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Question

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

A
Father's age =80 years, Son's age =25 years
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B
Father's age =60 years, Son's age =30 years
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C
Father's age =75 years, Son's age =42 years
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D
Father's age =40 years, Son's age =10 years
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Solution

## The correct option is C Father's age =40 years, Son's age =10 yearsLet the father present age =x years and son present age =y yearsAccording to the first condition5 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+15⇒x=3y+10....eq1According to the second condition5 years ago father was (x−5) years old and son was (y−5) years old.⇒x−5=7(y−5)⇒x−5=7y−35⇒x−7y=−30....eq2Put the value of x from eq1⇒3y+10−7y=−30⇒−4y=−40⇒y=10Put y=10 in eq1⇒x=3×10+10=40 Hence, Father present age =40 years Son present age =10 years

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