MathematicsA person on tour has Rs 360 for his expenses. If he extends his tour for 4 days, then he has to cut down his daily expenses by Rs 3. What is the original duration of the tour?

A person on tour has Rs 360 for his expenses. If he extends his tour for 4 days, then he has to cut down his daily expenses by Rs 3. What is the original duration of the tour?


  1. A
    20 days
  2. B
    10 days
  3. C
    30 days
  4. D
    11 days 

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    Solution:

    Given that a person on a trip has Rs 360 for costs. If he extends his tour for four days, he must reduce his daily expenses by Rs three.
    Let the number of days be x.
    So, daily expense initially is 360x.
    Daily expense when number of days are increased by 4 is 360x+4.
    According to the given condition, 360x-360x+4=3
    ⇒360x+1440-360xx(x+4)=3
    ⇒1440=3x2+12x
    ⇒x2+4x-480=0
    Factorize and simplify.
    ⇒x2+24x-20x-480=0
    ⇒x(x+24)-20(x+24)=0
    ⇒(x+24)(x-20)=0
    ⇒ x = -24 and x = 20
    Since the duration of days cannot be negative, x = 20.
    The original duration of the tour is 20 days.
    Hence, option 1 is correct.
     

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