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  • 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. 
      In, ?ABC, D and E are the mid-points of AB and AC respectively. Find the ratio of the areas of ?ADE and ?ABC.

    • Options
    • A. 1 2
    • B. 1 4
    • C. 3 4
    • D. 1 8
    • Discuss
    • 2. 
      22020 ÷ 0.011=?

    • Options
    • A. 20020
    • B. 2000000
    • C. 200200
    • D. 200002
    • Discuss
    • 3. 
      How many times are the hands of a clock is at right angle in a day?

    • Options
    • A. 22
    • B. 24
    • C. 44
    • D. 48
    • Discuss
    • 4. The unit digit in the product (784 x 618 x 917 x 463) is:

    • Options
    • A. 2
    • B. 3
    • C. 4
    • D. 5
    • Discuss
    • 5. If the true discount on s sum due 2 years hence at 14% per annum be Rs. 168, the sum due is:

    • Options
    • A. Rs. 768
    • B. Rs. 968
    • C. Rs. 1960
    • D. Rs. 2400
    • Discuss
    • 6. 
      ?. 8x 2 + 6x = 5
      ?. 12y 2 ? 22y + 8 = 0

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 7. 
      15, 31, 63, 127, 255, (...)?

    • Options
    • A. 513
    • B. 511
    • C. 517
    • D. 523
    • Discuss
    • 8. 
      Find the probability that a vowel selected at random from the 5 vowels is an 'i'.?

    • Options
    • A. 4/5
    • B. 1/3
    • C. 1/5
    • D. 1/2
    • Discuss
    • 9. 396, 462, 572, 427, 671, 264

    • Options
    • A. 396
    • B. 427
    • C. 671
    • D. 264
    • Discuss
    • 10. 
      If 90% of A = 30% of B and B = C% of A,then the value of C is?

    • Options
    • A. 900
    • B. 800
    • C. 600
    • D. 300
    • Discuss


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