Question

The ratio of ages of the mother and her daughter at present is 13 : 4. Six years hence, the ratio will be 5 : 2. Find their present ages.

Answer 1

The present age of mother is 39 years. The present age of daughter is 12 years

Solution:

Given that the ratio of ages of the mother and her daughter at present is 13 : 4

Let the ages of the mother and her daughter at present be 13x and 4x respectively

Six years hence, the ratio will be 5 : 2

Therefore:-

$\frac{13 x+6}{4 x+6}=\frac{5}{2}$

On solving for "x" we get,

$2 \times(13 x+6)=5 \times(4 x+6)$

26x + 12 = 20x + 30

26x – 20x = 30 -12

6x = 18

x = 18 ÷ 6 = 3

Therefore value of "x" is 3

Present age of mother = 13x = 13(3) = 39 years old

Present age of daughter = 4x = 4(3) = 12 years old

Learn more about problems on ages

The sum of ages of father and mother is the 6 times the sum of ages of their children. two years before the sum of ages of father and mother is the 10 times the sum of ages their children. six years hence the sum of ages of father and mother will be 3 times the sum of ages of their children. find the number of children they have.

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Answer 2

Let the initial age of the mother and daughter be y and x respectively.

y/x=13/4= initial ratio => y=13 x/4

After six years -

Age of mother = y+6

Age of daughter = x+6

y+6/x+6=5/3 =ratio of age after six years

(13x/4 +6)/x+6 = 5/3 [y=13x/4]

On solving the equation -

=> x=12 , y=39.