Question

two numbers are in the ratio 4:5 . If 7is subtracted from each of them, then the ratio becomes 3:4.find the numbers
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Answer 1

Answer:

Let the numbers have a common ratio x.

Then the numbers are 4x and 5x

On subtracting 7 from each , we get the numbers as 4x-7 and 5x-7.

ATP,

4x-7/5x-7 =3/4

on cross multiplying,

we get 16x -28 = 15x - 21

16x-15x = 28-21

x =7

so the numbers are 4x , 5x

4(7) , 5(7)

28 , 35

Answer 2

Step-by-step explanation:

Given:-

• Two numbers are in the ratio 4 : 5

• If 7 is subtracted from each of the number then the ration becomes 3 : 4

To Find:-

• The two numbers.

Solution:-

Let the common ratio between the numbers be x

Case 1:-

Given, the two numbers are in the ratio 4 : 5

Then,

The 1st number = 4x

The 2nd number = 5x

Case 2:-

If 7 is subtracted from each of them, then the ratio becomes 3 : 4

If 7 is subtracted from the 1st number

The 1st number becomes 4x - 7

If 7 is subtracted from 2nd number

The 1st number becomes 5x - 7

Given, the ratio becomes 3 : 4

$\rm \dashrightarrow \dfrac{4x -7 }{5x - 7} = \dfrac{3}{4}$

By cross multiplication:-

$\rm \dashrightarrow {4(4x -7) } = {3(5x - 7)}$

$\rm \dashrightarrow 16x - 28 =15x - 21$

$\rm \dashrightarrow 16x -15x = 28 - 21$

$\rm \dashrightarrow x = 7$

The 1st number = 4x = 4 × 7 = 28

The 2nd number = 5x = 5 × 7 = 35

$\underline{\boxed{\purple{\rm \therefore The \: two \: numbers \: are \: 28 \: and \: 35}}}$