At present Asha's age is 2 more than the square of her daughter Nisha's age.
When Nisha grows to her mother's present age Asha's age would be 1 year less than 10 times present age of Nisha.
Find their present ages.
Answers
Answer:
Let Asha,s age be x and her daughter's age be y.
Now,
x=2+y^2
Again,
10y-1=x+(x-y)
10y-1=2x-y
11y-1=2x
11y-1=2(2+y^2)
11y-1=4+2y^2
2y^2-11y+4+1=0
2y^2-11y+5=0
2y^2-10y-y+5=0
2y(y-5)-1(y-5)=0
(y-5)(2y-1)=0
Either, or,
y-5=0 2y-1=0
y=5 y=1/2(It is not a solution)\
x=2+y^2=2+5^2=27
Therefore, the age of Asha is 27 and of her daughter is 5.
Answer:
Let, Nisha’s present age be = x year
Therefore, according to the first condition, Asha's present age = x2 + 2
Nisha grows to her mother's present age after [(x² + 2) – x] years.
Then, Asha's age will become (x² + 2) + [(x² + 2) –x] years.
• According to the question :
⟹ (x² + 2) + [(x² + 2) – x] = 10x – 1
⟹ 2x² – x + 4 = 10x – 1
⟹ 2x² – 11x + 5 = 0
⟹ 2x² – 10x – x + 5= 0
⟹ 2x (x – 5) –1(x – 5) = 0
⟹ (x – 5) (2x – 1) = 0
⟹ (x – 5) = 0 or (2x – 1) = 0
⟹ x = 5 or 1/2
Ignoring x = 1/2 because then Asha’s age = x² + 2 = which is not possible.
Hence, Present Age of Nisha = 5 years
And Present Age of Asha = x² + 2 = (5)² + 2 = 25 + 2 = 27 years