Question

SOLVE
1) AGES OF ATHUL AND ANIL IN THE RATIO 5:7. IF ATHUL WAS 9 YEARS OLDER AND ANIL 9 YEARS YOUNGER. THE AGE OF ATHUL WOULD BE TWICE THE AGE OF ANIL. FIND THEIR AGES.

2)THE PRESENT AGEOF RAM'S MOTHER IS 3 TIMES OF RAM. AFTER 10 YEARS RAM'S MOTHER WILL BE TWICE AS RAM FIND THEIR PRESENT AGES.

Answer 1

1)
let the ages be x and y.
now, x/y=5/7, so, 7x=5y.
and we also know that x+9/y-9=2
from this last equation, we get x= 2y-27
from the first equation, we get x=5y/7
therefore, 5y/7=2y-27.
solving, we get y=21.
now we know that x:y::5:7, so x must be 21/7*5, whish is 15.

Ans,
Athul=15 yrs old
Anil=21 yrs old

We can also check by what the  question has given us. 
"IF ATHUL WAS 9 YEARS OLDER AND ANIL 9 YEARS YOUNGER. THE AGE OF ATHUL WOULD BE TWICE THE AGE OF ANIL. FIND THEIR AGES."
so, 15+9 should be double of 21-9.
24=2(12). So we know our answer is right.

2)
let the ages be x and y
3x=y.
in ten years, 
ram and his mother will be x+10 and y+10 respectively.
so, 2(x+10)=y+10
 
solving to get x in both equations we get:
x= y/3, and,
x= y-10/2.
therefore, y/3=y-10/2
cross multiplying, we get:
2y = 3y-30 
3y-2y=30. y=30.
hence ram's age =30/3=10
RAM=10 yrs old
RAM'S mother=30 years old.