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Mathematical Aptitude - Averages

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6. A question is followed by two statements I and II that contain certain data. Tell by selecting one of the answer choices given, whether the data given in the statements are sufficient for answering the question.
Question: A horse ran 100 miles without stopping. What was the average speed in miles per hour?
Statements
I. The horse ran 20 miles per hour for the first 50 miles.
II. The entire journey starts from 8 pm on day one to 4 am the following day.

  • Option : B
  • Explanation : First statement is not sufficient to answer the question because the speed of the second half of the distance is not given here but statement II can answer as information to calculate average speed = distance/time is given in the statement.
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7. A and B start from the same destination and take the same route. A starts at 8 a.m. and drives at a speed of 40 kmph. B starts at 9 a.m. and drives at a speed of 50 kmph. If the destination is 350 km away from the starting point, then how far will A be from the destination when B reaches there?

  • Option : B
  • Explanation : Time taken by B to reach destination = 350/50 = 7 hours
    If A has a head start of 1 hour then the distance travelled by A when B reaches the destination
    = 40 × (7 + 1) = 320 km
    Hence, A has to still travel 30 km while B has reached the destination.
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8. A train runs for 2 hours at a speed of 35 kmph. It runs for 3 1/2 hours at the speed of 60 kmph and then runs for 2 1/2 hours at the speed of 70 kmph. Find the average speed of the train.

  • Option : D
  • Explanation : Distance travelled in 2 hours = 35 × 2 = 70 km
    Distance travelled in next 3 1/2 hours = 60 × 3.5 = 210 km
    Distance travelled in next 2 1/2 hours = 70 × 2.5 = 175 km
    Total distance = 70 + 210 + 175 = 455 km
    Average speed = Total distance/Total time taken = (70 + 210 + 175)/(2 + 3.5 + 2.5) = 455/8 = 56.87 kmph
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9. The average age of a husband and wife was 22 years when they were married five years back. What is the present average age of the family if they have a three- year-old child?

  • Option : A
  • Explanation : The present total age of husband and wife = 2 × (22 + 5) = 54 years
    Total age of family (including child) = 54 + 3 = 57 years
    Average age of family = 57/3 = 19 years
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10. A man’s monthly income is Rs 1400. What should be his average monthly expenditure so that he is able to save 3600 in a year?

  • Option : B
  • Explanation : Monthly saving = 3600/12 = Rs 300
    Hence, monthly expenditure = income − saving = 1400 – 300 = Rs 1100
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