Question

Two number are such that the ratio between them is 3:5. If each is increased by 10 the ratio between the new number so formed 5:7.Find the original number​

Answer 1

GIVEN:

• Ratio of two numbers = 3:5
• If the numbers are increased by 10, then the new ratio = 5:7

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TO FIND:

The original numbers.

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SOLUTION:

We are given that ratio between the two numbers is 3:5.

So,

$\bigstar {\sf {\green {Let\ the\ first\ number\ be\ 3x.}}}$

$\bigstar {\sf {\green {Let\ the\ second\ number\ be\ 5x.}}}$

If the two numbers are increased by 10, then the ratio between the two new numbers will be 5:7.

So,

$\sf \dfrac{3x + 10}{5x + 10} = \dfrac{5}{7}$

$\bigstar {\sf {\red {Cross\ Multiplication.}}}$

$\implies {\sf {7(3x+10) = 5(5x+10)}}$

$\implies {\sf {21x+70 = 25x+50}}$

$\implies {\sf {70-50 = 25x-21x}}$

$\implies {\sf {20 = 4x}}$

$\implies {\sf \dfrac{20}{4} = x}$

$\boxed {\bf {\orange {5=x}}}$

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VERIFICATION:

On substituting the value of x as 5 in the equation,

LHS: $\sf \dfrac {3x+10}{5x+10}$

RHS: $\sf \dfrac {5}{7}$

$\sf \dfrac{3x + 10}{5x + 10} = \dfrac{5}{7}$

$\implies {\sf \dfrac{3 \times 5 + 10}{5 \times 5 + 10} = \dfrac{5}{7}}$

$\implies {\sf \dfrac{15+ 10}{25 + 10} = \dfrac{5}{7}}$

$\implies {\sf \dfrac{25}{35} = \dfrac{5}{7}}$

$\implies {\sf \dfrac{5}{7} = \dfrac{5}{7}}$

LHS = RHS

Hence Verified!

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THE NUMBERS ARE:

• First number = 3x

= 3×5

= 15

• Second number = 5x

= 5×5

= 25

$\boxed {\sf {\purple {The\ two\ required\ numbers\ are\ 15\ and\ 25.}}}$