Multiple choice

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. (only quantity is to be considered) Quantity I : Present ages of A and B are in the ratio of 4 : 5 respectively. Present ages of C and D are in the ratio of 5 : 6 respectively. Present average age of A, B, C and D is 40 years and 6 months. Age of A after 2 years will be half the age of D 6 years hence. Find the present average age of B and C. Quantity II : The average marks of four students in Mathematics is 68. Later it was found that, one of the students got 88 marks and due to error in marking he got 76. Find the actual average marks of the four students.

  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
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Quantity I: A/B = 4/5, C/D = 5/6. Average age of (A,B,C,D) = 40.5 years, so sum = 162 years. (A+2) = (D+6)/2, so A = (D+6)/2 - 2 = D/2 + 1. Let A = 4x, B = 5x, C = 5y, D = 6y. Then 4x = 3y + 1. Also 4x + 5x + 5y + 6y = 162, so 9x + 11y = 162. Solving: x = 11, y = 63/11 = 5.73. Average of B and C = (5x + 5y)/2 = (55 + 28.65)/2 = 41.8 years. Quantity II: Original average = 68, so sum = 272. Correct sum = 272 - 76 + 88 = 284. New average = 284/4 = 71. So Quantity I (41.8) < Quantity II (71).

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