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.
Let the original duration of the tour be x days.
Total expenditure on tour = Rs. 360
∴ Expenditure per day
Person extends his tour by 4 days.
Duration of extended tour = ( x + 4) days
∴ New expenditure per day
It is given that expenditure per day is cut down by Rs.3
⇒ 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.