Question

5 year hence ratio of ages of a and b will be 7 : 5 and difference between their ages will be 4 years. what are present ages (in years) of a and b respectively?

Answer 1

Solution :-

Let the present ages of a and b be x years and y years respectively.

Case I : 5 year hence ratio of ages of a and b will be 7 : 5

=> (x - 5)/(y - 5) = 7/5

=> 5(x - 5) = 7(y - 5)

=> 5x - 25 = 7y - 35

=> 5x - 7y = - 10 _______(i)

Case II : Difference between their ages will be 4 years.

=> x - y = 4

=> x = 4 + y _______(ii)

Put the value of x in equation (i)

=> 5(4 + y) - 7y = - 10

=> 20 + 5y - 7y = - 10

=> 2y = 30

=> y = 15

Now, put the value of y in equation (ii) we get,

=> x = 4 + 15 = 19

Hence,

The present ages of a and b are 19 years and 15 years respectively

Answer 2

☞ 5 year hence ratio of ages of a and b will be 7 : 5.

Let present age of a be 'M' and present age of b be 'N'.

• 5 years hence

Age of a = M - 5

And age of b = N - 5

• Ratio of their ages is 7 : 5

=> $\dfrac{M\:-\:5}{N\:-\:5}$ = $\dfrac{7}{5}$

Cross-multiply them

=> 5(M - 5) = 7(N - 5)

=> 5M - 25 = 7N - 35

=> 5M - 7N = - 35 + 25

=> 5M - 7N = - 10 _________(eq 1)

_____________________________

☞ Difference between their (a and b) ages is 4 years.

=> M - N = 4

=> M = 4 + N __________(eq 2)

• Put value of M in (eq 1)

=> 5(4 + N) - 7N = - 10

=> 20 + 5N - 7N = - 10

=> - 2N = - 10 - 20

=> - 2N = - 30

=> 2N = 30

=> N = 15

• Put value of N in (eq 2)

=> M = 4 + (15)

=> M = 19

______________________________

Present age of a = M = 19 years

and

Present age of b = N = 15 years

______________[ANSWER]