A man, after a tour, finds that he had spent every day as many rupees as the number of days he had been on tour. How long did his tour last, if he had spent in all ₹1,296?

Let number of days he had been on tour be $x$.

Rupees spent every day = number of days he had been on tour = $x$

Total rupees spent = ₹1,296

Hence,

$x \times x = ₹1,296\\[1em] ⇒ x^2 = 1,296\\[1em] ⇒ x = \sqrt{1,296}\\[1em] ⇒ x = \sqrt{36 \times 36}\\[1em] ⇒ x = 36$

So, the man was on tour for 36 days.