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.​

Answer 1

To Find:-

• Find the two numbers.

Given:-

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

Solution:-

Let the two numbers be in the ratio of 2x : 3x

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

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

$\tt\implies \: 5( 2x - 4 ) = 3( 3x - 4 )$

$\tt\implies \: 10x - 20 = 9x - 12$

$\tt\implies \: 10x - 9x = 20 - 12$

$\tt\implies \: x = 8$

Hence,

• $\tt \: First \: \: digit \: \: is \: \: 2x = 2(8) = 16$

• $\tt \: Second \: \: digit \: \: is \: \: 3x = 3(8) = 24$

Answer 2

Answer:

✰To find:

Find the two numbers.

✰Given:-

Two numbers are in the ratio 2 : 3.

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

✰Solution:-

Let the two numbers be in the ratio of 2x : 3x

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

$\longrightarrow \: \frac{2x - 4}{3x - 4} = \frac{3}{5} \\ \longrightarrow 5(2x - 4) = 3(3x - 4) \\ \longrightarrow10x - 20 = 9x - 12 \\ \longrightarrow 10x - 9x = 20 - 12 \\ \implies x = 8$

Hence,

⍟The first digit is 2x=2(8)=16

⍟The second digit is 3x=3(8)=24