Question

Two numbers are in the ratio 3:4. When each of them is reduced by 10, the ratio
becames 1:3. What are the numbers​

Answer 1

† GiveN †

• Ratio of two number is 3:4
• When each number reduced by 10 , the ratio become 1:3

† To FinD †

• The two number.

† SolutioN †

Let ,

• $\bold{the \: {1}^{st} \: number \: be \: 3x}$
• $\bold{the \: {2}^{nd} \: number \:be \: 4x}$

Then ,

$\bold{ \frac{3x - 10}{4x - 10} = \frac{1}{3} }$

$\bold{ \implies \: 3(3x - 10) = 1(4x - 10)}$

$\bold{ \implies \: 9x - 30 = 4x - 10}$

$\bold{ \implies \: 9x - 4x = - 10 + 30}$

$\bold{ \implies \:5x = 20 }$

$\bold{ \implies \:x = \frac{20}{5} }$

$\bold{ \implies \:x = 4 }$

By putting the value of x

$\bold{the \: \: {1}^{st} \: number </p><p>\: = 3x} \\ \\ \bold{3 \times 4} \\ \\ \bold{ = 12}$

$\bold{the \: {2}^{nd} \: number </p><p>= 4x} \\ \\ \bold{ = 4 \times 4} \\ \\ \bold{ = 16}$

So , required numbers are 12 and 16.