = x - 9

• Second number = 5x - 9

Thus,

$\rm :\longmapsto\:\dfrac{x - 9}{5x - 9} = \dfrac{1}{9}$

$\rm :\longmapsto\:9(x - 9) = 5x - 9$

$\rm :\longmapsto\:9x - 81 = 5x - 9$

$\rm :\longmapsto\:9x - 5x = 81 - 9$

$\rm :\longmapsto\:4x = 72$

$\rm \implies\:\boxed{ \tt{ \: x \: = \: 18 \: }}$

Hence,

• First number = 18

• Second number = 18 × 5 = 90

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Basic Concept Used :-

Writing System of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.