A person on tour has Rs 360 for his expenses. If he extends his tour for 4 days, he has to cut down his daily expenses by Rs 3. Find the original duration of the tour.

Let x days be the original duration of the tour

Total expenditure on tour = Rs 360

Expenditure per day = Rs 360/x

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

Expenditure per day according to new schedule = Rs (360/x+4)

Given that daily expenses are cut down by Rs 3

Therefore,

As per the given condition

[latex]\frac{360}{x}-\frac{360}{x+4}=3\\\frac{360(x+4)-360x}{x(x+4)}=3\\\frac{360x+1440-360x}{x(x+4)}=3\\\frac{1440}{x^{2}+4x}=3[/latex]

On further calculation, we get,

x2 + 4x – 480 = 0

x2 + 24x – 20x – 480 = 0

x(x + 24) – 20 (x + 24) = 0

x – 20 = 0 or x + 24 = 0

x = 20 or x = -24

Since the number of days cannot be negative. So, x = 20

Therefore, the original duration of the tour was 20 days

Was this answer helpful?

 
   

0 (0)

(0)
(0)

Choose An Option That Best Describes Your Problem

Thank you. Your Feedback will Help us Serve you better.

Leave a Comment

Your Mobile number and Email id will not be published. Required fields are marked *

*

*

BOOK

Free Class

Ask
Question