Mr. Iyer distributed Rs. 24 amongst his grandchildren. Had there been 4 grandchildren fewer, each would have received Re. 1 more. How many grandchildren does he have?

Let the number of grandchildren be $x$. Then each gets $\frac{24}{x}$ rupees, and if there were 4 fewer, each would get $\frac{24}{x-4}$ rupees. Given $\frac{24}{x-4}=\frac{24}{x}+1$, we get $24x=(24+x)(x-4)$, so $x^2-4x-96=0=(x-12)(x+8)$. Thus $x=12$ or $x=-8$, and only the positive value is valid. So he has 12 grandchildren.