Finding Number of ₹50 and ₹100 Notes

Video Explanation

Question

Meena withdrew ₹2000 from a bank in ₹50 and ₹100 notes only. She received a total of 25 notes. Find how many ₹50 notes and ₹100 notes she received.

Solution

Step 1: Let Variables

Let number of ₹50 notes = \(x\)

Let number of ₹100 notes = \(y\)

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Step 2: Form Equations

Total number of notes:

\[ x + y = 25 \quad (1) \]

Total amount:

\[ 50x + 100y = 2000 \quad (2) \]

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Step 3: Simplify

Divide (2) by 50:

\[ x + 2y = 40 \quad (3) \]

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Step 4: Solve Linear Equations

Subtract (1) from (3):

\[ (x + 2y) – (x + y) = 40 – 25 \]

\[ y = 15 \]

Then:

\[ x = 25 – 15 = 10 \]

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Step 5: Final Answer

\[ \text{₹50 notes} = 10,\quad \text{₹100 notes} = 15 \]

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Verification

Total notes: \(10 + 15 = 25\) ✔

Total amount: \(500 + 1500 = 2000\) ✔