CAT 2025 Slot1 Quant: The ratio of the number of students in the morning shift and afternoon shift
February 20, 2026 2026-02-20 22:14CAT 2025 Slot1 Quant: The ratio of the number of students in the morning shift and afternoon shift
Since the total number of students stays constant in the first shift move, make the total of ratios equal.
Initial $(13+9=22)$, After move $(19+14=33)$. LCM of $22$ and $33$ is $66$.
New Ratios: $39:27 \to 38:28$. Loss of $1$ unit $= 21$ students.
Current Students: Morning $= 38 \times 21 = 798$, Afternoon $= 28 \times 21 = 588$.
Detailed Step-by-Step Solution
Step 1: Find Initial Number of Students
Let Morning $(M) = 13x$ and Afternoon $(A) = 9x$.
After 21 move: $\frac{13x - 21}{9x + 21} = \frac{19}{14}$
$14(13x - 21) = 19(9x + 21) \implies 182x - 294 = 171x + 399$
$11x = 693 \implies x = 63$.
Students after move: $M = 13(63)-21 = 798$, $A = 9(63)+21 = 588$.
Step 2: Add New Students
Let new students be $3k$ and $8k$.
$\frac{798 + 3k}{588 + 8k} = \frac{5}{4}$
$4(798 + 3k) = 5(588 + 8k) \implies 3192 + 12k = 2940 + 40k$
$28k = 252 \implies k = 9$.
Step 3: Calculate Total New Students
Total new students $= 3k + 8k = 11k$.
Total $= 11 \times 9 = \mathbf{99}$.
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