Question

a person on tour has rupees 360 for his daily expenses.If he extends his tour by four days,he has cut down his daily expenses by rupees 3 find the original duration of tour

Answer 1

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Amount that the person has = Rs. 360

Let the original no. of tour days = x days

Daily expenses = Rs. 360 / x per day

The person has extended his tour for four days. ( given )

So, daily expenses per day = Rs. 360 / ( x + 4 )

Now, A.TQ.

[ 360 ( x + 4 ) – 360x ] / [ x ( x + 4 ) ] = 3

( 360x + 1440 – 360x ) / ( x² + 4x ) = 3

1440 / ( x² + 4x ) = 3

1440 = 3 ( x² + 4x )

3x² + 12x – 1440 = 0

x² + 4x – 480 = 0

x² – 20x + 24x – 480 = 0

x ( x – 20 ) + 24 ( x – 20 ) = 0

( x – 20 ) ( x + 24 ) = 0

( x – 20 ) = 0 or ( x + 24 ) = 0

x = 20 or x = – 24

Thus, amount can't be negative.

Therefore, the original duration of tour is 20 days.