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ICSE-VIII-Mathematics

10: Direct and Inverse Variations Class 8 Maths

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  • #1
    In which of the following tables, x and y vary directly: (i) (ii) (iii) (i) (ii) (iii)
    Ans : (i) 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. (ii) 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. (iii) 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. (i) 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. (ii) 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. (iii) 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.
  • #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.