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

A 30

B 15

C 20

D 45

E None of these

Correct Answer: Option C

Let Mr. Arun is on tour for x days.

Then, According to the question,

Difference in expenses per day for original and extended tour = 3

\(\frac{{360}}{x} - \frac{{360}}{{x + 4}} = 3\)

\(\Rightarrow \frac{1}{x} - \frac{1}{{x + 4}} = \frac{3}{{360}} = \frac{1}{{120}}\)

\(\Rightarrow \frac{{x + 4 - x}}{{x\left( {x + 4} \right)}} = \frac{1}{{120}}\)

⇒x(x+4) = 4×120=480

⇒ x² + 4x – 480 = 0

⇒ x² + 24x – 20x – 480 = 0

⇒ x(x + 24) – 20(x + 24) = 0

⇒ (x + 24) (x - 20) = 0

∴ x = 20

(we ignore negative value of x, that is, - 24 because days cannot be negative)

Hence, the required answer is 20,