Question

The ratio between the present ages of A and B is 3 : 5 respectively. If the

difference between B's present age and A's after 7 year is 3 what is the total of A's

and B's present age?​

Answer 1

$\mathsf \red{Given : } \\ \\ \mathsf{ratio \: of \:A \: and \: B \: present \: age \: = \: 3 :5 \: respectively} \\ \\ \mathsf{let \: thier\: age \: be \: 3x \: and \: 5x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \\ \mathsf {A's \: age \: After \: 7 \: years \: is \: : \: 3x + 7\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \\ \mathsf \red{the \: age \: difference \: of \: B \: and \: A \: after \: 7 \: \: years \: = \: 3} \\ \\ \mathsf{5x - (3x + 7) = 3} \\ \\ \mathsf{5x - 3x - 7 = 3} \\ \\ \mathsf{2x = 3 + 7} \\ \\ \mathsf{2x = 10} \\ \\ \mathsf{x = \frac{10}{2} } \\ \\ \boxed {\mathsf{x = 5}} \\ \\ \mathsf \red{Therefore : \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \\\mathsf{A's \: present \: age \: = \: 3x = 3 \times 5 = 15} \\ \\ \mathsf{B's \: present \: age \: = 5x = 5 \times 5 = 25}$

$\mathsf{}$

${\sf{\fcolorbox{black}{pink}{© \: ITZBFF}}}$

Answer 2

Step-by-step explanation:

Let present age of A be x years and present age of B be y years

The ratio between the present ages of A and B is 3:5 respectively.

x/y = 3/5

5x = 3y

y = 5x/3,,,,,,Eq..1

If the difference between B present age and A age after 7 years i.e x + 4 is 3.

y - (x + 7) = 3

y - x - 7 = 3

y - x = 3 + 7

y - x = 10

y = 10 + x,,,,,, Eq..2

Now substituting value of y from Eq..2 to Eq..1

5x/3 = 10 + x

5x= 3(10+x)

5x=30+3x

5x-3x=30

2x=30

x=15

Present age of A is 15 years

Now substitute value of x in Eq..1 to derive value of y.

y = 5x/3

y= 5×15/3

y=25

age of B will be 25 years