{"id":585387,"date":"2022-03-16T06:50:17","date_gmt":"2022-03-16T06:50:17","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=585387"},"modified":"2022-03-17T05:31:18","modified_gmt":"2022-03-17T05:31:18","slug":"maharashtra-board-solutions-class-8-maths-practice-set-7-1-chapter-7-variation","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/maharashtra-board-solutions-class-8-maths-practice-set-7-1-chapter-7-variation\/","title":{"rendered":"Maharashtra Board Solutions Class 8-Maths (Practice Set 7.1): Chapter 7- Variation"},"content":{"rendered":"\n

Class 8: Maths Chapter 7 solutions. Complete Class 8 Maths Chapter 7 Notes.<\/p>\n\n\n\n

Maharashtra Board Solutions Class 8-Maths (Practice Set 7.1): Chapter 7- Variation<\/h2>\n\n\n\n

Maharashtra Board 8th Maths Chapter 7, Class 8 Maths Chapter 7 solutions<\/p>\n\n\n\n

Question 1.
Write the following statements using the symbol of variation.<\/strong><\/p>\n\n\n\n

  1. Circumference (c) of a circle is directly proportional to its radius (r).<\/li>
  2. Consumption of petrol (l) in a car and distance traveled by that car (d) are in direct variation.<\/li><\/ol>\n\n\n\n

    Solution:<\/strong><\/p>\n\n\n\n

    1. c \u221d r<\/li>
    2. l \u221d d<\/li><\/ol>\n\n\n\n

      Question 2.
      Complete the following table considering that the cost of apples and their number are in direct variation.<\/strong><\/p>\n\n\n\n

      Number of apples (x)<\/strong><\/td>1<\/td>4<\/td>__<\/td>12<\/td>__<\/td><\/tr>
      Cost of apples (y)<\/strong><\/td>8<\/td>32<\/td>56<\/td>__<\/td>160<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

      Solution:
      <\/strong>The cost of apples (y) and their number (x) are in direct variation.
      \u2234y \u221d x
      \u2234y = kx \u2026(i)
      where k is the constant of variation<\/p>\n\n\n\n

      i. When, x = 1, y = 8
      \u2234 Substituting, x = 1 and y = 8 in (i), we get y = kx
      \u2234 8 = k \u00d7 1
      \u2234 k = 8
      Substituting k = 8 in (i), we get
      y = kx
      \u2234 y = 8x \u2026(ii)
      This the equation of variation<\/p>\n\n\n\n

      ii. When,y = 56, x = ?
      \u2234 Substituting y = 56 in (ii), we get
      y = 8x
      \u2234 56 = 8x
      \u2234 x = \\frac { 56 }{ 8 }
      \u2234 x = 7<\/p>\n\n\n\n

      iii. When, x = 12, y = ?
      \u2234 Substituting x = 12 in (ii), we get
      y = 8x
      \u2234 y = 8 \u00d7 12
      \u2234 y = 96<\/p>\n\n\n\n

      iv. When, y = 160, x = ?
      \u2234 Substituting y = 160 in (ii), we get
      y = 8x
      \u2234 160 = 8x
      \u2234 x = \\frac { 160 }{ 8 }
      \u2234 x = 20<\/p>\n\n\n\n

      Number of apples (x)<\/strong><\/td>1<\/td>4<\/td>7<\/td>12<\/td>20<\/td><\/tr>
      Cost of apples (y)<\/strong><\/td>8<\/td>32<\/td>56<\/td>96<\/td>160<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

      Question 3.
      If m \u221d n and when m = 154, n = 7. Find the value of m, when n = 14.
      Solution:<\/strong>
      Given that,
      m \u221d n
      \u2234 m = kn \u2026(i)
      where k is constant of variation.
      When m = 154, n = 7
      \u2234 Substituting m = 154 and n = 7 in (i), we get
      m = kn
      \u2234 154 = k \u00d7 7
      \u2234 k=\\frac { 154 }{ 7 }
      \u2234 k = 22
      Substituting k = 22 in (i), we get
      m = kn
      \u2234 m = 22n \u2026(ii)
      This is the equation of variation.
      When n = 14, m = ?
      \u2234 Substituting n = 14 in (ii), we get
      m = 22n
      \u2234 m = 22 \u00d7 14
      \u2234 m = 308<\/p>\n\n\n\n

      Question 4.
      If n varies directly as m, complete the following table.<\/strong><\/p>\n\n\n\n

      m<\/strong><\/td>3<\/td>5<\/td>6.5<\/td>__<\/td>1.25<\/td><\/tr>
      n<\/strong><\/td>12<\/td>20<\/td>__<\/td>28<\/td>__<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

