Question

A person on tour has Rs. $360$ for his expenses. If he extends his tour for $4$ days, he has to cut down his daily expenses by Rs. $3$. Find the original number of days of the tour.

• A. $24$ days
• B. $16$ days
• C. $18$ days
• D. $20$ days

Answer 1

Answer: (D)

$20$ days

Let the original duration of the tour be $x$ days
Total expenditure $=Rs.360$
Expenditure per day $=Rs\frac{360}{x}$
Expenditure per day according to new schedule $=\frac{360}{x+4}$
As per question, $\frac{360}{x}-\frac{360}{x+4}=3$

$360(x=4-x)=3x(x+4)$

$x^2+4x=480$

$x^2+4x-480=0$

$(x+240)(x-20)=0$
$x=20$