Question:
A person wanted to withdraw X rupees and Y paise from the bank. The cashier made a mistake and gave him Y rupees and X paise instead. Neither the person nor the cashier noticed the error. After spending 20 paise, the person counted the money and found he had exactly double the amount he originally wanted to withdraw. Find X and Y. (1 Rupee = 100 Paise)
A person wanted to withdraw X rupees and Y paise from the bank. The cashier made a mistake and gave him Y rupees and X paise instead. Neither the person nor the cashier noticed the error. After spending 20 paise, the person counted the money and found he had exactly double the amount he originally wanted to withdraw. Find X and Y. (1 Rupee = 100 Paise)
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Write both amounts in paise, use the doubling condition to form one equation, then test option values.
Updated On: Jul 15, 2026
- X = 3, Y = 6
- X = 26, Y = 53
- X = 15, Y = 30
- X = 9, Y = 36
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The Correct Option is B
Solution and Explanation
Step 1: Represent the two amounts in paise.
The person wanted to withdraw X rupees and Y paise, which equals (100X + Y) paise. The cashier, by mistake, handed over Y rupees and X paise, which equals (100Y + X) paise.
Step 2: Use the condition given after spending.
After spending 20 paise from the wrong amount he received, the money left with him is (100Y + X - 20) paise. The problem states this leftover amount is exactly double what he originally wanted to withdraw, so: 100Y + X - 20 = 2(100X + Y).
Step 3: Simplify the equation.
100Y + X - 20 = 200X + 2Y, so 98Y - 199X = 20.
Step 4: Test the given options in this equation.
Option (2): X = 26, Y = 53. Check: 98(53) - 199(26) = 5194 - 5174 = 20. This satisfies the equation exactly.
Option (1): X = 3, Y = 6: 98(6) - 199(3) = 588 - 597 = -9, not 20.
Option (3): X = 15, Y = 30: 98(30) - 199(15) = 2940 - 2985 = -45, not 20.
Option (4): X = 9, Y = 36: 98(36) - 199(9) = 3528 - 1791 = 1737, not 20.
Only X = 26, Y = 53 fits the equation.
Step 5: Sanity check the answer.
Wanted amount = 100(26) + 53 = 2653 paise. Received amount = 100(53) + 26 = 5326 paise. After spending 20 paise: 5326 - 20 = 5306 paise. Double the wanted amount = 2 x 2653 = 5306 paise. This matches exactly, confirming X = 26 and Y = 53.
The person wanted to withdraw X rupees and Y paise, which equals (100X + Y) paise. The cashier, by mistake, handed over Y rupees and X paise, which equals (100Y + X) paise.
Step 2: Use the condition given after spending.
After spending 20 paise from the wrong amount he received, the money left with him is (100Y + X - 20) paise. The problem states this leftover amount is exactly double what he originally wanted to withdraw, so: 100Y + X - 20 = 2(100X + Y).
Step 3: Simplify the equation.
100Y + X - 20 = 200X + 2Y, so 98Y - 199X = 20.
Step 4: Test the given options in this equation.
Option (2): X = 26, Y = 53. Check: 98(53) - 199(26) = 5194 - 5174 = 20. This satisfies the equation exactly.
Option (1): X = 3, Y = 6: 98(6) - 199(3) = 588 - 597 = -9, not 20.
Option (3): X = 15, Y = 30: 98(30) - 199(15) = 2940 - 2985 = -45, not 20.
Option (4): X = 9, Y = 36: 98(36) - 199(9) = 3528 - 1791 = 1737, not 20.
Only X = 26, Y = 53 fits the equation.
Step 5: Sanity check the answer.
Wanted amount = 100(26) + 53 = 2653 paise. Received amount = 100(53) + 26 = 5326 paise. After spending 20 paise: 5326 - 20 = 5306 paise. Double the wanted amount = 2 x 2653 = 5306 paise. This matches exactly, confirming X = 26 and Y = 53.
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