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प्रश्न
A person on tour has ₹ 10800 for his expenses. If he extends his tour by 4 days, he has to cut down his daily expenses by ₹ 90. Find the original duration of the tour.
उत्तर
Let the original duration of the tour be x days.
∴ Original daily expenses = ₹ `(10,800)/x`
If he extends his tour by 4 days, then his new daily expenses =₹`(10,800)/(x+4)`
According to the given condition,
`Rs10800/x-Rs(10,800)/(x+4)=Rs90`
⇒`(10800x+43200-10800x)/(x(x+4))=90`
⇒`43200/(x^2+4x)=90`
⇒`x^2+4x=480`
⇒`x^2+4x-480=0`
⇒`x^2+24x-20x-480=0`
⇒`x(x+24)-20x-480=0`
⇒`x(x+24)-20(x+24)=0`
⇒`(x+24) (x-20)=0`
⇒`x+24=0 or x-20=0`
⇒`x=-24 or x=20`
∴` x=20` (Number of days cannot be negative)
Hence, the original duration of the tour is 20 days.
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