Question

The present ages of A and B are in the ratio 2:3. After 5 years their ages will be in the ratio 7:8, then find their present ages.​

Answer 1

Given : The present ages of A and B are in the ratio 2:3 & after 5 years their ages will be in the ratio 7:8.

Exigency to find : The Present age of A & B .

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❍ Let's Consider the Present age of A and B be 2x and 3x yrs respectively.

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$\qquad \bf{ After\:5\:years \:there \:age \::}$

• Age of A will be (2x + 5 ) yrs .
• Age of B will be ( 3x + 5 ) yrs .

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⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:According \: To \: Given \:\: Question \::}}$⠀⠀⠀⠀⠀

━━━ After 5 years their ages will be in the ratio 7:8 , therefore ,

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$\qquad \longmapsto \sf \dfrac{2x + 5}{3x + 5} = \dfrac{7}{8}$

$\qquad \longmapsto \sf 8(2x + 5) = 7(3x + 5)$

$\qquad \longmapsto \sf 16x + 40 = 7(3x + 5)$

$\qquad \longmapsto \sf 16x + 40 = 21x + 35$

$\qquad \longmapsto \sf 40 - 35 = 21x - 16x$

$\qquad \longmapsto \sf 5 = 5x$

$\qquad \longmapsto \sf \cancel {\dfrac{5}{5}} = x$

$\qquad \longmapsto \sf 1 = x$

$\qquad \longmapsto \frak{\underline{\purple{\:x = 1 \:yrs }} }\bigstar$

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Therefore,

• The age of A is 2x = 1(2) = 2 yrs .
• The age of B is 3x = 1(3) = 3 yrs .

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Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Present\:Age \:of\:A \:\:\&\:\:B \:is\:}\bf{2 \:yrs\:\:\&\:\:3\:yrs\:}\sf{,respectively}}}$

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Answer 2

❍ Let the present age of A be 2x years and the present age of B be 3x years respectively.

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— After five years their ages;

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• A's age = (2x + 5) years
• B's age = (3x + 5) years

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$\underline{\bigstar\;\boldsymbol{According\;to\;the\;given\; Question:}}$

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• After 5 years their ages will be in the ratio 7:8.

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Therefore,

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$\sf{⇢\;\dfrac{2x+5}{3x+5}=\dfrac{7}{8}}\\\\\\\sf{⇢\; 8(2x+5)=7(3x+5)}\\\\\\\sf{⇢\; 16x+40=21x+35}\\\\\\\sf{⇢\; 40-35=21x-16x}\\\\\\\sf{⇢\; 5=5x}\\\\\\\sf{⇢\; x=\cancel{\dfrac{5}{5}}}\\\\\\⇢\; \underline{\boxed{\pink{\frak{x=1}}}}{\;\bigstar}$

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Hence,

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• A's present age = 2x = 2(1) = 2 years
• B's present age = 3x = 3(1) = 3 years

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$\therefore\;\sf{\underline{Hence,\;the\; present\;ages\;of\;A\;and\;B\;are\;{\textsf{\textbf{2\;years\;\&\;3\;years}}}.}}$

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