Question

A person wanted to withdraw X rupees and Y paise from the bank. But cashier made a mistake and gave him Y rupees and X paise. Neither the person nor the cashier noticed that. After spending 20 paise, the person counts the money. To his surprise, he has double the amount he wanted to
withdraw. Find X and Y. (1 Rupee = 100 Paise)

• A. X=3, Y=6
• B. X=26, Y=53
• C. X=15, Y=30
• D. X=9, Y=36

Answer 1

The Correct Option is B

To solve the problem, we need to find the values of X (rupees) and Y (paise) such that the conditions given are satisfied. Let's analyze the situation step by step:

1. The person intended to withdraw X rupees and Y paise, which in total is equivalent to an amount: A = 100X + Y paise.

2. Due to an error, the cashier gave him Y rupees and X paise, which equals: B = 100Y + X paise.

3. After spending 20 paise, the money he has is: B - 20 paise.

4. According to the problem, this remaining amount is twice the original intended amount: B - 20 = 2A.

5. Substituting the expressions for A and B, we get: 100Y + X - 20 = 2(100X + Y).

6. Simplifying this equation, we have:

100Y + X - 20 = 200X + 2Y

98Y - 199X = 20.

7. The equation needs to be satisfied by any of the given options. Testing each option, we find:

8. For X = 26 and Y = 53, substituting into the equation gives:

98(53) - 199(26) = 20

5194 - 5174 = 20

20 = 20.

9. This matches the equation perfectly, confirming the correct values are: X = 26, Y = 53.