SBI PO Prelims 8 Mar 2025 Shift 3 Paper

Concept:Set up equations using the relationship between total weight, number of students, and average weight, then solve for the original average.Explanation:Let the original number of students be $x$ and the original average weight be $y$ kg.Original total weight = $xy$ kg.Condition 1: Adding one student of 30 kg increases the average by 2 kg.Equation: $\frac{xy + 30}{x + 1} = y + 2$Multiply both sides: $xy + 30 = (x+1)(y+2) = xy + 2x + y + 2$Simplify: $30 = 2x + y + 2 \implies 2x + y = 28$ — (1)Condition 2: Adding two students with average weight 27 kg (total $2 \times 27 = 54$ kg) increases the average by 3 kg.Equation: $\frac{xy + 54}{x + 2} = y + 3$Multiply: $xy + 54 = (x+2)(y+3) = xy + 3x + 2y + 6$Simplify: $54 = 3x + 2y + 6 \implies 3x + 2y = 48$ — (2)Solve the two equations:Multiply (1) by 2: $4x + 2y = 56$Subtract (2) from this: $(4x+2y) - (3x+2y) = 56 - 48 \implies x = 8$Substitute $x = 8$ into (1): $2(8) + y = 28 \implies 16 + y = 28 \implies y = 12$.Thus, the original average weight is 12 kg.Answer:12 kg (Option B)