Question

Ratio of the ages of jay and wayne is 3:5.Five year ago,their ages was in the ratio 2:5. What are their present ages

Answer 1

Let the age of Jay be x

Let the age of Jay be xLet the age of Wayne be y

Now, According to the Question

x/y = 3/5

=> 5x = 3y

=> 5x - 3y = 0 ... Eq. 01

Also given that Five years go their ages were in ratio 2:5 which means

(x - 5)/(y - 5) = 2/5

=> 5(x - 5) = 2(y - 5)

=> 5x - 25 = 2y - 10

=> 5x - 2y = 15 ... Eq. 02

Now we will solve both the Equations by using substitution method :-

5x = 3y ( from eq. 01)

=> x = 3y/5

Putting this value in Equation 02

5x - 2y = 15

=> 5 × 3y/5 - 2y = 15

=> 3y - 2y = 15

=> y = 15

Hence if y = 15 putting this value in Eq. 01 will be,

5x - 3y = 0

=> 5x - 3 × 15 = 0

=> 5x - 45 = 0

=> 5x = 45

=> x = 9

Hence age of Jay is 9 yrs and that of Wayne is 15yrs.

VERIFICATION

We can verify answers simply by putting both the values in Equation 02

LHS

=5x - 2y

= 5 × 9 - 2 × 15

= 45 - 30

= 15

=RHS

Hence LHS = RHS , our answer is correct.

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....

$\boxed{SOLUTION:-}$

$let, \: their \: present \: ages \: be \: 8x,5x \\ \\ therefore \: after \: 8yrs \: there \: ages \: will \: be \: 8x + 6 ,5x + 6 \\ \\ so,8x + 6 \ratio5x + 6 = 11 \ratio8 \\ \\ \frac{8x + 6}{5x + 6} = \frac{11}{8} \\ cross \: multiply \: it \\ 8(8x + 6) = 11(5x + 6) \\ now \: solve \: it \: for \: value \: of \: x \: we \: have \\ x = 2 \\ so, \: present \: age \: jai = 8x = 8 \times 2 = 16 \\ present \: age \: of \: amy = 5x = 5 \times 2 = 10$