Question

12 years ago the ratio between the age of A and B was 2:3 while the ratio of their presents age 5:6. Find the their present
age.​

Answer 1

Answer:

refer to the attachment

Answer 2

$\huge\sf{\underline{\underline{\red{Solution}}}}$

$\sf{Age \: of \: A = 8 \: yrs.}$

$\sf{And, Age \: of \: B = 12 \: yrs.}$

$\huge\sf{\underline{Explanation:}}$

$\sf{Present \: age \: ratio \: of \: A \: and \: B =2:3}$

$\sf{Let \: the \: present \: age \: of \: A \: is \: 2x }$

$\sf{and \: that \: of \: B \: is \: 3x}$

After 12 years,

Age of A will be 2x+12 and that of B will be 3x+12 , and their ratio = 5:6.

So,

$\sf{\large \frac{2x + 12}{3x + 12} } = \frac{5}{6}$

$:\implies\sf{\large \: 5(3x + 12 = 6(2x + 12)}$

$:\implies\sf{\large \: 15x + 60 = 12x + 72}$

$:\implies\sf{\large \: 15x - 12x = 72 - 60}$

$:\implies\sf{\large \: 3x = 12}$

$:\implies\sf{\large \: x = \frac{12}{3}}$

$:\implies\sf{\large \: x = 4}$

So,

$\red\mapsto\sf{Present \: age \: of \: A =2x=2×4=8}$

$\red\mapsto\sf{Present \: age \: of \: B =3x=3×4=12}$