Question

age of L and H are in ratio 7:5 ten years hence ratio of their age will be 9:7 .find present age

Answer 1

L/H = 7/5
⇒ L = 7H/5

after 10 years,
(L+10)/(H+10) = 9/7
⇒ 7(L+10) = 9(H+10)
⇒ 7L + 70 = 9H + 90
⇒ 7(7H/5) - 9H = 90 - 70
⇒ 49H/5 - 9H = 20
⇒ 4H/5 = 20
⇒ H = 5*20/4 = 25
L = 7H/5 = 7*25/5 = 35

Age of L = 35
Age of H = 25

Answer 2

L / H = 7 / 5
5 L - 7 H = 0

(L+10) / (H+10) = 9 / 7
7L + 70 =  9 H + 90
7 L - 9 H - 20 = 0
 
   0     5     -7      0                     L = 140/4 = 35  yrs
  20    7     -9     20                   H  = 100/4 = 25  yrs
     H          L