Question

Two number are in the ratio 3:4 if 8 is added to each number they became in the ratio 4:5 find the number.​

Answer 1

Answer:

k=8

Step-by-step explanation:

1st number 3k

2nd number 4k

Adding 8 to each number

1st number is 3k+8

2nd number is 4k+8

3k+8 : 4k+8 :4: 5

5×(3k+8 )= 4(4k+8)

15k -16k = 32 -- 40

-k = -8

K= 8

The number 24 and 32

Answer 2

Step-by-step explanation:

Given:-

• Two numbers are in the ratio 3 : 4

• If 8 is added to each number then the ratio becomes 4 : 5

To Find:-

• The two numbers.

Solution:-

Case 1:-

Let the common ratio between the numbers be x

Then:-

The 1st number = 3x

And The 2nd number = 4x

Case 2:-

If 8 is added to both the numbers.

The 1st number becomes = 3x + 8

The 2nd number becomes = 4x + 8.

Given, The ratio becomes 4 : 5

$\longrightarrow\sf (3x + 8) : (4x + 5) = 4 : 5$

$\longrightarrow\sf \dfrac{3x + 8}{4x + 5} = \dfrac{4}{5}$

$\sf \underline{ By \: cross \: multiplication:-}$

$\sf \longrightarrow 5(3x + 8) = 4(4x + 8)$

$\sf \longrightarrow 15x + 40= 16x + 32$

$\sf \longrightarrow 15x - 16x = 32 - 40$

$\sf \longrightarrow -x = -8$

$\sf \longrightarrow x = 8$

The numbers are:-

⇢ 3x = 3 × 8 = 24

⇢ 4x = 4 × 8 = 32

Therefore:-

The 1st number = 24

The 2nd number = 32