At present asha's age is 2 years more than the square of her daughter nisha's age. When nisha grows to her mother's present age asha 's will be 10 times the present age of nisha -1 year .Find their present ages
Answers
Answer:
Nisha = 5 year
Asha = 27 Years
Step-by-step explanation:
Let present age of Asha = x
Let present age of Nisha = y
x = 2 + y^2
x + (x-y) = 10y -1
2x = 11y -1
2x = 4 + 2y^2
11y - 1 = 4 + 2y^2
2y^2 -11y + 5 = 0
2y^2 - 10y - y +5 = 0
2y(y-5) -1 (y-5) = 0
y = 1/2 or 5
when y = 1/2 then
2x = 11/2 -1 => x = 9/4
This is not practical possible as at the age of 9/4 year Asha can not be a mother
when y = 5
2x = 11*5-1 => x = 27
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