A's present age is to B's present age is 7:9. twelve years ago, their ages were in ratio 3:5 when would the ratio of their ages be 6:7
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Given:
A's present age is to B's present age is 7:9.
Let A's and B's present age be 7x and 9x respectively.
Twelve years ago, their ages were in ratio 3:5.
Let A's and B's age before 12yrs be (7x - 12) and (9x - 12) respectively.
Solution:
ATQ.
(7x - 12) / (9x - 12) = 3 / 5
=⟩ 5(7x - 12) = 3(9x - 12)
=⟩ 35x - 60 = 27x - 36
=⟩ 35x - 27x = 60 - 36
=⟩ 8x = 24
=⟩ x = 24 / 8
= 3
Therefore; A's present age = 7x
= 7 × 3 = 21yrs
B's present age = 9x
= 9 × 3 = 27yrs
Now,
Let after y yrs be the ratio of A's to B's ages be 6:7
Therefore, ATQ.
(21 + y) / (27 + y) = 6 / 7
=⟩ 7(21 + y) = 6(27 + y)
=⟩ 147 + 7y = 162 + 6y
=⟩ 7y - 6y = 162 - 147
=⟩ y = 15yrs
Hence, after 15 yrs, the ratio of the ages of A and B would be 6:7.
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