A person goes to a bank and quotes x Rs and y Paise on a cheque. The cashier…
2025
A person goes to a bank and quotes x Rs and y Paise on a cheque. The cashier misreads it and gives y Rs and x Paise. The man comes out and donates 5 Paise to a beggar. Now, the man has exactly double the amount he has quoted on the cheque. sum of x and y will be
- A.
89
- B.
29
- C.
34
- D.
94
Attempted by 3 students.
Show answer & explanation
Correct answer: D
Concept: When a stated amount of "x Rupees and y Paise" has its two parts read in swapped order, express both the quoted and the swapped amount in a single unit (paise) — quoted = 100x + y paise, received (swapped) = 100y + x paise. Any relationship stated between the two amounts (a difference, a multiple, etc.) then becomes a linear equation in x and y, which must be solved for integer digit values, since x and y are just rupee/paise counts.
Let the man quote x Rs and y Paise on the cheque, i.e. an amount of (100x + y) paise.
The cashier misreads the digits and hands over y Rs and x Paise instead, i.e. (100y + x) paise.
After donating 5 Paise to a beggar, the man is left holding (100y + x) − 5 paise.
This remaining amount is stated to be exactly double what he originally quoted: (100y + x) − 5 = 2(100x + y).
Expanding: 100y + x − 5 = 200x + 2y, which simplifies to 98y − 199x = 5.
Solving this equation for integers with 0 ≤ x, y ≤ 99 gives x = 31 and y = 63, since 98 × 63 − 199 × 31 = 6174 − 6169 = 5.
Therefore, x + y = 31 + 63 = 94.
Cross-check: the quoted amount is Rs 31.63 and the misread amount handed over is Rs 63.31. Removing the 5 Paise donated to the beggar leaves Rs 63.26, and 2 × Rs 31.63 = Rs 63.26 — an exact match, confirming x + y = 94.