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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?
Let the value of cheque be x Rs and y ps and the amount she received is y Rs and x ps.
After 50 ps is deducted she has the amount which is 3 times the amount on cheque,
So 100y+x-50=3(100x+y) (After converting the amount in paise)
y= (299x+50)/97 = 3x+ (8x+50)/97
Since x is an integer, 3x will definitely be an integer. Now, (8x+50)/97 has to be an integer for y to be an integer.
So, 8x+50 has to be a multiple of 97.
8x+50= 97
$$\Rightarrow$$ x = 47/8, this value of x is not an integer.
8x+50= 97*2 = 194
8x = 144
$$\Rightarrow$$ x = 144/8 = 18. Here, we got an integer.
So, the amount has to be 18 rupees and some paise. Hence, option D is correct.
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