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?

Solution

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

Now both x and y are integers, so from options we put x=18, (8x+50)/97 = 194/97 =2 which is an integer. Hence, D is the answer.

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