Question

A person on tour having 360 Rs for his expenses due to some reason he have to extent his journey 4 days.Find the number of days for his tour if his daily expenditure is reduced by 3 Rs per day?

Answer 1

Amount with the person = Rs 360
Let the original number of duration of the tour be x days
Daily expenses per day = Rs 360/x
Given that his tour is extended for 4 days
Hence daily expenses per days = Rs 360/(x + 4)
Therefore


⇒ 360x + 1440 – 360x = 3(x2 + 4x)
⇒ 1440 = 3x2 + 12x
⇒ 3x2 + 12x – 1440 = 0
⇒ x2 + 4x – 480 = 0
⇒ x2 + 24x – 20x – 480 = 0
⇒ x(x + 24) – 20(x + 24) = 0
⇒ (x + 24)(x – 20) = 0
⇒ (x + 24) = 0 or (x – 20) = 0
∴ x = –24 or x = 20
Since x cannot be negative, x = 20
Hence his original duration of the tour is Rs 20

Answer 2

let the no of days be x
then daily expenditure= 360/x
if his journey is extended for 4 days
then no of days=x+4
his daily expenditure= 360/x+4
a/q
360/x-360/x+4=3
[360(x+4)-360x]/ x(x+4)= 3
360x+ 1440-360x= 3(x^2+4x)
1440= 3x^2+12x
3x^2+12x-1440=0
3(x^2+4x-480)=0
x^2+4x-480=0
x^2+24x-20x-480=0
x(x+24)-20(x+24)=0
(x+24)(x-20)=0
no of days can't be negative
so no of days =20 ans