Finding Money of A and B

Video Explanation

Question

A and B each have some money. If A gives ₹30 to B, then B will have twice the money left with A. If B gives ₹10 to A, then A will have thrice as much as B. Find how much money each has.

Solution

Step 1: Let Variables

Let money with A = \(x\)

Let money with B = \(y\)

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Step 2: Form Equations

First condition: After A gives 30 to B:

A → \(x – 30\), B → \(y + 30\)

\[ y + 30 = 2(x – 30) \quad (1) \]

— Second condition: After B gives 10 to A:

A → \(x + 10\), B → \(y – 10\)

\[ x + 10 = 3(y – 10) \quad (2) \]

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Step 3: Simplify

From (1):

\[ y + 30 = 2x – 60 \]

\[ y = 2x – 90 \quad (3) \]

From (2):

\[ x + 10 = 3y – 30 \]

\[ x = 3y – 40 \quad (4) \]

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Step 4: Solve Linear Equations

Substitute (3) into (4):

\[ x = 3(2x – 90) – 40 \]

\[ x = 6x – 270 – 40 \]

\[ x = 6x – 310 \]

\[ 5x = 310 \]

\[ x = 62 \]

Then:

\[ y = 2(62) – 90 = 34 \]

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Conclusion

\[ \text{Money with A} = ₹62,\quad \text{Money with B} = ₹34 \]

Verification

After A gives 30: A = 32, B = 64 → B = 2×A ✔

After B gives 10: A = 72, B = 24 → A = 3×B ✔