Question

The ratio of the present ages of Jai and Amy is 8:5. If their ages after 6 years would be in the ratio 11:8, find their present ages.​

Answer 1

Answer:

Given -

• Ratio of jai's and amy's present age = 8 : 5
• After 6 years ratio of their age will be 11 : 8

To find -

• Their present ages

Solution -

Let jai's age be 8x and Amy's age be 5x.

Now, after 6 years their age will be 11 : 8. Then,

$\\ \sf \dfrac{(8x + 6)}{(5x + 6)} = \frac{11}{8} \\ \\ \\ \implies \sf \: 64x + 48 = 55x + 66 \\ \\ \\ \implies \sf \: 64x - 55x = 66 - 48 \\ \\ \\ \implies \sf \: 9x = 18 \\ \\ \\ \implies \sf \: x = \dfrac{18}{9} \\ \\ \\ \implies \sf { \underline{x = 2.}}$

• Jai's present age = 8 × 2 = 16 years.
• Amy's present age = 5 × 2 = 10 years.

Answer 2

$\boxed{GIVEN:-}$

Ratio of their present ages :- 8:5

Ratio of their ages after 6yrs :- 11:8

$\boxed{FIND:-}$

WE HAVE TO FIND THEIR PRESENT AGES....

$\boxed{<strong>SOLUTION:-</strong>}$

$<strong>let</strong><strong>, \: their \: present \: ages \: be \: 8x,5x</strong>$

$therefore<strong> \: after \: 8yrs \: there \: ages \: will \: be \: 8x + 6 ,5x + 6</strong>$

$so,8x + 6 \ratio5x + 6 = 11 \ratio8 \\ \\ \frac{8x + 6}{5x + 6} = \frac{11}{8}$

$cross \: multiply \: it \\ 8(8x + 6) = 11(5x + 6)$

$now \: solve \: it \: for \: value \: of \: x \: we \: have \\ x = 2 \\ so, \: present \: age \: jai = 8x = 8 \times 2 = 16 \\ present \: age \: of \: amy = 5x = 5 \times 2 = 10$