Multiple choice

Ravish tells his daughter Aarushi, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be. If present ages of Aarushi and Ravish are x and y years respectively, represent this situation algebraically and find their present ages.

  1. $x=12,y=49$
  2. $x=12,y=42$
  3. $x=10,y=49$
  4. $x=10,y=42$
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B Correct answer
Explanation

Let Ravish's age be y and Aarushi's be x. Seven years ago: y - 7 = 7(x - 7). Three years from now: y + 3 = 3(x + 3). Solving these equations, y - 7 = 7x - 49 implies y = 7x - 42. Substituting into the second: 7x - 42 + 3 = 3x + 9, so 4x = 48, x = 12. Then y = 7(12) - 42 = 42.

AI explanation

Seven years ago, the equation was y minus 7 equals 7 times x minus 7, simplifying to y equals 7x minus 42. Three years from now, the equation is y plus 3 equals 3 times x plus 3, simplifying to y equals 3x plus 6. Equating the expressions gives 7x minus 42 equals 3x plus 6, so 4x equals 48 and x equals 12. Substituting x back gives y equals 3 times 12 plus 6, which is 42. The present ages are x equals 12 and y equals 42.

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