Transposed rupees and paise cheque problem

CAT 2007 Slot 1 · QA · Medium · Linear Equations

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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?

  1. A.

    Over Rupees 13 but less than Rupees 14

  2. B.

    Over Rupees 7 but less than Rupees 8

  3. C.

    Over Rupees 22 but less than Rupees 23

  4. D.

    Over Rupees 18 but less than Rupees 19

  5. E.

    Over Rupees 4 but less than Rupees 5

Answer

D

Explanation

Let the cheque be for XX rupees and YY paise. Received amount = 100Y+X100Y + X paise. Given: 100Y+X−50=3(100X+Y)  ⟹  97Y−299X=50  ⟹  Y=299X+5097100Y + X - 50 = 3(100X + Y) \implies 97Y - 299X = 50 \implies Y = \frac{299X + 50}{97}. For YY to be an integer between 0 and 99, X=18X = 18, giving Y=56Y = 56. So the cheque was for 18 rupees and 56 paise.

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