UGC NET Paper I 6 Jan 2025 Shift 2 Paper

Concept:This is a word problem where we translate the given statements into algebraic equations and solve for the unknown number of cards each person has.Explanation:Let $A$, $B$, $C$, $D$ represent the number of cards with A, B, C, D respectively.From the first statement: If A gives 8 cards to B, then B has as many as C. So $B + 8 = C$. (Equation 1)After giving 8 cards, A has 3 less than C. So $A - 8 = C - 3$. (Equation 2)From the second statement: If A takes 6 cards from C, then A has twice as many as D. So $A + 6 = 2D$. (Equation 3)Also, B and D together have 50 cards: $B + D = 50$. (Equation 4)From Equation 1, $C = B + 8$. Substitute into Equation 2: $A - 8 = (B + 8) - 3$, so $A = B + 13$. (Equation 5)Substitute Equation 5 into Equation 3: $(B + 13) + 6 = 2D$, so $B + 19 = 2D$, thus $D = (B + 19)/2$. (Equation 6)Substitute Equation 6 into Equation 4: $B + (B + 19)/2 = 50$. Multiply by 2: $2B + B + 19 = 100$, so $3B = 81$, giving $B = 27$.Now $C = B + 8 = 35$, and $A = B + 13 = 40$, and $D = (27 + 19)/2 = 23$.Answer:A has 40 cards. Correct option is D.