Mathematical Aptitude - Averages

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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