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ICSE-VIII-Mathematics

10: Direct and Inverse Variations Class 8 Maths

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    Section : A
  • Qstn #1
    In which of the following tables, x and y vary directly:
  • #1-i
    Ans : x1/y1 = 3/4.5 = 1/1.5
    x2/y2 = 5/7.5 = 1/1.5
    x3/y3 = 8/12 = 1/1.5
    x4/y4 = 11/16.5 = 1/1.5
    ⇒ x1/y1 = x2/y2 = x3/y3 = x4/y4
    Yes, x and y vary directly.
  • #1-ii
    Ans : x1/y1 = 16/32 = ½
    x2/y2 = 30/60 = ½
    x3/y3 = 40/80 = ½
    x4/y4 = 56/84 =28/42 = 14/21 = 7/3
    ⇒ x1/y1 = x2/y2 = x3/y3 = x4/y4
    x and y are not in direct variation.
  • #1-iii
    Ans : x1/y1 = 27/81 = 3/9 = 1/3
    x2/y2 = 45/150 = 15/50 = 3/10
    x3/y3 = 54/216 = 18/72 = ¼
    x4/y4 = 75/225 = 25/45 = 5/9
    ⇒ x1/y1 ≠ x2/y2 ≠ x3/y3 ≠ x4/y4
    x and y are not in direct variation.
  • Qstn #2
    If x and y vary directly, find the values of x, y and z:
    Ans : x and y are in direct variation
    ∴ 3/36 = x/60 = y/96 = 10/z
    ⇒ 3/36 = x/60, 3/36 = y/96, 3/36 = 10/z
    x = 3/36 × 60, y = 3/36 × 96
    z = 10 × 36/3
    ⇒ x = 5, y = 8, z = 120
  • Qstn #3
    A truck consumes 28 litres of diesel for moving through a distance of 448 km. How much distance will it cover in 64 litres of diesel?
    Ans : Let the truck cover x km in 64 litres of diesel.

    It is the case of direct variation
    ⇒ x1/y1 = x2/y2 = 28/448 = 64/x
    i.e., 28x = 64 × 448
    ⇒ x = (64 × 448)/28
    ⇒ x = 1024 km
  • Qstn #4
    For 100 km, a taxi charges ₹ 1,800. How much will it charge for a journey of 120 km?
    Ans : Let a charges of car is ₹ x in 120 km

    Since it is the case of direct variation
    ⇒ x1/y1 = x2/y2
    ⇒ 1800/100 × x/100
    ⇒ 100x = 1800 × 120
    ⇒ x = (1800 × 120)/100
    ⇒ x = ₹2160
  • Qstn #5
    If 27 identical articles cost ₹ 1,890, how many articles can be bought for ₹ 1,750?
    Ans : Let x number of articles be purchased in ₹1750

    Since, it is a case of direct variation
    ⇒ 1890/27 = 1750/x
    ⇒ x = (1750 × 27)/1890
    ⇒ x = 25 articles
  • Qstn #6
    7 kg of rice costs ₹ 1,120. How much rice can be bought for ₹ 3,680?
    Ans : Rice : Cost :: Rice : Cost
    7 kg : ₹1120 : : x kg : ₹3680
    ∴ x = (7 x 3680)/1120
    ⇒ x = 23 kg
  • Qstn #7
    6 note-books cost ₹ 156, find the cost of 54 such note-books.
    Ans : Notebooks : Cost :: Notebooks : Cost
    6 : ₹156 :: 54 : ₹x
    ∴ x = (156 × 54)/6
    ⇒ x = ₹ 1404
  • Qstn #8
    22 men can dig a 27 m long trench in one day. How many men should be employed for digging 135 m long trench of the same type in one day?
    Ans : Men : Length trench :: Men : Length of trench
    22 : 27m :: x : 135 m
    x = (22 × 135)/27
    ⇒ x = 110 men
  • Qstn #9
    If the total weight of 11 identical articles is 77 kg, how many articles of the same type would weigh 224 kg?
    Ans : No. of : Weight :: No. of articles : Weight articles
    11 : 77kg :: x : 224 kg
    x = (11 × 224)/77
    ⇒ x = 32 articles
  • Qstn #10
    A train is moving with uniform speed of 120 km per hour.
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