Correct Option (1)
Let A, B, C, and D represent the amounts of money held by Alok, Bhupesh, Chander, and Dinesh, respectively.
From the problem statement, the following conditions are established:
- A + B + C + D = 100 (Total money)
- A + B = C + D (Alok and Bhupesh's combined money equals Chander and Dinesh's combined money)
- C = (1/2)D (Chander has half the money Dinesh has)
- A = D + 5 (Alok has ₹5 more than Dinesh)
Substitute the second condition (A + B = C + D) into the first equation (A + B + C + D = 100):
(C + D) + (C + D) = 100
2(C + D) = 100
C + D = 50
Now, substitute the third condition (C = (1/2)D) into the equation C + D = 50:
(1/2)D + D = 50
(3/2)D = 50
D = 50 × (2/3) = 100/3
Using the value of D, calculate C:
C = (1/2)D = (1/2) × (100/3) = 50/3
Using the fourth condition (A = D + 5), calculate A:
A = (100/3) + 5 = (100 + 15)/3 = 115/3
Finally, using A + B = C + D and the derived value C + D = 50, calculate B:
A + B = 50
(115/3) + B = 50
B = 50 - (115/3) = (150 - 115)/3 = 35/3
The amounts of money held by each person are:
- Alok (A) = ₹115/3 ≈ ₹38.33
- Bhupesh (B) = ₹35/3 ≈ ₹11.67
- Chander (C) = ₹50/3 ≈ ₹16.67
- Dinesh (D) = ₹100/3 ≈ ₹33.33
Comparing these calculated amounts, Alok possesses the maximum amount of money.
Incorrect Options:
Based on the derived amounts:
- Bhupesh has ₹35/3, which is less than Alok's ₹115/3.
- Chander has ₹50/3, which is less than Alok's ₹115/3.
- Dinesh has ₹100/3, which is less than Alok's ₹115/3.
Therefore, Bhupesh, Chander, and Dinesh do not hold the maximum amount of money among the four persons.