Neha’s present age is 3rd of her aunt’s present age. Neha’s brother is 18 years
older to Neha. The respective ratio between t

2 thoughts on “Neha’s present age is 3rd of her aunt’s present age. Neha’s brother is 18 years<br />older to Neha. The respective ratio between t”

1. Given :-

   • Neha’s age is ⅓ rd of her aunt’s age
   • Neha’s brother is 18 years older than Neha
   • The ratio of the brother’s and aunt’s age is 17:24

   Aim :-

   • To find Neha’s present age.

   Answer :-

   Let us assume Neha’s aunt’s present age to be y.

   According to the question,

   Neha’s age :-

   [tex] \implies \sf \dfrac{1}{3} \times y[/tex]

   [tex] \implies \sf \dfrac{y}{3} [/tex]

   Neha’s brother’s age :-

   Neha’s brother is 18 years more than Neha. Hence,

   [tex] \implies \sf \cfrac{y}{3} + 18[/tex]

   Taking LCM as 3,

   [tex] \implies \sf \dfrac{y +54 }{3}[/tex]

   Ratio :-

   Ratio is the comparison between two or more quantities in it’s simplest form.

   The ratio of Neha’s brother and aunt’s age is given as 17:24

   [tex] \implies \sf \dfrac{ \dfrac{y + 54}{3} }{y} = \dfrac{17}{24} [/tex]

   [tex] \implies \sf \dfrac{y + 54}{3} \div y = \dfrac{17}{24} [/tex]

   [tex] \implies \sf \dfrac{y + 54}{3} \times \dfrac{1}{y} = \dfrac{17}{24} [/tex]

   [tex] \implies \sf \dfrac{y + 54}{3y} = \dfrac{17}{24} [/tex]

   By cross multiplication,

   [tex] \implies \sf24(y + 54) = 17(3y)[/tex]

   [tex] \implies \sf 24y + 1286 = 51y[/tex]

   Transposing 24y,

   [tex] \implies \sf1286 = 51y – 24y[/tex]

   [tex] \implies \sf 1286 = 27y[/tex]

   Transposing 27,

   [tex] \dfrac{1286}{27} = y[/tex]

   [tex] \implies \sf 48 = y[/tex]

   Now that we have the value of y, Neha’s age will be ⅓ that of y.

   Neha’s age :-

   [tex] \implies \sf \dfrac{1}{3} \times 48[/tex]

   Reducing to the lowest terms we get :-

   [tex] \implies \sf 16 \: years[/tex]

   Verification :-

   Let us verify the answer by seeing the brother’s and aunt’s ratio matches or not.

   Neha’s brother’s age = 16 + 18 => 34 years

   RATIO :-

   [tex] \dfrac{34}{48} = \dfrac{17}{24} [/tex]

   LHS :–

   => 34 : 48

   reducing to the lowest terms (dividing by the common factor 2)

   => 17:24

   RHS :–

   => 17:24

   LHS = RHS

   Hence Verified

   Option (5) 16 years is correct ✓

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2. Answer:

   so neha’s present age is 5 years

   Step-by-step explanation:

   Let Nisha’s age is x years

   Aisha’s age = (x² + 2) years

   Now, A/C to question , when Nisha grows to her mother present age .means Nisha’s grows = Aisha’s present age – Nisha’s present age = x² + 2 – x

   Then, this time Aisha’s age = Aisha’s present age + growing time = x² + 2 + x² + 2 – x = 2x² – x + 4

   Now, question said , Aisha’s age = 10× times of Nisha’s age -1

   2x² – x + 4 = 10x -1

   2x² – 11x + 5 = 0

   2x² -10x – x + 5 = 0

   x = 5 and 1/2 x ≠ 1/2 because age doesn’t in moths

   Hence , Nisha’s present age = 5 years

   Aisha’s present age = (5)² + 2 = 27 years

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