Given below are three quantities named A, B and C. Based on the given information, determine the relation among the three quantities. A man divided his property amongst his three children P, Q and R, such that P received 50% more than 80% of Q, while Q received 40% less than 150% of R. Quantity A: P’s share is what percentage more than R’s share? Quantity B: P’s share is what percentage more than Q’s share? Quantity C: Q’s share is what percentage less than R’s share?

Given below are three quantities named A, B and C. Based on the given information, determine the relation among the three quantities. A man divided his property amongst his three children P, Q and R, such that P received 50% more than 80% of Q, while Q received 40% less than 150% of R. Quantity A: P’s share is what percentage more than R’s share? Quantity B: P’s share is what percentage more than Q’s share? Quantity C: Q’s share is what percentage less than R’s share? Correct Answer Quantity A < Quantity B > Quantity C

P’s share = (100 + 50)% of 80% of Q’s share = 1.5 × 0.8 × Q’s share

⇒ P’s share = 1.2 × Q’s share      ----(1)

Q’s share = (100 – 40)% of 150% of R’s share = 0.6 × 1.5 × R’s share

⇒ Q’s share = 0.9 × R’s share      ----(2)

Substituting (2) in (1),

⇒ P’s share = 1.2 × 0.9 × R’s share

⇒ P’s share = 1.08 × R’s share      ----(3)

Solving for Quantity A:

From eq. (3), we get,

P’s share = 108% of R’s share = R’s share + 8% of R’s share

⇒ Quantity A = 8%

Solving for Quantity B:

From eq. (1), we get,

P’s share = 120% of Q’s share = Q’s share + 20% of Q’s share

⇒ Quantity B = 20%

Solving for Quantity C:

From eq. (2), we get,

Q’s share = 90% of R’s share = R’s share – 10% of R’s share

⇒ Quantity C = 10%