Question

A diplomat has gone to tour with 1000 expenses. now if he reduces his tour by 15 days, then he can spend 15 rupees more per day during his tour. find the original duration of the tour​

Answer 1

The original duration of the tour is 40 days.

Step-by-step explanation:

A diplomat has gone to tour with 1000 expenses.

Let the number of days he has gone for tour = x days

Let the expense of the tour = Rs. y

Total expense of tour = xy

=> xy = 1000 ...............(i)

Let he reduces his tour by 15 days = (x - 15) days

Let he can spend 15 rupees more per day = (y + 15)

Total expense of the tour = (x - 15)(y + 15)

=> (x - 15)(y + 15) = 1000

=> xy + 15x - 15y - 225 = 1000

=> xy + 15x - 15y = 1000 + 225 = 1225

=> 1000 + 15x - 15$(\frac{1000}{x})$ = 1225

=> 15x - 15$(\frac{1000}{x})$ = 1225 - 1000 = 225

=> 15x² - 15000 = 225x

=> x² - 1000 = 15x

=> x² - 15x - 1000 = 0

=> x² - 40x + 25x - 1000 = 0

=> x(x - 40) + 25(x - 40) = 0

=> (x - 40)(x + 25) = 0

=> x = -25, 40

x cannot be negative. Hence, x = 40 days.

Hence, the original duration of the tour is 40 days.