Question

six years ago the ratio of the ages of dexter and debra was 6 : 5. four years hence the ratio of their ages will be 11 : 10. what is debra's present age?

Answer 1

Let x and y be the present ages of Dexter and Debra

So,

(x-6)/(y-6) = 6/5

5(x-6) = 6(y-6)

5x -30 = 6y - 36

5x - 6y = -6...............................1)

Now, As per second condition,

(x + 4)/ (y+ 4)= 11/10

10 (x +4) = (y +4) 11

10x + 40 = 11y + 44

10x - 11y= 4......................................2)

Multiplying equation 1) by 2 and then substracting it by 2) we get,

y = 12 + 4

y = 16

So,

Debra's present age is 16 years

Answer 2

Let the present age of Dexter be x years and Debra be y years.

Given that 6 years ago, their ages was in the ratio 6:5.

$= > \frac{x - 6}{y - 6} = \frac{6}{5}$

= > 5(x - 6) = 6(y - 6)

= > 5x - 30 = 6y - 36

= > 5x - 6y = -6.

Given that After 4 years the ratio of their ages will be 11:10.

$= > \frac{x + 4}{y + 4} = \frac{11}{10}$

= > 10(x + 4) = 11(y + 4)

= > 10x + 40 = 11y + 44

= > 10x - 11y = 4 -------- (2)

On solving (1) * 2 & (2), we get

= > 10x - 12y = -12

= > 10x - 11y = 4

----------------------

-y = -16

y = 16.

Therefore the present age of Debra is 16 years.

Hope this helps!