Question 47

2 years ago, one-fifth of Amita’s age was equal to one-fourth of the age of Sumita, and the average of their age was 27 years. If the age of Paramita is also considered, the average age of three of them declines to 24. What will be the average age of Sumita and Paramita 3 years from now?

Solution

Let 'A', 'S' and 'P' be Amita's, Sumita's and Paramita's present age. 

It is given that 2 years ago, one-fifth of Amita’s age was equal to one-fourth of the age of Sumita, and the average of their age was 27 years.

$$\dfrac{(A-2)+(S-2)}{2} = 27$$

$$A+S = 58$$  ... (1)

Also, $$\dfrac{A-2}{5} = \dfrac{S-2}{4}$$

$$4A-8 = 5S-10$$

$$5S - 4A = 2$$ ... (2) 

From equation (1) and (2) we can say that S = 26, A = 32.

Average age of Amita, Sumita and Paramita before 2 years = 24. 

 $$\dfrac{(A-2)+(S-2)+(P-2)}{3} = 24$$

 $$A+S+P = 78$$. Hence, P = 20.

Therefore, the average age of Sumita and Paramita 3 years from now? = $$\dfrac{(S+3)+(P+3)}{2}$$ = $$\dfrac{(26+3)+(20+3)}{2}$$ = 26 years.

Hence, option B is the correct answer.


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