Question

Two numbers are in the ratio 5 : 9. on subtracting 3 form each, the ratio becomes 1 : 2. Find the numbers​

Answer 1

Given :

• Two numbers are in the ratio 5:9 .
• On subtracting 3 from each number , the ratio becomes 1:2 .

To Find :

• Numbers .

Solution :

$\longmapsto\tt{Let\:first\:Number\:be=5x}$

$\longmapsto\tt{Let\:second\:Number\:be=9x}$

Now ,

• On subtracting 3 from each number the ratio becomes 1:2 .

$\longmapsto\tt{First\:Number=5x-3}$

$\longmapsto\tt{Second\:Number=9x-3}$

A.T.Q :

$\longmapsto\tt{\dfrac{5x-3}{9x-3}=\dfrac{1}{2}}$

$\longmapsto\tt{2(5x-3)=1(9x-3)}$

$\longmapsto\tt{10x-6=9x-3}$

$\longmapsto\tt{10x-9x=-3+6}$

$\longmapsto\tt\bf{x=3}$

Value of x is 3 .

Therefore :

$\longmapsto\tt{First\:Number=5(3)}$

$\longmapsto\tt\bf{15}$

$\longmapsto\tt{Second\:Number=9(3)}$

$\longmapsto\tt\bf{27}$

So , The numbers are 15 and 27 .

Answer 2

Answer:

Given :-

• Two numbers are in the ratio of 5:9.
• By subtracting 3 from each the ratio becomes 1:2.

To Find :-

• What is the number.

Solution :-

Let, the first number be 5x

And, the second number be 9x

Again, by substracting 3 from each number, the ratio becomes 1:2.

First number will be 5x - 3

And, the second number will be 9x - 3

According to the question,

↦ $\sf\dfrac{5x - 3}{9x - 3} =\: \dfrac{1}{2}$

By doing cross multiplication we get,

↦ 2(5x - 3) = 9x - 3

↦ 10x - 6 = 9x - 3

↦ 10x - 9x = - 3 + 6

➠ x = 3

Hence, the required numbers are,

✧ First number = 5x = 5 × 3 = 15

✧ Second number = 9x = 9 × 3 = 27

$\therefore$ The numbers are 15 and 27.