Question

The ratio between the ages of a and b is 7:9. 9 years ago, their ages were in the ratio of 2:3. Find their present ages.

Answer 1

Step-by-step explanation:

a/b=7:9

9a=7b

9a-7b=0--(1)

a-9/b-9=2:3

3a-27=2b-18

3a-2b=8-----(2)

Now solve this two equatin

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

$\textbf{\underline{Ratio\;of\;A\;and\;B}}$

= 7 : 9

Assumption :-

$\textbf{\underline{Present\;ages\;of\;A\;be\;7p}}$

$\textbf{\underline{Present\;ages\;of\;B\;be\;9p}}$

Nine years ago,

Ratio of the ages of A and B

= 2 : 3

Nine years ago,

Age of A

= (7p - 9) years

Nine years ago,

Age of B

= (9p - 9) years

Situation :-

$\tt{\rightarrow\dfrac{7p-9}{9p-9}=\dfrac{2}{3}}$

⇒ 21p - 27 = 18p - 18

⇒ 21p - 18x = -18 + 27

⇒ 3p = 9

$\tt{\rightarrow p=\dfrac{9}{3}}$

⇒ p = 3

Substitute the value of p :-

Present age of A

= 7 × 3

= 21 years

Present age of B

= 9 × 3

= 27 years.

${\boxed{\sf\:{Present\;age\;of\;A=21\;years\;and\;B=27\;years}}}$