Question

Two numbers are on the ratio 2:3. If 4 be subtracted from each, they are in the ratio 3:5. The Numbers are.....​

Answer 1

Solution

Ratio of 2 numbers = 2 : 3

Let the 2 numbers be 2x, 3x

Given

If 4 is subtracted from each, the ratio becomes 3 : 5.

$\implies \dfrac{2x - 4}{3x - 4} = \dfrac{3}{5}$

By cross multiplication

→ 5(2x - 4) = 3(3x - 4)

→ 10x - 20 = 9x - 12

→ 10x - 9x = - 12 + 20

→ x = 8

One of the number = 2x = 2 * 8 = 16

Another number = 3x = 3 * 8 = 24

Hence, 16 and 24 are the required numbers.

Answer 2

Question :

Two numbers are in the ratio 2:3. If 4 be subtracted from each, they are in the ratio 3:5. Find the numbers.

Solution :

$\underline{\bold {Given:}}$

• The numbers in the ratio = 2:3

$\underline{\bold {To\:Find:}}$

• The numbers.

Let the two numbers be 2x and 3x respectively.

Atq,

$\implies \frac{2x - 4}{3x - 4} = \frac{3}{5} \\ \implies 5(2x - 4) = 3(3x - 4) \\ \implies 10x - 20 = 9x - 12 \\ \implies 10x - 9x = - 12 + 20 \\ \implies x = 8$

$\boxed{\green{\therefore {The \:numbers\:are\:(2\times 8)=16\:and\:(3\times 8)=24}}}$

$\underline{\bold {Verification:}}$

$\implies \frac{2x - 4}{3x - 4} =\frac{3}{5} \\\implies \frac{2\times 8 - 4}{3\times 8 - 4} = \frac{3}{5} \\\implies \frac{16-4}{24-4}=\frac{3}{5}\\\implies \frac{12}{20}=\frac{3}{5}\\\implies \frac{3}{5} =\frac{3}{5}$