Eighteen years ago thirteen times Tom's age equals eight times his brother john's age.Their present ages are in the ratio 5:7 what is Tom's resent age?

Question

What is Toms resent age?

Answer 1

Let T=Tom’s age and rT be John’s age where r is the ratio of the brothers’ ages.

18 years ago their ages were T-18 and rT-18, also:

13(T-18)=8(rT-18), 13T-234=8rT-144, 13T-8rT=90, T=90/(13-8r).

We know that r=5/7 or 7/5, so T (a whole number)=90/(13-8(5/7)) or 90/(13-8(7/5)), that is, 210/17 or 50. So Tom is 50 years old, r=7/5 (making John 70 years old). Also, 210/17=12 approx, so 18 years ago Tom wasn’t even born!

Answer 2

Let age of Tom and Johin in present day is x and y respectively.

Then 18 years back their age is given by the following equation.

13(x-18) = 8(y-18)  ----------------------------(1)

Now their current age is given by

x/y = 5/7

or y = 7x/5

On substituting the value of y in eq(1) we get:

13(x-18) = 8(7x/5-18)

13x - 234 = 56x/5 - 144

13x-56x/5 = 234-144

(65x-56x)/5 = 90

9x = 450

x = 50

So current age of Tom is 50  years