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
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+15⇒x=3y+10....eq1
According to the second condition
5 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....eq2
Put the value of x from eq1
⇒3y+10−7y=−30⇒−4y=−40⇒y=10
Put y=10 in eq1
⇒x=3×10+10=40
Hence, Father present age =40 years
Son present age =10 years