Question

If the present ages of A and B are in the ratio 9:4 and seven years hence,the ratio of their ages will be 5:3, then find their present ages

Answer 1

Solutions :-

Given :
The present ages of A and B are in the ratio 9 : 4
After seven years,
The ratio of their ages will be 5 : 3

Let the present age of A and B be 9x and 4x respectively.


According to the question,

$= > \frac{9x + 7}{4x + 7} = \frac{5}{3} \\ \\ = > 3( 9x + 7) = 5(4x + 7) \\ \\ = > 27x + 21 = 20x + 35 \\ \\ = > 27x - 20x = 35 - 21 \\ \\ = > 7x = 14\\ \\ = > x = \frac{14}{7} = 2$


Hence,
Present age of A = 9x = 9 × 2 = 18 years
Present age of B = 4x = 4 × 2 = 8 years


_______________________

✯ @shivamsinghamrajput ✯

Answer 2

$\Huge\bigstar\:\tt\underline\red{:ANSWER:}$

$\huge\mathscr\orange{:Let:}$

${\implies}$Present age of A is$\red{\tt{9x}}$ and B is $\purple{\tt{4x}}$

$\huge\mathscr\pink{:By problem:}$

${\implies}$After seven years A's age is =${9x+7}$

${\implies}$After seven years B's age is = ${4x+7}$

${\implies}$$\frac{9x+7}{4x+7}$=$\frac{5}{3}$

$\large\mathscr\red{:By Cross Multiplication:}$

${\implies}$${5(4x+7)=3(9x+7)}$.

${\implies}$${20x+35=27x+21}$.

${\implies}$${20x-27x=21+35}$.

${\implies}$$\cancel{-}$${7x=}$$\cancel{-}$${14}$.

${\implies}$${7x=14}$

${\implies}$${x=\frac{14}{7}}$

${\implies}$$\therefore{x=2}$.

$\therefore$ present age of A = ${9x=9×2=18}$

$\therefore$present age of B =${4x=4×2=8}$.