Question

The present age of mother and daughter is in the ratio 3 :1 After 5 years if the ratio of their age will be 5:2 find their present age

Answer 1

The present age of mother and daughter is in the ratio 3 :1 After 5 years if the ratio of their age will be 5:2 find their present age

The present age of mother and daughter is in the ratio= 3 :1 .

After 5 year ,

The ratio of their age will be = 5:2

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Let present age of mother and daughter be 3x and x .

So , 3x+5/x+5 = 5/2

[ Calculation is given in the attachment sheet ]

So present age of mother = 45

And present age of daughter = 15

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

The present age of mother and daughter is in the ratio 3 : 1.

Let assume that

Present age of mother is 3x years

Present age of daughter is x years

After 5 years,

Age of mother is 3x + 5 years

Daughter age is x + 5 years

Further given that, after 5 years, the ratio of their age will be 5 : 2

$\rm \: 3x + 5 \: : \: (x + 5) = 5 \: : \: 2$

$\rm \: \dfrac{3x + 5}{x + 5} = \dfrac{5}{2}$

$\rm \: 2(3x + 5) = 5(x + 5)$

$\rm \: 6x + 10 = 5x + 25$

$\rm \: 6x - 5x = 25- 10$

$\rm\implies \:x = 15$

So,

Present age of mother is 3x = 3 × 15 = 45 years

Present age of daughter is x = 15 years

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Alternative Method :- Using two variables.

Given that,

The present age of mother and daughter is in the ratio 3 : 1

Let assume that

Present age of mother is x years

Present age of daughter is y years

So, According to statement,

$\rm \: x \: : \: y \: = \: 3 \: : \: 1 \:$

$\rm \: \dfrac{x}{y} = 3$

$\rm\implies \:x = 3y - - - (1)$

After 5 years,

Age of mother is x + 5 years

Age of daughter is y + 5 years

According to statement, After 5 years if the ratio of their age will be 5 : 2

$\rm \: x + 5 \: : \: y + 5\: = 5 \: : \: 2 \:$

$\rm \: \dfrac{x + 5}{y + 5} = \dfrac{5}{2}$

$\rm \: 2(x + 5) = 5(y + 5)$

$\rm \: 2x + 10 = 5y + 25$

On substituting the value of x from equation (1), we get

$\rm \: 2(3y) + 10 = 5y + 25$

$\rm \: 6y - 5y = 25 - 10$

$\rm\implies \:y = 15$

On substituting the value of y in equation (1), we get

$\rm\implies \:x = 45$

Hence,

Present age of mother is 45 years

Present age of daughter is 15 years