At present Asha's age is 2 more than the square of her daughter Nisha's age. When Nisha's grows to her mother's present age, Asha's age would be one year less than 10 times the present age of Nisha. Find their present ages.

Asked by Nethraa Kannan | 20th Feb, 2014, 01:56: PM

Expert Answer:

Let 'x' be the present age of Nisha.
 
Thus the present age of Asha, Nisha's mother = x squared plus 2
 
Thus, the age difference between Asha and Nisha = x squared plus 2 minus x
When Nisha reaches the age of Asha, Asha's age would be = x squared plus 2 space plus open parentheses x squared plus 2 minus x close parentheses
Given that, after x squared plus 2 minus x years, Asha's age would be = 10 x space minus 1
 
Equating the above two equations, we have
 
x squared plus 2 plus x squared plus 2 minus x equals 10 x minus 1 rightwards double arrow 2 x squared plus 4 minus x equals 10 x minus 1 rightwards double arrow 2 x squared plus 4 minus x minus 10 x plus 1 equals 0 rightwards double arrow 2 x squared minus 11 x plus 5 equals 0 rightwards double arrow 2 x squared minus 10 x minus x plus 5 equals 0 rightwards double arrow 2 x open parentheses x minus 5 close parentheses minus open parentheses x minus 5 close parentheses equals 0 rightwards double arrow open parentheses 2 x minus 1 close parentheses open parentheses x minus 5 close parentheses equals 0 rightwards double arrow 2 x minus 1 equals 0 space o r space x minus 5 equals 0 rightwards double arrow x equals 1 half space o r space x equals 5 I f space y o u space c o n s i d e r space n i s h a apostrophe s space p r e s e n t space a g e space t o space b e space x equals 5 comma space t h e n space A s h a apostrophe s space a g e space w o u l d space b e space 27.

Answered by  | 21st Feb, 2014, 08:58: AM

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