Question

(c) The sum of two numbers is 135 and they are in the ratio of 4:5. Find the number​

Answer 1

Given -

• Sum of two number = 135

• Ratio of number = 4 : 5

To find -

• The number

Solution -

In the question, we are provided with the sum of two numbers, and their ratio is 4 : 5, and we need to find the original numbers. First we will take a common ratio, then we will find the value of that ratio, then we will multiply that value, which we will obtain, with the ratio given, hence, we will obtain the original numbers, Let's do it !

So -

Let the common ratio be x

4 = 4x

5 = 5x

sum = 135

Now -

We will, find the value of x, by dividing the obtained value by 135, then we will have the value of x.

On substituting the values -

$\longrightarrow$ $\tt{4x\:+\:5x\:=\:135}$

$\longrightarrow$ $\tt{9x\:=\:135}$

$\longrightarrow$ x = $\tt\cancel\dfrac{135}{9}$

$\longrightarrow$ $\tt{x\:=\:15}$

At the end -

We will find the original numbers, by multiplying 15 with 4x and 5x.

$\longrightarrow$ 4 × 15 = 60

$\longrightarrow$ 5x = 5 × 15 = 75

Verification -

For verification, we will add up, both the numbers we have obtained, and will put it equal to 135.

$\longrightarrow$ 60 + 75 = 135

$\longrightarrow$ 135 = 135

$\therefore$ The two numbers are 60 and 75.

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Answer 2

Given:-

$\longmapsto$ The sum of two numbers = 135

$\longmapsto$ The given ratio = 4:5

To find:-

$\longmapsto$ The numbers

Solution:-

Let the two numbers be x and y

x + y = 135-------(1)

The y are in the ratio 4:5

x / y = 4 / 5

Cross multiplication

4y = 5x

y = 5x/4--------(2)

Substituting the value of y in equation (1)

$\Longrightarrow$ x + y = 135

$\Longrightarrow$ x = 5x / 4 = 135

$\Longrightarrow$ (4x + 5x) / 4 = 135

$\Longrightarrow$ 9x / 4 = 135

$\Longrightarrow$ 9x = 135 × 4

$\Longrightarrow$ x = (135 × 4) / 9

$\Longrightarrow$ x = 15 × 4

$\Longrightarrow$ x = 60

One number is "60"

Substituting the value of x in equation (1) to derive the value of y

$\Longrightarrow$ x + y = 135

$\Longrightarrow$ 60 + y = 135

$\Longrightarrow$ y = 135 - 60

$\Longrightarrow$ y = 75

The another number is "75"

Therefore, The numbers are "60 and 75".