Mr. Arun is on tour and he has Rs.360 for his expenses. If he exceeds his tour by 4 days, he must cut down his daily expenses by Rs.3. For how many days is Mr. Arun out on tour?
Correct Answer: Description for Correct answer:
Let Mr. Arun is on tour for x days
Then, according to the question,
Difference in expenses per day for original and extended tour = 3
\( \Large \frac{360}{x}-\frac{360}{x+4}=3 \)
=>\( \Large \frac{1}{x}-\frac{1}{x+4}=\frac{3}{360}=\frac{1}{120} \)
\( \Large \frac{x+4-x}{x \left(x+4\right) }=\frac{1}{120} \)
=>\( \Large x \left(x+4\right)=4 \times 120 = 480 \)
=>\( \Large x^{2}+4x-480 = 0 \)
=>\( \Large x^{2}+24x-20x-480 = 0 \)
=>\( \Large x \left(x+24\right)-20 \left(x+24\right) = 0 \)
=> \( \Large \left(x+24\right) \left(x-20\right) = 0 \)
Therefore, x = 20.
(we ignore -ve value of x, that is, -24 because days cannot be negative)
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