      Solution:
      <\/strong>Given, n varies directly as m
      \u2234 n \u221d m
      \u2234 n = km \u2026(i)
      where, k is the constant of variation<\/p>\n\n\n\n

      i. When m = 3, n = 12
      \u2234 Substituting m = 3 and n = 12 in (i), we get
      n = km
      \u2234 12 = k \u00d7 3
      \u2234 k=\\frac { 12 }{ 3 }
      \u2234 k = 4
      Substituting, k = 4 in (i), we get
      n = km
      \u2234 n = 4m \u2026(ii)
      This is the equation of variation.<\/p>\n\n\n\n

      ii. When m = 6.5, n = ?
      \u2234 Substituting, m = 6.5 in (ii), we get
      n = 4m
      \u2234 n = 4 \u00d7 6.5
      \u2234 n = 26<\/p>\n\n\n\n

      iii. When n = 28, m = ?
      \u2234 Substituting, n = 28 in (ii), we get
      n = 4m
      \u2234 28 = 4m
      \u2234 28 = 4m
      \u2234 m=\\frac { 28 }{ 4 }
      \u2234 m = 7<\/p>\n\n\n\n

      iv. When m = 1.25, n = ?
      \u2234 Substituting m = 1.25 in (ii), we get
      n = 4m
      \u2234 n = 4 \u00d7 1.25
      \u2234 n = 5<\/p>\n\n\n\n

      m<\/strong><\/td>3<\/td>5<\/td>6.5<\/td>7<\/td>1.25<\/td><\/tr>
      n<\/strong><\/td>12<\/td>20<\/td>26<\/td>28<\/td>5<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

      Question 5.
      y varies directly as square root of x. When x = 16, y = 24. Find the constant of variation and equation of variation.
      Solution:<\/strong>
      Given, y varies directly as square root of x.
      \u2234 y \u221d \u221a4x
      \u2234 y = k \u221ax \u2026(i)
      where, k is the constant of variation.
      When x = 16 ,y = 24.
      \u2234 Substituting, x = 16 and y = 24 in (i), we get
      y = k\u221ax
      \u223424 = k\u221a16
      \u223424 = 4k
      \u2234 k=\\frac { 24 }{ 4 }
      \u2234 k = 6
      Substituting k = 6 in (i), we get
      y = k\u221ax
      \u2234 y = 6\u221ax
      This is the equation of variation
      \u2234 The constant of variation is 6 and the equation of variation is y = 6\u221ax .<\/p>\n\n\n\n

      Question 6.
      The total remuneration paid to laborers, employed to harvest soybean is in direct variation with the number of laborers. If remuneration of 4 laborers is Rs 1000, find the remuneration of 17 laborers.
      Solution:<\/strong>
      Let, m represent total remuneration paid to laborers and n represent number of laborers employed to harvest soybean.
      Since, the total remuneration paid to laborers, is in direct variation with the number of laborers.
      \u2234 m \u221d n
      \u2234 m = kn \u2026(i)
      where, k = constant of variation
      Remuneration of 4 laborers is Rs 1000.
      i. e., when n = 4, m = Rs 1000
      \u2234 Substituting, n = 4 and m = 1000 in (i), we get m = kn
      \u2234 1000 = k \u00d7 4
      \u2234 k=\\frac { 1000 }{ 4 }
      \u2234 k = 250
      Substituting, k = 250 in (i), we get
      m = kn
      \u2234 m = 250 n \u2026(ii)
      This is the equation of variation
      Now, we have to find remuneration of 17 laborers.
      i. e., when n = 17, m = ?
      \u2234 Substituting n = 17 in (ii), we get
      m = 250 n
      \u2234 m = 250 \u00d7 17
      \u2234 m = 4250
      \u2234 The remuneration of 17 laborers is Rs 4250.<\/p>\n\n\n\n

      Intext Questions and Activities<\/strong><\/p>\n\n\n\n

      Question 1.
      If the rate of notebooks is Rs 240 per dozen, what is the cost of 3 notebooks?
      Also find the cost of 9 notebooks, 24 notebooks and 50 notebooks and complete the following table. (Textbook pg. no. 35)<\/strong><\/p>\n\n\n\n

      Number of notebooks (x)<\/strong><\/td>12<\/td>3<\/td>9<\/td>24<\/td>50<\/td>1<\/td><\/tr>
      Cost (In Rupees) (y)<\/strong><\/td>240<\/td>__<\/td>__<\/td>__<\/td>__<\/td>20<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

      Solution:
      <\/strong>As the number of notebooks increases their cost also increases.
      \u2234 Number of notebooks and cost of notebooks are in direct proportion.<\/p>\n\n\n\n

      i.
      \"Maharashtra
      \u2234 y = 3 \u00d7 20
      \u2234 y = 60<\/p>\n\n\n\n

      ii.
      \"Maharashtra
      \u2234 y = 9 \u00d7 20
      \u2234 y = 180<\/p>\n\n\n\n

      iii.
      \"Maharashtra
      \u2234 y = 24 \u00d7 20
      \u2234 y = 480<\/p>\n\n\n\n

      iv.
      \"Maharashtra
      \u2234 y = 50 \u00d7 20
      \u2234 y = 1000<\/p>\n\n\n\n

      Number of notebooks (x)<\/strong><\/td>12<\/td>3<\/td>9<\/td>24<\/td>50<\/td>1<\/td><\/tr>
      Cost (In Rupees) (y)<\/strong><\/td>240<\/td>60<\/td>180<\/td>480<\/td>1000<\/td>20<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

      Download PDF<\/strong><\/h2>\n\n\n\n

      Maharashtra Board Solutions Class 8-Maths (Practice Set 7.1): Chapter 7- Variation<\/p>\n\n\n\n

      Download PDF<\/strong>: Maharashtra Board Solutions Class 8-Maths (Practice Set 7.1): Chapter 7- Variation PDF<\/a><\/p>\n\n\n\n

      Chapterwise Maharashtra Board Solutions Class 8 Maths :<\/strong><\/h2>\n\n\n\n