# Find the number of children of the parents from the following?

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Presently the sum of the ages of parents is six times the sum of the ages of children. If two years ago sum of the ages of parents was ten times the sum of the ages of children and six years hence the sum of the ages of parents would be three times the ages of children, what is the number of children?

Presently the sum of the ages of parents is six times the sum of the ages of children. If two years ago sum of the ages of parents was ten times the sum of the ages of children and six years hence the sum of the ages of parents would be three times the ages of children, what is the number of children?

##### 2 Answers

3 children

#### Explanation:

Let a, b and x be the sum of the ages of man and his his wife, sum of the ages of their children and number of their children respectively:

substitute 6b for a in eq-2 and eq-3:

simplify the above equations:

or:

The couple have

#### Explanation:

Let the number of children be

the sum of the ages of parents at present be

Hence **................(A)**

two years ago the sum of the ages of children would have been

**................(1)**

Similarly six years hence the sum of the ages of children would be

**................(2)**

Multiplying (1) by

or

or

Hence, the couple have