UGC-NET-Paper1

Let the number of cards with A, B, C, and D be denoted as A, B, C, and D respectively.

Step 1: Forming equations from the given conditions

1st condition: A says to B, “If I give you 8 cards, you will have as many as C has, and I shall have 3 less than what C has.”

Mathematically, this gives:

B + 8 = C ----(1)
A - 8 = C - 3
=> A - C = 5 ----(2)

2nd condition: “If I take 6 cards from C, I shall have twice as many as D has.”

(A + 6) = 2D ----(3)

3rd condition: “B and D together have 50 cards.”

B + D = 50 ----(4)

Step 2: Solve for A

From equation (1):

B = C - 8 ----(5)

Substituting equation (5) into equation (4):

(C - 8) + D = 50
=> C + D = 58 ----(6)

From equation (2):

A = C + 5 ----(7)

From equation (3):

C + 5 + 6 = 2D
=> C + 11 = 2D
=> 2D - C = 11 ----(8)

Step 3: Solve for C and D

Adding equations (6) and (8):

(C + D) + (2D - C) = 58 + 11
=> 3D = 69
=> D = 23

Substituting D = 23 in equation (6):

C + 23 = 58
=> C = 35

Step 4: Find A

From equation (7):

A = C + 5
A = 35 + 5
A = 40

Thus, the number of cards A has is **40**.

Answer: **(4) 40**