A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja, giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise, Shailaja noticed that she was left with exactly three times as much as the amount on the cheque. Which of the following is a valid statement about the cheque amount?
Explanation:
Let the amount on Shailaja’s cheque be Rs. x and paise y = (100x + y) paise (x and y are positive integers)
The teller gives her (100y + x) paise.
Now, 100y + x – 50 = 3(100x + y)
∴ 97y – 299x = 50
∴ y = (50 + 299x)/97 = [50 + 8x + 291x]/97 = [(50 + 8x)/97] + 3x
Now as y is an integer, (50 + 8x) has to be a multiple of 97 with x, y ≤ 99
50 + 8x = 97k (k is an integer) ∴ k = 2, 10, 18… ∴ x = 18, 115, 212… ∴ x = 18 is the only possible value.
This implies that y = 5
∴ The amount on Shailaja’s cheque is over Rs. 18 but less than Rs. 19.
Hence, option (d).
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