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} + 4*x* = 480

*⇒* *x* ^{2} + 4*x* – 480 = 0

*⇒ x* ^{2} + 24*x* – 20*x* – 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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