Question

Five years 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.

Answer 1

Here, let A’s present age = a and,

B’s present age = b,

According to the given conditions:

(1) Five years ago, A’s age was 5 years less than twice B’s age:

a − 5 = 2(b − 5) − 5

a − 5 = 2b − 10 − 5

a − 5 = 2b − 15

a = 2b − 15 + 5

a = 2b − 10     ...(I)

(2) Three years from now, one-third of B’s age will be 12 years less than A’s age:

`1/3(b + 3) = (a + 3) - 12`

`1/3(b + 3) = a - 9`

Multiplying expression by 3,

`3(1/3(b + 3)) = 3(a - 9)`

b + 3 = 3a − 27

b = 3a − 27 − 3

b = 3a − 30     ...(II)

Substituting equation (II) into (I):

a = 2(3a − 30) − 10

a = 6a − 60 − 10

a = 6a − 70

70 = 5a

a = `70/5`

∴ a = 14

Now substitute a = 14 into equation (II):

b = 3(14) − 30

b = 42 − 30

∴ b = 12

Hence, the present ages of the A and B are 14 years and 12 years, respectively.