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?

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.