UPSC Prelims 2014·CSAT·Logical Reasoning·Deductive Logic

Four persons, Alok, Bhupesh, Chander and Dinesh have a total of Rs. 100 among themselves. Alok and Bhupesh between them have as much money as Chander and Dinesh between them, but Alok has more money than Bhupesh; and Chander has only half the money that Dinesh has. Alok has in fact Rs. 5 more than Dinesh has. Who has the maximum amount of money?

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  1. AAlokCorrect
  2. BBhupesh
  3. CChander
  4. DDinesh

Explanation

Let the money with Alok, Bhupesh, Chander, and Dinesh be A, B, C, and D respectively.

  1. Total money: A + B + C + D = 100
  2. Alok and Bhupesh have as much as Chander and Dinesh: A + B = C + D

From (1) and (2), we can deduce: (A + B) + (C + D) = 100 (C + D) + (C + D) = 100 2(C + D) = 100 C + D = 50

Also, A + B = 50.

  1. Chander has only half the money that Dinesh has: C = D / 2

Substitute C = D / 2 into C + D = 50: D / 2 + D = 50 3D / 2 = 50 3D = 100 D = 100 / 3

Now find C: C = D / 2 = (100 / 3) / 2 = 50 / 3

  1. Alok has Rs. 5 more than Dinesh has: A = D + 5

Substitute D = 100 / 3 into A = D + 5: A = 100 / 3 + 5 A = 100 / 3 + 15 / 3 A = 115 / 3

  1. Find Bhupesh's money using A + B = 50: 115 / 3 + B = 50 B = 50 - 115 / 3 B = 150 / 3 - 115 / 3 B = 35 / 3

Now we have the amounts for each person: Alok (A) = 115 / 3 (approximately Rs. 38.33) Bhupesh (B) = 35 / 3 (approximately Rs. 11.67) Chander (C) = 50 / 3 (approximately Rs. 16.67) Dinesh (D) = 100 / 3 (approximately Rs. 33.33)

Comparing these values, Alok has the largest amount (115/3).

The final answer is A.

Logical Reasoning: Four persons, Alok, Bhupesh, Chander and Dinesh have a total of Rs. 100 among themselves. Alok and Bhupesh between them
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