five year's ago, A's age was 5 years less than twice B's age. three years from now,one third of B's age will be 12 years less than A's age find their present ages
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- Five year's ago, A's age was 5 years less than twice B's age. three years from now,one third of B's age will be 12 years less than A's age.
Present ages of :-
- A and B
Let present age of A be x years and B be y years
then,
➤ According to 1st condition :-
✑ 5 - years ago,
- A's age = (x - 5) years
- B's age = ( y - 5) years
➥ A's age = 2(B's age) - 5
➭ (x - 5) = 2 (y - 5) - 5
➭ x - 5 = 2y - 10 - 5
➭ x - 5 = 2y - 15
➭ x = 2y - 15 + 5
➭ x = 2y - 10. --(1)
➤ According to 2nd condition :-
✑ 3 - years later,
- A's age = (x + 3) years
- B's age = (y + 3) years
➥ 1/3 ( B's age) = (A's age) - 12
➭ 1/3 × (y + 3) = (x + 3) - 12
➭ (y + 3)/3 = x - 9
➭ y + 3 = 3(x - 9)
➭ y + 3 = 3x - 27
➭ y = 3x - 27 - 3
➭ y = 3x - 30. --(2)
Put value of (1) in (2) , we get ,
➭ y = 3x - 30
➭ y = 3(2y - 10) - 30
➭ y = 6y - 30 - 30
➭ 6y - y = 60
➭ 5y = 60
➭ y = 60/5
➭ y = 12
Put y = 12 in (1) , we get,
➭ x = 2y - 10
➭ x = 2×12 - 10
➭ x = 24 - 10
➭ x = 14
Hence,
- A's age = x = 14 years
- B's age = y = 12 years
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