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    Question

    Read the following data carefully and answer the questions: The table given below shows the total number of pencils, ratio of number of pencils to the number of pens used by the children of four different schools (A, B, C and D). The line graph shows the difference between these stationary items (pencils and pens) used by the children. Note: (i) Not more than one stationary item is used by one child. (ii) Not all the children of the schools used the stationary items. (iii) Pencils used by the child of each school are more than the pens used by them.

    In school D, total number of children who didn’t used any of the stationary items are 115 and the ratio of girls who used the stationary items to that who didn’t used any of the items are 4:7 respectively. If 40 boys used both the items, then find the number of boys who didn’t use any of the items.

    A 10 Correct Answer Incorrect Answer
    B 14 Correct Answer Incorrect Answer
    C 12 Correct Answer Incorrect Answer
    D 18 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    In school A, Let total number of pencils and pens used be px and qx respectively. According to the question, => px – qx = 40 => 120 – qx = 40 => qx = 80 Ratio = px : qx = 120 : 80 = 3:2 Total number of pencils used = px = 120 Total number of pens used = qx = 80 In school B, Let total number of pencils and pens used be 3x and 2x respectively. According to the question, => 3x – 2x = 90 => x = 90 So, 3x = 270 and 2x = 180 Now, (m2 + 45) = 270 => m2 = 225 => m = 15 Total number of pencils used = 3x = 270 Total number of pens used = 2x = 180 In school C, Let total number of pencils and pens used be gx and hx respectively. According to the question, => gx = 8m – 70 => gx = (8 × 15) – 70 => gx = 50 So, hx = 50 – 20 = 30 Ratio = gx : hx = 50 : 30 = 5:3 Total number of pencils used = gx = 50 Total number of pens used = hx = 30 In school D, Let total number of pencils and pens used be tx and x respectively. According to the question, => tx = 75 So, tx – x = 50 => 75 - x = 50 => x = 25 Ratio = tx : x = 75 : 25 = 3:1 Total number of pencils used = tx = 75 Total number of pens used = x = 25 Total number of children who used both items = 75 + 25 = 100 Girls who used the both the items = 100 – 40 = 60 Girls who didn’t used any of the items = (7/4) × 60 = 105 Number of boys who didn’t use any of the items = 115 – 105 = 10

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