Question

# A person on tour has $₹4200$ for his expenses. If he extends his tour for $3$ days, he has to cut down daily expenses by $₹70$. Find the original duration of the tour.

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Solution

## Step:Find the original duration of the tour.Given, Total money a person has$=₹4200$Let $x$ days be the duration of the tour.Expense in a day $=\frac{4200}{x}$Duration of the extended tour $=3days$Then, Expense in a day $=\frac{4200}{x+3}$As per the question, we get$\frac{4200}{x}-\frac{4200}{x+3}=70$$4200\left(\frac{1}{x}-\frac{1}{x+3}\right)=70$$⇒\left(\frac{1}{x}-\frac{1}{x+3}\right)=\frac{70}{4200}$$⇒\left(\frac{1}{x}-\frac{1}{x+3}\right)=\frac{1}{60}$$⇒\frac{x+3-x}{x\left(x+3\right)}=\frac{1}{60}$$⇒\frac{3}{{x}^{2}+3x}=\frac{1}{60}$$⇒{x}^{2}+3x=180$$⇒{x}^{2}+3x-180=0$$⇒{x}^{2}+15x–12x–180=0$$⇒x\left(x+15\right)–12\left(x+15\right)=0$$⇒\left(x+15\right)\left(x–12\right)=0$$⇒x+15=0orx–12=0$$⇒x=-15orx=12$Since x cannot be a negative So, $x=12$Hence, the original duration of the tour is $12$ days.

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