Q29 of 180 Page 3

Five years hence, the age of Anjali will be three times that of Dimple. Five years ago, Anjali’s age was seven times that of Dimple. What are their present ages?

Let the present age of Anjali be x and of Dimple be y.


Five years hence,


Age of Anjali = (x + 5) years


Age of Dimple = (y + 5) years


Age of Anjali = 3(Age of Dimple)


x + 5 = 3(y + 5)


x + 5 = 3y + 15


x – 3y = 10……(1)


Five years ago,


Age of Anjali = (x – 5)


Age of Dimple = (y – 5)


Age of Anjali = 7(Age of Dimple)


x – 5 = 7(y – 5)


x – 5 = 7y – 35


x – 7y = -30……(2)


Subtracting equation 2 from equation 1, we get,


(x – 3y) – (x – 7y) = 10 – (-30)


x – 3y – x + 7y = 10 + 30


4y = 40


y = 10 years


Putting the value of ‘y’ in equation 1, we get,


x – 3 × 10 = 10


x – 30 = 10


x = 40 years


Hence, the age of Anjali is 40 years and age of Dimple is 10 years.


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