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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. 
      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
    • 2. 
      750.0003 ÷ 19.999 =?

    • Options
    • A. 49
    • B. 18
    • C. 22
    • D. 38
    • Discuss
    • 3. 
      105, 85, 60, 30, 0, - 45, - 90?

    • Options
    • A. 0
    • B. 85
    • C. -45
    • D. 60
    • Discuss
    • 4. 
      Let A = {1, 2, {3, 4}, 5}. Which of the following statements is true?

    • Options
    • A. {3, 4} ? A
    • B. {3, 4} ? A
    • C. 1 ? A
    • D. {1, 2, 5} ? A
    • Discuss
    • 5. 
      Two vessels A and B contains milk and water mixed in the ratio 5 : 3 and 2 : 3. When these mixtures are mixed to form a new mixture containing half milk and half water, they must be taken in the ratio ?

    • Options
    • A. 2 : 5
    • B. 3 : 5
    • C. 4 : 5
    • D. 7 : 3
    • Discuss
    • 6. 
      1, 2, 4, 8, 16, 32, 64, (...), 256?

    • Options
    • A. 148
    • B. 128
    • C. 154
    • D. 164
    • Discuss
    • 7. 
      A tree is 12 m tall and casts an an 8 m long shadow. At the same time, a flag pole caste a 100 m long shadow. How long is the flag pole?

    • Options
    • A. 150 m
    • B. 200 m
    • C. 125 m
    • D. 115 m
    • Discuss
    • 8. 
      8% of 96 =? of 1/25

    • Options
    • A. 19.2
    • B. 7.68
    • C. 1.92
    • D. None of these
    • Discuss
    • 9. A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?

    • Options
    • A. Rs. 35
    • B. Rs. 245
    • C. Rs. 350
    • D. Cannot be determined
    • E. None of these
    • Discuss
    • 10. 
      If the hands of a clock coincide in every 65 minutes (true time), in 24 hours the clock will gain:

    • Options
    • A. 10 10 minutes. 143
    • B. 9 12 minutes. 143
    • C. 11 12 minutes. 143
    • D. 12 10 minutes. 143
    • Discuss


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