Question

a) Two numbers are in the ratio of 3/4 . If 5 is subtracted from 1^ * number and 10 added to 2nd number, ratio becomes 1/2 Find the numbers.​

Answer 1

Answer :-

• The numbers are 30 and 40.

To find :-

• The numbers.

Step-by-step explanation :-

• Here, it is given that two numbers are in the ratio 3 : 4.

Let :-

• The numbers be "3x" and "4x" respectively.

If 5 is subtracted from the 1st number,

• We get "3x - 5".

If 10 is added to the 2nd number,

• We get "4x + 10".

It is given that :-

• If 5 is subtracted from the first number and 10 is added to the 2nd number, the ratio becomes 1 : 2.

Therefore,

$\rm\longrightarrow \: \dfrac{3x - 5}{4x + 10} = \dfrac{1}{2}$

$\rm\longrightarrow \: 1 \: (4x + 10) = 2 \: (3x - 5)$

$\rm\longrightarrow \: 4x + 10 = 6x - 10$

$\rm\longrightarrow \: 4x - 6x = - 10 - 10$

$\rm\longrightarrow \: - 2x = - 20$

$\rm\longrightarrow \: x = \cancel{\dfrac{ - 20}{ - 2}}$

$\rm\longrightarrow \: x = 10$

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Hence, the numbers are :-

$\purple{\bf3x = 3 \times 10 = 30.}$

$\purple{ \bf4x = 4 \times 10 = 40.}$