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Question
A person was given Rs. 3000 for a tour. If he extends his tour programme by 5 days, he must cut down his daily expenses by Rs. 20. Find the number of days of his tour programme.
Solution
Let the number of days of tour programme = x
Amount = Rs. 3000
∴ Express for each day = `(3000)/x`
In second case, no of days = x + 5
then expenses of each day = `(3000)/(x + 5)`
Now according to the condition,
`(3000)/x - (3000)/(x + 5)` = 20
⇒ `3000(1/x - 1/(x + 5))` = 20
⇒ `3000((x + 5 - x))/(x^2 + 5x)` = 20
⇒ 3000 x 5 = 20x2 + 100x
⇒ 20x2 + 100x - 15000 = 0
⇒ x2 + 5x - 750 = 0 ...(DIviding by 20)
⇒ x2 - 25x + 30x - 750 = 0
⇒ x(x - 25)(x + 30) = 0
⇒ (x - 25)(x + 30) = 0
EIther x - 25 = 0,
then x = 25
or
x + 30 = 0,
then x = -30,
but it is not possible as it is in negative.
∴ Number days = 25.
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