A person was given ₹3000 for a tour. If he extends his tour programme by 5 days, he must cut down his daily expense by ₹20. Find the number of days of his tour programme.

Let number of days for which person plans trip be x

Total expense for trip = ₹3000

∴ Expense of each day = ₹$\Big(\dfrac{3000}{x}\Big)$

Days extended = 5 , so total days = (x + 5)

Daily expense to be cut down is ₹20,

∴ New Expense of each day = ₹$\Big(\dfrac{3000}{x} - 20\Big)$

According to question,

$\Rightarrow (x + 5)\Big(\dfrac{3000}{x} - 20\Big) = 3000 \\[1em] \Rightarrow (x + 5)\Big(\dfrac{3000 - 20x}{x}\Big) = 3000 \\[1em] \Rightarrow (x + 5)(3000 - 20x) = 3000x \text{ (Cross multiplying) } \\[1em] \Rightarrow 3000x - 20x^2 + 15000 - 100x = 3000x \\[1em] \Rightarrow -20x^2 + 3000x - 3000x -100x + 15000 = 0 \\[1em] \Rightarrow -20x^2 - 100x + 15000 = 0 \\[1em] \Rightarrow -20(x^2 + 5x - 750) = 0 \\[1em] \Rightarrow x^2 + 5x - 750 = 0 \\[1em] \Rightarrow x^2 + 30x - 25x - 750 = 0 \\[1em] \Rightarrow x(x + 30) - 25(x + 30) = 0 \\[1em] \Rightarrow (x - 25)(x + 30) = 0 \\[1em] \Rightarrow x - 25 = 0 \text{ or } x + 30 = 0 \\[1em] x = 25 \text{ or } x = -30$

Since, number of days cannot be negative hence, x ≠ -30

∴ x = 25

Hence, the number of days of tour programme are 25.