A person on tour has Rs 360 for his daily expenses If he exceeds his tour programme by - Maths - Quadratic Equations

Question

A person on tour has Rs 360 for his daily expenses If he exceeds
his tour programme by four days, he must cut down his daily
expenses by Rs 3 per day Find the no of days of his tour
programme

Ankush Jain · Accepted Answer

Let the original duration of the tour be x days.

Total expenditure on tour = Rs. 360

∴ Expenditure per day $= Rs. \frac{360}{x}$

Person extends his tour by 4 days.

Duration of extended tour = ( x + 4) days

∴ New expenditure per day $= Rs \frac{360}{x + 4}$

It is given that expenditure per day is cut down by Rs.3

$∴ \frac{360}{x} - \frac{360}{x + 4} = 3 \Rightarrow 360 [\frac{1}{x} - \frac{1}{x + 4}] = 3 \Rightarrow 360 [\frac{x + 4 - x}{x (x + 4)}] = 3 \Rightarrow 120 � \frac{(4)}{x^{2} + 4 x} = 1 \Rightarrow \frac{480}{x^{2} + 4 x} = 1$

⇒ x ² + 4x = 480

⇒ x ² + 4x – 480 = 0

⇒ x ² + 24x – 20x – 480 = 0

⇒ x ( x + 24) – 20 ( x + 24 ) = 0

⇒ ( x – 20 ) ( x + 24) = 0

⇒ either ( x + 24 ) = 0 or ( x – 20) = 0

⇒ either x = – 24 or x = 20

But number of days can't be negative. So, x = 20.

Hence, original number of days of the tour was 20 days.

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A person on tour has Rs. 360 for his daily expenses. If he exceeds his tour programme by four days, he must cut down his daily expenses by Rs. 3 per day. Find the no. of days of his tour programme.