Question

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13. Two numbers are in the ratio 5 : 9. On subtracting 3 from each, the ratio becomes 1 : 2. Find
the numbers.​

Answer 1

Given :

• Two numbers are in tbe ratio 5:9 .
• On subtracting 3 from each other , the ratio becomes 1:2 .

To Find :

• Numbers .

Solution :

${\longmapsto\tt{Let\:1st\:No.\:be=5x}}$

${\longmapsto\tt{Let\:2nd\:No.\:be=9x}}$

On Subtrating 3 :

$\longmapsto\tt{First\:No.=5x-3}$

$\longmapsto\tt{Second\:No.=9x-3}$

A.T.Q :

$\longmapsto\tt{\dfrac{5x-3}{9x-3}=\dfrac{1}{2}}$

$\longmapsto\tt{2(5x-3)=1(9x-3)}$

$\longmapsto\tt{10x-6=9x-3}$

$\longmapsto\tt{10x-9x=-3+6}$

$\longmapsto\tt\bf{x=3}$

Value of x is 3 ...

Therefore :

$\longmapsto\tt{1st\:No.=5(3)}$

$\longmapsto\tt\bf{15}$

$\longmapsto\tt{2nd\:No.=9(3)}$

$\longmapsto\tt\bf{27}$