Question

The present ages of Meeta and Aarushi are in the ratio 5:4. Eight years from

now, the ratio of their ages will be 6:5. Find their present ages.​

Answer 1

$\bold{Given}\begin{cases} \sf \: The \: present \: ages \: of \: meeta \: and \: khushi \: are \: in \: the \: ratio \: \bold{5 : 4}. \\ \\ \sf \: The \: ratio \: of \: their \: ages \: eight \: years \: from \: now \: will \: be \: \bold{6 : 5}.\end{cases}$

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Need to find : Their present ages.

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Put k in the ratio of their ages. Then their present ages are :

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• Meeta's present age = 5k
• Khushi's present age = 4k

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After 8 years, their ages will be :

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• Meeta's age = 5k + 8
• Khushi's age = 4k + 8

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It is also given to that after 8 years, their ages will be in the ratio 6 : 5.

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$\bold {\underline{According \: to \: the \: question \: : }}$

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$\sf :\implies \: \dfrac{5k + 8}{4k + 8} = \dfrac{6}{5} \\ \\ \\ \sf :\implies \:5(5k + 8) = 6(4k + 8) \\ \\ \\ \sf :\implies \:25k + 40 = 24k + 48 \\ \\ \\ \sf :\implies \:25k - 24k = 48 - 40 \\ \\ \\ \sf :\implies \:\underline{\boxed{\mathfrak\purple{k = 8}}} \: \bigstar$

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Now, Put the value of k .

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• Meeta's present age = 5k = 5(8) = 40 years
• Khushi's present age = 4k = 4(8) = 32 years

$\: \: \:$

$\sf\therefore{\underline{Hence, \: the \: present , \: ages \: of \: Meeta \: and \: Khushi \: are \: \bold{40 \: years} \: and \: \bold{32 \: years} \: respectively. }} \:$

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Answer 2

Solution:

Let the present ages of Meeta and Aarushi be m and n respectively.

According to the first condition:

» m/n = 5/4

» 4m - 5n = 0 ... (1)

According to the second condition:

» (m + 8) / (n + 8) = 6/5

» 5m + 40 - 6n - 48 = 0

» 5m - 6n - 8 = 0 ... (2)

Now, (By Cross Multiplication)

» m/(40) = -n/(-32) = 1

Therefore, m = 40 years & n = 32 years.

Hence, Meena's age is 40 years and Aarushi's age is 40 years.