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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. Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.

    • Options
    • A. 2 : 3
    • B. 1 : 1
    • C. 3 : 4
    • D. 4 : 3
    • Discuss
    • 2. A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?

    • Options
    • A. 65 sec
    • B. 89 sec
    • C. 100 sec
    • D. 150 sec
    • Discuss
    • 3. What was the day of the week on 17th June, 1998?

    • Options
    • A. Monday
    • B. Tuesday
    • C. Wednesday
    • D. Thursday
    • Discuss
    • 4. The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:

    • Options
    • A. 279
    • B. 283
    • C. 308
    • D. 318
    • Discuss
    • 5. 
      1872/ ? ? = 234

    • Options
    • A. 324
    • B. 64
    • C. 8
    • D. 256
    • Discuss
    • 6. 
      For every 4 leaps taken by a dog, a cat takes 5 leaps in the same time. But distance covered in 3 leaps of dog is same as that of 4 leaps of cat. Then what is the ratio of speed of dog and cat?

    • Options
    • A. 15 : 14
    • B. 16 :15
    • C. 12 :11
    • D. 10 : 9
    • Discuss
    • 7. 
      A come of height 7 cm and base radius 3 cm is curved from a rectangular block of wood 10 cm x 5 cm x 2 cm. The percentage of wood wasted is?

    • Options
    • A. 34%
    • B. 46%
    • C. 54%
    • D. 66%
    • Discuss
    • 8. 
      1, 9, 25, 49, 81,?

    • Options
    • A. 90
    • B. 135
    • C. 121
    • D. 125
    • Discuss
    • 9. 
      An accurate clock shows the time as 3:00 after hour hand has moved 135°, the time would be?

    • Options
    • A. 7:30
    • B. 6:30
    • C. 8:00
    • D. 9:30
    • Discuss
    • 10. 
      P.V. Narsihma Rao was elected party leader on 29th may, 1991. What was the day of the week?

    • Options
    • A. Tuesday
    • B. Friday
    • C. Wednesday
    • D. Sunday
    • Discuss


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