Multiple choice

Three years ago, ratio of ages of Amisha and Namisha was 8 : 9. 3 years from now the ratio will become 11 : 12. What is the present age of Amisha?

  1. 2 years

  2. 16 years

  3. 19 years

  4. 21 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let ages 3 years ago be 8x and 9x. Present ages are 8x+3 and 9x+3. In 3 years, ages will be 8x+6 and 9x+6. Given (8x+6)/(9x+6) = 11/12. Solving: 12(8x+6) = 11(9x+6) => 96x + 72 = 99x + 66 => 3x = 6 => x = 2. Amisha's present age = 8(2) + 3 = 19.

AI explanation

Let the present ages of Amisha and Namisha be x and y respectively. Three years ago, their ages were x minus 3 and y minus 3, giving the equation (x minus 3) / (y minus 3) = 8 / 9, which simplifies to 9x minus 8y = minus 3. Three years from now, their ages will be x plus 3 and y plus 3, giving (x plus 3) / (y plus 3) = 11 / 12, which simplifies to 12x minus 11y = minus 3. Solving these simultaneous equations gives x = 19 and y = 21. Therefore, Amisha's present age is 19 years.

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