Question

Two numbers are in the ratio of 4 : 5. if 4 added to each number, then their ratio is 5 : 6, find the numbers.

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Answer 1

Answer:

x=2/9

Step-by-step explanation:

let the numbers be 4x and 5x

(4x+4)+(5x+4)=5x+6x

9x+9=11x

9=11x-9x

9=2x

X=2/9

Answer 2

Given question:

• Two numbers are in the ratio of 4:5. If 4 is added to each number, then their ratio is 5:6.

To find:

• Find the numbers.

Solution:

Given two numbers are

$\frac{4x}{5x}$

If 4 is added to the each then the ratio will be 5:6

$\frac{4x + 4}{5x + 4} = \frac{5}{6}$

We will do cross multiplication,

$6(4x + 4) = 5(5x + 4)$

$24x + 24 = 25x + 20$

$24 - 20 = 25x - 24x$

$4 = x$

Hence the value of x is 4.

Substitute x value in the given fraction.

$\frac{4x}{5x}$

$4x = 4(4) = 16$

$5x = 5(4) = 20$

Therefore the fraction is,

$\frac{16}{20}$

$= \frac{4}{5}$

It's confusing know. Don't worry I will verify it.

$\frac{4(4)+ 4}{5(4) + 4} = \frac{5}{6}$

$\frac{16 + 4}{20 + 4} = \frac{5}{6}$

$\frac{20}{24} = \frac{5}{6}$

$6(20) = 5(24)$

$120 = 120$

Hence verified.