Introduction :
To solve simple practical problems based on age, linear equations are very useful. There is a wide variety of word problems related to our day-to-day life. Here problems usually involve a comparison of ages in the present, several years from now, or several years ago. In this chapter, we find the method of solving such age problems.
Linear equation:
An equation involving only one unknown variable is called a linear equation.
Solution of a linear equation :
The value of the unknown variable which when substituted, satisfies the given equation is called the solution of the equation.
Guide lines to solve Age Problems :
1. Read the problem carefully and denote the unknown age by some variable x.
2. Convert the statements of the problem step-by-step into mathematical equations, to the extent possible.
3. Solve the equations for the unknown.
4. Check whether the obtained value of the variable satisfies the conditions given in the problem.
EXAMPLE PROBLEMS
1. The ages of Prabhu and Soniya are in the ratio of 5 : 7. Sixteen years ago their ages were in the ratio of 3 : 5. The present age of Prabhu is
a) 20 years b) 30 years c) 45 years d) 40 years
Ans : d
Solution :
Let the present age of Prabhu and Soniya be x and y years.
given x/y = 5/7 => y= 7x/5............................(1)
16 years ago, (x-16)/(y-16)= 3/5 =>5x-80= 3y-48
5x-3y=32..................(2) by using 1 and 2 we get
5x-3 (7x/5)= 32=> 25x-21x=160=> 4x160 =>x=40
Prabhu age = 40 years .