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Home Aptitude Linear Equation See What Others Are Saying!
  • Question
  • A person on tour has total ?360 for his daily expenses. He decides to extend his tour programme by 4 days which leads to cutting down daily expenses by ?3 a day . The numbers of days of tour are :


  • Options
  • A. 15
  • B. 20
  • C. 18
  • D. 16

  • Correct Answer
  • 20 

    Explanation

    Method 1 to solve this question.
    Let us assume the numbers of days of tour before extending the tour are D and daily expenses is E.
    According to question,
    Total expenses on tour = per day expenses x total number of days
    Total expenses on tour = E x D = ED
    360 = ED
    ? ED = 360
    ? E = 360/D .................(1)
    Again according to question,
    After extending the tour by 4 days, Number of days of tour = D + 4
    Expenses will be reduced by 3 rupees, then everyday expenses = E - 3
    so total expenses = (D + 4) x (E - 3)
    360 = (D + 4) x (E - 3)
    (D + 4) x (E - 3) = 360 .............................................(2)
    Put the value of E in Equation (2). we will get,
    (D + 4) x (360/D - 3) = 360
    ? (D + 4) x ( (360 - 3D)/D ) = 360
    ? (D + 4) x ( (360 - 3D) ) = 360 x D
    ? (D + 4) x (360 - 3D) = 360 x D
    After multiplication by algebra law,
    ? 360 x D - 3D x D + 4 x 360 - 4 x 3D = 360D
    ? 360 x D - 3D + 1440 - 12 D = 360 D
    ? - 3 D + 1440 - 12 D = 360 D - 360 x D
    ? - 3 D + 1440 - 12 D = 0
    ? 3 D - 1440 + 12 D = 0
    ? D - 480 + 4 D = 0
    ? D + 4 D - 480 = 0
    ? D + 24 D - 20 D - 480 = 0
    ? D( D + 24) - 20( D + 24) = 0
    ? ( D + 24) ( D - 20) = 0
    Either ( D + 24) = 0 or ( D - 20) = 0
    So D = - 24 or D = 20
    But days cannot be negative so D = 20 days.

    Method 2 to solve this question.
    Let us assume the original day of tour is d days.
    Given that his tour is extended for 4 days
    Hence daily expenses per days = 360/(d + 4)
    Therefore, According to question,
    360/d - 360/(d + 4) = 3
    ? (360(d + 4) - 360d)/d x (d + 4) = 3
    ? (360(d + 4) - 360d)/d x (d + 4) = 3
    ? 360(d + 4) - 360d = 3d x (d + 4)
    ? 360d + 1440 ? 360d = 3(d 2 + 4d)
    ? 1440 = 3d 2 + 12d
    ? 3d 2 + 12d ? 1440 = 0
    ? d 2 + 4d ? 480 = 0
    ? d 2 + 24d ? 20d ? 480 = 0
    ? d(d + 24) ? 20(d + 24) = 0
    ? (d + 24)(d ? 20) = 0
    ? (d + 24) = 0 or (d ? 20) = 0
    ? d = ?24 or d = 20
    Since days cannot be negative, d = 20
    Hence his original duration of the tour is 20 days.


  • More questions

    • 1. 
      The value of 47 / 10000 is?

    • Options
    • A. .0047
    • B. .0470
    • C. .00047
    • D. .000047
    • Discuss
    • 2. If 4x = 18y, then the value of ( x/y - 1) is

    • Options
    • A. 1 3
    • B. 7 2
    • C. 2 3
    • D. 3 2
    • Discuss
    • 3. 
      If the price of 23 toys is Rs. 276, then what will the price (Rs.) of 12 toys?

    • Options
    • A. 144
    • B. 158
    • C. 159
    • D. 166
    • Discuss
    • 4. 
      .02 =(......?.....)%

    • Options
    • A. 20
    • B. 2
    • C. .02
    • D. .2
    • Discuss
    • 5. 
      If 36 men can do a piece of work in 25 hours, in how many hours will 15 men do it?

    • Options
    • A. 45
    • B. 55
    • C. 60
    • D. 72
    • Discuss
    • 6. 
      2?63 / 11 =233

    • Options
    • A. 4
    • B. 3
    • C. 6
    • D. 5
    • Discuss
    • 7. 
      When 121012 is divided by 12, the remainder is

    • Options
    • A. 0
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 8. 
      Aarti can do a piece of work in 6 days. In how many days will she complete three time of work of same type?

    • Options
    • A. 18 days
    • B. 21 days
    • C. 3 days
    • D. 6 days
    • Discuss
    • 9. 
      750.0003 ÷ 19.999 =?

    • Options
    • A. 49
    • B. 18
    • C. 22
    • D. 38
    • Discuss
    • 10. 
      105, 85, 60, 30, 0, - 45, - 90?

    • Options
    • A. 0
    • B. 85
    • C. -45
    • D. 60
    • Discuss


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