Question

The ratio of Mary's age 8 years ago and julia's age after 8 years is 1 : 1. Presently.the ratio of their ages is 9 : 7. Find the ratio between Mary's age 2 years hence andjulia's age 2 years ago.

Answer 1

Ratio will be 37:27

Solution pic given

Answer 2

Answer: The ratio is 37:27.

Step-by-step explanation:  Let x and y be the present ages of Mary and Julia.

According to the given information, we have

(Mary's age 8 yrs ago) : (Julia's age after 8 yrs) = 1 : 1

i.e.,

$(x-8) : (y+8) = 1 : 1\\\Rightarrow \dfrac{x-8}{y+8}=\dfrac{1}{1}\\\\\Rightarrow x-8=y+8\\\Rightarrow x= y+16.$

Also,

(Present age of Mary) : (Present age of Julia) = 9 : 7

i.e.,

$x : y= 9 : 7\\\\\Rightarrow \dfrac{x}{y}=\dfrac{9}{7}\\\\\Rightarrow x=\dfrac{9}{7}y.$

Therefore, from the above two equations, we can write

$x=y+16\\\\\Rightarrow \dfrac{9}{7}y-y=16\\\\\Rightarrow \dfrac{2}{7}y=16\\\\\Rightarrow y=56,$

and $x=y+16=56+16=72.$

So, required ratio=(Mary's age 2 yrs hence) : (Julia's age 2 yrs ago)=(x+2) : (y-2)=74 : 54 = 37 : 27.

Thus, the ratio is 37 : 27.