A prize fund of ₹840 was to be shared equally among the winners of a quiz. Four more students won than expected, so each winner actually received ₹35 less. The number of winners expected was:

If $n$ winners were expected, $840/n-840/(n+4)=35$. Clearing denominators gives $3360=35n(n+4)$, so $n^2+4n-96=0$ and $(n-8)(n+12)=0$, leaving $n=8$ (the negative root is rejected). Check: ₹840 ÷ 8 = ₹105 and ₹840 ÷ 12 = ₹70, a drop of exactly ₹35. (12 is the number who actually shared the money, $n+4$, not the number expected; 10 and 6 are near misses giving drops of ₹24 and ₹56.)