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ICSE-VIII-Mathematics

10: Direct and Inverse Variations Class 8 Maths

with Solutions - page 2

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  • #10-i
    How far will it travel in 36 minutes?
    Ans : Speed of train in 60 minutes = 120 km
    i.e., distance covered in 60 minutes = 120/60
    Distance covered in 36 minutes = (120 × 36)/60
    = 2 × 36
    = 73 km
  • #10-ii
    In how much time will it cover 210 km?
    Ans : If distance covered is 120 km then time taken = 60 minutes
    If distance covered is 1 km them time taken = 60/120
    If distance covered is 210 km then time taken = 60/120 × 210
    = 105 minutes
    = 1 hour 45 minutes.
  • #
    Section : B
  • Qstn #1
    Check whether x and y vary inversely or not.
    Ans : x and y are inversely proportional.
    Then xy are equal.
  • #1-i
    Ans : xy = 4 × 6 = 24
    xy = 3 × 8 = 24
    xy = 12 × 2 = 24
    xy = 1 × 24 = 24
    xy in each case is equal.
    x and y are inversely proportional
  • #1-ii
    Ans : xy = 30 × 60 = 1800
    xy= 120 × 30 = 3600
    xy = 60 × 30= 1800
    xy = 24 × 75 = 1800
    xy in each case is not equal.
    x and y are not inversely proportional.
  • #1-iii
    Ans : xy = 10 × 90 = 900
    = 30 × 30 = 900
    = 60 × 20 = 1200
    = 10 × 90 = 900
    xy in each case is not equal.
    x and y are not inversely proportional.
  • Qstn #2
    If x and y vary inversely, find the values of l, m and n :
    Ans : ∵ x and y are inversely proportional
    ∴ xy is equal.
  • #2-i
    Ans : xy = 4 × 4 = 16
    8 × l = 16 ⇒ l = 16/8 = 2
    2 × m = 16 ⇒ m = 16/2 = 8
    32 × n = 16 ⇒ n = 16/32 = 0.5
  • #2-ii
    Ans : xy = 32 × 12 = 384
    24 × l = 384 ⇒ l = 384/24 = 16
    m × 8 = 384 ⇒ m = 384/8 = 48
    16 × n = 384 ⇒ n = 384/16 = 24
  • Qstn #3
    36 men can do a piece of work in 7 days. How many men will do the same work in 42 days?
    Ans : Men : Days : : Men : Days
    36 : 7 : : x : 42
    ∴ By inverse proportional
    36 × 6 = x × 42
    ⇒ x = (36 × 7)/42 = 6 men
  • Qstn #4
    12 pipes, all of the same size, fill a tank in 42 minutes. How long will it take to fill the same tank, if 21 pipes of the same size are used?
    Ans : Pipes : Time :: Pipes : Time
    12 : 2x :: 21 : 42
    ∴ By inverse proportional
    12 × 42 = 21 × x
    ⇒ x = (12 × 42)/21
    = 24 minutes
  • Qstn #5
    In a fort 150 men had provisions for 45 days. After 10 days, 25 men left the fort. How long would the food last at the same rate?
    Ans : After 10 days:
    For 150 men, provision will last (45 - 10)
    Days = 35days
    ⇒ For 1 man, the provisions will last = 150 × 35 days
    And for (150 - 25) = 125 men, the provisions will last for = (150 × 35)/125
    = 42 days
  • Qstn #6
    72 men do a piece of work in 25 days. In how many days will 30 men do the same work?
    Ans : Men : Days : : Men : Days
    72 : 25 : : 30 : x
    ∴ By inverse proportion
    72 × 25 = 30 × x
    ⇒ x = (25 × 72)/30
    = 60 days
  • Qstn #7
    If 56 workers can build a wall in 180 hours, how many workers will be required to do the same work in 70 hours?
    Ans : Workers : Hours : : Workers : Hours
    56 : 180 : : x : 70
    ∴ By inverse proportion
    56 × 180 = x × 70
    ⇒ x = (180 × 56)/70
    = 144 workers
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