Question

The ages of a and b are in the ratio 5:7, 8 years ago, there ages were in the ratio 7:13 find their ages

Answer 1

Answer:

x=10 ; y=14

Step-by-step explanation:

Let age of A be x

And age of B be y

x/y=5/7

7x=5y

7x-5y=0 →1

from this                  

Y=7x/5

8 yrs before

x-8/y-8 = 7/13

13x-104=7y-56

13x-7y=48 →2

Substitute the Y value

13x-7(7x/5)=48

13x-49x/5=48

(65x-49x)/5=48x

24x=240

X=10

Y=7(10)/5=70/5

Y=14

Therefore A’s age is 10

And B’s age is 14

Answer 2

$\underline{\underline{\bold{Question:}}}$

The ages of a and b are in the ratio 5:7, 8 years ago, there ages were in the ratio 7:13 .Find their ages.

$\bold{\textsf{Let the age of a and b be 5x and 7x years respectively.}}$

8 years ago,

• The age of a = (5x - 8) years.
• The age of b = (7x - 8) years.

According to question,

$\implies{\bold{\dfrac{5x-8}{7x-8}=\dfrac{7}{13}}}\\\\\\\implies{\bold{(5x-8)13=(7x-8)7}}\\\\\\\implies{\bold{65x-104=49x-56}}\\\\\\\implies{\bold{16x=48}}\\\\\\\implies{\bold{x=\dfrac{48}{16}=3.}}\\\\\\\boxed{\boxed{\bold{The\:age\:of\:a\:and\:b=15\:and\:21\:years\:respectively.}}}$