Sazid is planning a tour, and he has $360 for his expenses. If he extends his tour by 4 days, he must cut down his daily expenses by $3. What is the length of Sazid's tour in days?/ সাজিদ একটি ভ্রমণের পরিকল্পনা করছেন, এবং তার খরচের জন্য ৩৬০ ডলার রয়েছে। যদি তিনি তার ভ্রমণ ৪ দিন বাড়ান, তাহলে তাকে দৈনিক খরচ ৩ ডলার কমাতে হবে। সাজিদের ভ্রমণের দৈর্ঘ্য কত দিন?

Let, x days be the original duration of the tour.

Total expenditure on tour = $ 360

Expenditure per day = $\frac{360}{x}$

Duration of the extended tour = (x + 4) days

Expenditure per day according to the new schedule $= \frac{360}{x + 4}$

Given that daily expenses are cut down by $3 As per the given condition = $\frac{360}{x}-\frac{360}{x+4}=3$

or,  $360 \left(\frac{1}{x}-\frac{1}{x+4}\right)=3$

or, $360 \left(\frac{1}{x}-\frac{1}{x+4}\right)=\frac{3}{360}$

or, $\frac{x+4-4}{x\left(x+4\right)} = \frac{1}{120}$

Of,  $\frac{4}{x\left(x+4\right)} = \frac{1}{120}$

or,  x(x + 4) = 480

or, x ² + 4x = 480

ог, x ² + 4x - 480 = 0

or, x² + 24x - 20x - 480 = 0

or, x(x + 24) - 20(x + 24) = 0

x + 24 = 0 or, x - 20 = 0

x = 20 or, x = - 24

Therefore, the original duration of the tour was 20 days