Finding Number of Students in Two Rooms

Video Explanation

Question

There are two examination rooms A and B. If 10 students are sent from A to B, both rooms have equal students. If 20 students are sent from B to A, then A has double the students of B. Find the number of students in each room.

Solution

Step 1: Let Variables

Let number of students in A = \(x\)

Let number of students in B = \(y\)

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Step 2: Form Equations

First condition: After transfer:

A → \(x – 10\), B → \(y + 10\)

\[ x – 10 = y + 10 \quad (1) \]

— Second condition: After transfer:

A → \(x + 20\), B → \(y – 20\)

\[ x + 20 = 2(y – 20) \quad (2) \]

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Step 3: Simplify

From (1):

\[ x – y = 20 \quad (3) \]

From (2):

\[ x + 20 = 2y – 40 \]

\[ x = 2y – 60 \quad (4) \]

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Step 4: Solve Linear Equations

Substitute (4) into (3):

\[ (2y – 60) – y = 20 \]

\[ y – 60 = 20 \]

\[ y = 80 \]

Then:

\[ x = 2(80) – 60 = 100 \]

—

Conclusion

\[ \text{Students in A} = 100,\quad \text{Students in B} = 80 \]

Verification

Check 1: \(90 = 90\) ✔

Check 2: \(120 = 2 \times 60\) ✔