Question

A cheque is written for x rupees and y paise, x and y both two-digit numbers. In error it is cashed for y rupees and x paise, the incorrect amount exceeding the correct amount by Rs. 17.82. Then:

• A. x cannot exceed 70
• B. y can equal 2x
• C. the amount of the cheque cannot be a multiple of 5
• D. the incorrect amount can equal twice the correct amount

Answer 1

The correct option is B y can equal 2x

Let x=10a+b, y=10c+d

Correct amount = $10a+b+\frac{c}{10}+\frac{d}{100}$

Incorrect amount = $10c+d+\frac{a}{10}+\frac{b}{100}$

Incorrect amount - Correct Amount = 17.82

$\frac{99(c-a)}{10}+\frac{99(d-b)}{100}17.82\frac{99}{100}\left(\right(10c+d)-(10a+b\left)\right)=17.82y-x=18$

x can exceed 20, if y is multiple of 5, then amount can be a multiple of 5.

$Ify+\frac{x}{100}=2(x+\frac{y}{100})\frac{98y}{100}=\frac{199x}{100}98y=199x$

But this is not possible.

$\therefore$ Incorrect amount cannot be twice the correct amount.

Let $y=2x$

$2x-x=18$

$x=18$

$\therefore y=36$ (Possible)

$\therefore$ y equals 2x.