Four persons, Alok, Bhupesh, Chander and Dinesh have a total of ₹ 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 ₹ 5 more than Dinesh has. Who has the maximum amount of money ?
- (a) Alok ✓ UPSC's answer
- (b) Bhupesh
- (c) Chander
- (d) Dinesh
Why the answer is (a)
• Let the amount with Dinesh be D. Since Chander has half of Dinesh's money, Chander has D/2.
• Alok has ₹5 more than Dinesh, so Alok has D + 5.
• The total money is ₹100, and Alok + Bhupesh = Chander + Dinesh, which implies each pair has ₹50.
• Therefore, Chander + Dinesh = D/2 + D = 50, which gives 3D/2 = 50, so D = 100/3 ≈ 33.33.
• Alok's amount is D + 5 = 100/3 + 5 = 115/3 ≈ 38.33.
• Bhupesh's amount is 50 - Alok = 50 - 115/3 = 35/3 ≈ 11.67.
• Comparing the amounts: Alok (38.33) > Dinesh (33.33) > Chander (16.67) > Bhupesh (11.67), so Alok has the maximum.
Why the other options are wrong
- (b) Bhupesh
- Bhupesh has the least amount (₹11.67), not the maximum.
- (c) Chander
- Chander has ₹16.67, which is less than Alok's ₹38.33.
- (d) Dinesh
- Dinesh has ₹33.33, which is less than Alok's ₹38.33.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2014, held on 24 August 2014. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.