Question

A cheque was written for M rupees and N paisa, both M and N being two-digit numbers, but was mistakenly cashed for N rupees and M paisa. The incorrect amount exceeded the correct amount by Rs. 1782 , Then

• A. M cannot be more than 70
• B. N can be equal to 2 M
• C. the amount of the cheque cannot be a multiple of 5.
• D. the incorrect amount can be twice the correct amount

Answer 1

The correct option is B N can be equal to 2 M

Correct amount on cheque $=M.N=100M+Npaid$

Mistaken amount on cheque $=N.M=100N+Mpaid$

Given, $N.M-M.N=1782$

$100N+M-100M-N=1782$

$99(N-M)=1782$

$N-M=18$

$M=71,N=89\left(possible\right)$ $\therefore \text{M can be more than to N}$

$\text{Amount on cheque}=100M+N$

$=1230$, for $M=12,N=30$

$=\text{Amount is multiple of 5}\left(possible\right)$

$(100N+M)=2(100M+N)$

$199M=98N$
$N-M=18$

N,M can't be integers

Incorrect amount can't be twice than correct

$N=2M$

$\therefore M=18,N=36\left(possible\right)$

$\therefore \text{N can be equal to 2M}$