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# Five years hence, a man’s age will be three times the sum of the ages of his son. Five years ago, the man was seven times as old as his son. Find their present ages.

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One of the most important and exam oriented question from linear equations in two variables in which we have been asked to find the present age of father and son if 5 years hence, a man’s age will be three times the sum of the ages of his son. Five years ago, the man was seven times as old as his son.

RS Aggarwal, Class 10, chapter 3E, question no 42

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1. ## Let the father present age =x years  and son present age =y years

According to the first condition
5 years later father will be (x+5) years old and son will be (y+5) years old.
x+5=3(y+5)
x+5=3y+15x=3y+10....eq1

According to the second condition
5 years ago father was (x5) years old and son was (y5) years old.
x5=7(y5)
x5=7y35
x7y=30....eq2

Put  the value of x from eq1
3y+107y=304y=40y=10

Put y=10 in eq1
x=3×10+10=40

Hence, Father present age =40 years
Son present age =10 years

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