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Mr. Arjun is on tour and he has ₹ 360 for his expenses. If he exceeds his tour by 4 days, he must cut down his daily expenses by ₹ 3. For how many days is Mr. Arjun out on tour ?
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- 40
- 20
- 60
- 15
- None of the above
Correct Option: B
Let Mr . Arjun is on tour for N days.
Then, according to the question,
Difference in expenses per day for original and extended tour = 3
360/N - 360/(N + 4) = 3
⇒ 1/N - 1/(N + 4) = 3/360 = 1/120
⇒ [N + 4 - N] / [ N x (N + 4)] = 1/120
⇒ N(N + 4) = 4 x 120 = 480
⇒ N2 + 4N - 480 = 0
⇒ N2 + 24 - 20x - 480 = 0
⇒ N(N + 24) - 20(N + 24) = 0
⇒ (N + 24) (N - 20) = 0
∴ N = 20
(we ignore -ve value of x, that is, -24 because days cannot be negative)
