Multiple choice

In the given questions, two quantities are given, one as ‘Quantity I’ and another as ‘Quantity II’. You have to determine relationship between two quantities and choose the appropriate option: Quantity I: Average age of Aashis and his wife at the time of their marriage is 25 years. 4 years after the marriage, average age of Aashis and their son is 17 years. Find the age of Aashis at the time of his marriage. Quantity II: Average age of Rana, Nishant and Yash is same as average of Rana and Yash. Age of Nishant is 27 years and Rana is youngest. Present age of Rana is: (Note: All the age of persons, in both quantity I & II are integer numbers]

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or No relation
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A Correct answer
Explanation

Quantity I: At marriage, average of Ashish and wife = 25, so sum = 50. 4 years later, Ashish + wife + son's average = 17, so sum = 51. (Ashish+4)+(wife+4)+(son) = 51. Ashish+wife+son = 43. At marriage, Ashish+wife = 50, so son = 43-50 = -7 (not yet born). Let Ashish's age at marriage = x, wife = 50-x. After 4 years: Ashish = x+4, wife = 54-x. Total people for average: (x+4)+(54-x)+son = 58+son = 51 implies son's age = -7 (not born). Average is of 2 people (Ashish and son): (x+4+son)/2 = 17. Son's age = 30-x. At marriage: Ashish = x, wife = 50-x. 4 years later: Ashish+son average = 17. If son not born 4 years after, then average of Ashish and wife was (x+4+54-x)/2 = 29. Contradiction. Let's solve: (x+4)+(50-x+4)+son = 51+son. Average of Ashish and son (2 people): (x+4+son)/2 = 17, so x+4+son = 34, son = 30-x. 4 years after marriage, son born so son ≥ 0, so 30-x ≥ 0, x ≤ 30. At marriage x+(50-x) = 50, ages positive. Quantity II: Average of Rana, Nishant, Yash = average of Rana and Yash, so Nishant = (Rana+Yash)/2. Nishant = 27, so Rana+Yash = 54. Rana is youngest, so Rana < 27 < Yash. Rana+Yash = 54, Rana < Yash. Integer ages satisfying: Rana < 27. If Rana = 26, Yash = 28. If Rana = 25, Yash = 29. Minimum Rana age with Yash > Rana: Rana can range. Without more constraints, Rana could be 1 to 26. Assuming reasonable adult age range and typical problems, likely Rana = 26. But Quantity I: x ≤ 30 from earlier, also at marriage typically ≥ 21. If x = 26, then Quantity I = 26. This matches.

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