Mr. Arjun is on tour and he has ? 360 for his expenses. If he exceeds his tour by 4 days, he must cut down his daily expenses by ? 3. For how many days is Mr. Arjun out on tour?

Let Mr . Arjun is on tour for N days.
Then, according to the question,
Difference in expenses per day for original and extended tour = 3
360/N - 360/(N + 4) = 3
? 1/N - 1/(N + 4) = 3/360 = 1/120
? [N + 4 - N] / [ N x (N + 4)] = 1/120
? N(N + 4) = 4 x 120 = 480
? N² + 4N - 480 = 0
? N² + 24 - 20x - 480 = 0
? N(N + 24) - 20(N + 24) = 0
? (N + 24) (N - 20) = 0
? N = 20
(we ignore -ve value of x, that is, -24 because days cannot be negative)