Question

A party of tourists booked a hotel for Rs. 1,200. Three of the members failed to pay. As a result, each of the others had to pay Rs. 20 more. How many tourists were there in the party ?

Answer 1

Let there be $n$ tourists and each have to pay $p$ Rs
$np=1200$

$\therefore p=\frac{1200}{n}$
$(n-3)(p+20)=1200$
$(n-3)(\frac{1200}{n}+20)=1200$
$(n-3)(1200+20n)=1200n$
$1200n-3600+20n^2-60n=1200n$
$n^2-3n-180=0$
$n^2-15n+12n-180=0$
$(n-15)(n+12)=0$
$n=15$ tourists