SBI Clerk Prelims 22 Feb 2025 Shift 3 Paper

Concept:Use weighted averages to relate the partial group's average to the overall average.Explanation:Let the total number of students be $a$ and the class average be $x$.Sum of marks of entire class = $a \times x$.The $\frac{3}{4}$ of the class has average = $80\%$ of $x = 0.8x = \frac{4}{5}x$.Number of students in this group = $\frac{3}{4}a$.Sum of marks of this group = $\frac{3}{4}a \times \frac{4}{5}x = \frac{3}{5} a x$.Remaining $\frac{1}{4}$ of the class has average = $y$ (unknown).Number of students = $\frac{1}{4}a$.Sum of marks of remaining = $\frac{1}{4}a \times y = \frac{a y}{4}$.Total sum = sum of both groups:$\frac{3}{5} a x + \frac{a y}{4} = a x$.Divide by $a$: $\frac{3}{5}x + \frac{y}{4} = x$.Bring $\frac{3}{5}x$ to RHS: $\frac{y}{4} = x - \frac{3}{5}x = \frac{2}{5}x$.Multiply by 4: $y = \frac{8}{5}x$.Thus $y : x = \frac{8}{5} : 1 = 8 : 5$.Answer:The ratio of the average score of the remaining class to that of the entire class is $8 : 5$ (Option E).