Reasoning : Logical Reasoning & Analytical Ability

Q 277 / 325

UPSC CSE Prelims 2013

Four friends A, B, C and D distribute some money among themselves in such a manner that A gets one less than B, C gets 5 more than D and D gets 3 more than B. Who gets the smallest amount?

EXPLANATION

To determine who receives the smallest amount, we establish the relationships between the amounts received by A, B, C, and D based on the given statements.

Correct Option (A)

Let the amounts received by A, B, C, and D be represented by the variables A, B, C, and D, respectively.

  • From the statement "A gets one less than B": A = B - 1. This implies that B receives more than A.
  • From the statement "D gets 3 more than B": D = B + 3. This implies that D receives more than B.
  • From the statement "C gets 5 more than D": C = D + 5. This implies that C receives more than D.

Now, we can express all amounts in terms of B:

  • A = B - 1
  • B = B
  • D = B + 3
  • Substitute D = B + 3 into the equation for C: C = (B + 3) + 5 = B + 8.

Comparing these expressions, we can establish the following order of amounts received:

  • A = B - 1
  • B = B
  • D = B + 3
  • C = B + 8

Arranging these in ascending order based on their values relative to B:

A < B < D < C

Therefore, A receives the smallest amount.

Incorrect Options:

Based on the derived order A < B < D < C:

  • Option B (B): B receives more than A (B = A + 1), making B not the smallest amount.
  • Option C (C): C receives the largest amount (C = B + 8), making C not the smallest amount.
  • Option D (D): D receives more than B (D = B + 3), making D not the smallest amount.