At present asha's age is 2 more than the square of daughters age. When nisha grows to her mother's present age. Asha's age would be one year less than 10 times the percentage of Nisha. Find the present ages of both Nisha and asha.
Answers
Answer: Nisha is 5 years and Asha is 27 years
Step-by-step explanation:
Let Nisha's age be m.
It is given that at present Asha's age is 2 more than the square of Nisha's age.
So Asha's age is (m²+2)
When Nisha grows to Asha's age, Nisha's age will be (m²+2) and Asha's age will be m²+2 + m²+2 - m = 2m²+4-m
But it is given that When Nisha grows to her mother's present age, Asha's age would be one year less than 10 times the present age of Nisha
So 2m²+4-m=10m-1
2m²-11m+5=0
(2m-1)(m-5)=0
m=1/2 or 5
So Nisha's age is 5 and Asha's age is 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