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  1. Quantity 1 > Quantity 2 > Quantity 3
  2. Quantity 2 < Quantity 3 < Quantity 1
  3. Quantity 3 = Quantity 2 < Quantity 1
  4. Quantity 1 < Quantity 2 < Quantity 3
  5. Quantity 1 = Quantity 2 = Quantity 1
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1 Answers

Option 1 : Quantity 1 > Quantity 2 > Quantity 3

Quantity 1:

Probability of getting a six = 1/6

Probability of not getting a six = 5/6

For B to win, A must not get a six and B must.

Probability = (5/6) × (1/6) + (5/6) × (5/6) × (5/6) × (1/6) + (5/6) × (5/6) × (5/6) × (5/6) × (5/6) × (1/6) + .......

This becomes a Geometric progression of infinite terms.

a = 5/6 × 1/6 = 5/36

r = 5/6 × 5/6 = 25/36 = 0.69

Sum of infinite terms = a/(1 - r) = (5/36)/(1 - 25/36) = 5/11

Quantity 2:

let the fraction be p/q.

Now, according to condition,

(p + 1)/q = 150% of p/q

On solving, p = 2

Now, 2/(q + 3) = 1/4

q + 3 = 8

q = 5

Fraction is p/q = 2/5 = 0.4

Quantity 3:

Excess weight than the average = (15.3 - 12.6) × 2 = 5.4 kg

Now, this excess weight will be divided in 14 people of the new group.

Increase in weight of every member = 5.4/14 = 0.39 kg.

Hence, Quantity 1 > Quantity 2 > Quantity 3

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