Question

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Present ages of Anu and Raj are in the ratio 4:5. Eight years from now the ratio of their ages will be 5:6. Find their present ages.


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Answer 1

Answer:-

• Anu's present age = 32 years.

• Raj's present age = 40 years.

Given:-

• Ratio of present ages of Anu and Raj = 4:5

• Ratio of their ages after 8 years = 5:6

To Find:-

• Their present ages.

Solution:-

Let the present ages of Anu and Raj be 4x years and 5x years.

Their ages after 8 years :-

Anu's age = $\rm{(4x+8) \:years}$

Raj's age = $\rm{(5x=8)\:years}$

So,

Ratio of their ages after 8 years =$\rm{\dfrac{4x+8}{5x+8} } = \dfrac{5}{6}$

By cross multiplication :-

$:\implies\:\: \rm \dfrac{4x+8}{5x+8} =\dfrac{5}{6}$

$:\implies\:\: \rm (4x +8)\times 6=(5x+8)\times 5$

$:\implies\:\: \rm 24x+48=25x+40$

$:\implies\:\: \rm 24x+48-40=25x$

$:\implies\:\: \rm 24x+8=25x$

$:\implies\:\: \rm 25x-24x=8$

$:\implies\:\: \rm x=8$

Therefore,

➼ Anu's present age = 4x = 4 × 8 = 32 years.

➼ Raj's present age = 5x = 5 × 8 = 40 years.

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Answer 2

Given, that the present ages of Anu and Raj are in the ratio 4:5. Eight years from now the ratio of their ages will be 5:6

☯we need to find their present ages.

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Let the present ages of Anu and Raj be 4x years and 5x years.

Now, 8 years later their ages will be (4x + 8) and (5x + 8) years.

According to the question,

After 8 years ages of Anu and Raj, will be in ratio of 5 : 6.

So,

$\star\;{\boxed{\sf{\pink{(Anu \;age):(Raj\;age)=5:6 }}}}$

$:\implies\sf (4x+8):(5x+8)=5:6$

$:\implies\sf \dfrac{(4x+8)}{(5x+8)}= \dfrac {5}{6}$

$:\implies\sf 6(4x+8)=5(5x+8)$

$:\implies\sf 24x+48=25x+40$

$:\implies\sf 48-40=25x-24x$

$:\implies\sf 8=x$

$:\implies{\boxed{\frak{\purple{ x=8}}}}\;\bigstar$

So,

Present age of Anu will be = 4x = 4(8) = 32 years.

Present age of Raj will be = 5x = 5(8) = 40 years.

$\therefore\;{\underline{\sf{Hence,\;the\;present \:ages\;of\;Anu\;and\;Raj\;will\;be\:\bf{32\:and\:40\:years}\;respectively.}}}$

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