Question

b) Two numbers are in the ratio 4:5. If 30 is subtracted from each of the numbers, the ratio becomes 1:2.
Find the number.
[3]​

Answer 1

Let the 2 numbers be x and y

$\sf{\dfrac{x}{y} = \dfrac{4}{5}}\\\\\\\Rightarrow \sf{4y = 5x}\\\\\\\Rightarrow \bf{y = \dfrac{5x}{4}}$

When 30 is subtracted,

$\sf{\dfrac{x-30}{y-30} = \dfrac{1}{2}}\\\\\\\dashrightarrow \: \sf{2(x - 30) = y - 30}\\\\\\\longrightarrow \: \sf{2x - 60 = y - 30}\\\\\longrightarrow \: \sf{2x = y + 30}\\\\\longrightarrow \: \bf{y = 2x - 30}$

Now, we have got the 2 values of y.

Equating them,

$\sf{\dfrac{5x}{4} = 2x - 30}\\\\\\\longrightarrow \: \sf{5x= 4(2x-30)}\\\\\\\longrightarrow \: \sf{5x = 8x - 120}\\\\\\\longrightarrow \: \sf{-3x = -120}\\\\\\\therefore \: \boxed{\bf{x = 40}}$

Substitute the value of y in any one of the above equations to find x.

y = 2x - 30

➝ y = 2(40) - 30

➝ y = 80 - 30

∴ y = 50

∴ The 2 numbers are 40 and 50

Answer 2

Given :-

Two numbers are in the ratio 4:5 if 30 is subtracted from each of the number, the ratio becomes 1:2

To Find :-

Numbers

Solution :-

Let the ratio be 4x and 5x

4x - 30/5x - 30 = 1/2

2(4x - 30) = 5x - 30

8x - 60 = 5x - 30

8x - 5x = 60 - 30

3x = 30

x = 30/3

x = 10

Numbers are

4x = 4(10) = 40

5x = 5(10) = 50