Practice Set 7.2 8th Std Maths Answers Chapter 7 Variation
Number of workers | 30 | 20 | __ | 10 | __ |
Days | 6 | 9 | 12 | 36 |
Let, n represent the number of workers and d represent the number of days required to complete a work.
Since, number of workers and number of days to complete a work are in inverse poportion.
∴
∴
where k is the constant of variation.
∴ n × d = k …(i)
i. When n = 30, d = 6
∴ Substituting n = 30 and d = 6 in (i), we get
n × d = k
∴ 30 × 6 = k
∴ k = 180
Substituting k = 180 in (i), we get
∴ n × d = k
∴ n × d = 180 …(ii)
This is the equation of variation
ii. When d = 12, n = 7
∴ Substituting d = 12 in (ii), we get
n × d = 180
∴ n × 12 = 180
∴ n =
∴ n = 15
iii. When n = 10, d = ?
∴ Substituting n = 10 in (ii), we get
n × d = 180
10 × d = 180
∴ d =
∴ d = 18
iv. When d = 36, n = ?
∴ Substituting d = 36 in (ii), we get
n × d = 180
∴ n × 36 = 180
∴ n =
∴ n = 5
Number of workers | 30 | 20 | 15 | 10 | 5 |
Days | 6 | 9 | 12 | 18 | 36
Question 2
Maharashtra Board Solution
Find constant of variation and write equation of variation for every example given below: i. ; if p = 15 then q = 4. ii. ; when z = 2.5 then w = 24. iii. ; if s = 4 then t = 5. iv. ; if x = 15 then y = 9.
Solution & Step-by-Step Answer:
i. …[Given] ∴ p = k × where, k is the constant of variation. ∴ p × q = k …(i) When p = 15, q = 4 ∴ Substituting p = 15 and q = 4 in (i), we get p × q = k ∴ 15 × 4 = k ∴ k = 60 Substituting k = 60 in (i), we get p × q = k ∴ p × q = 60 This is the equation of variation. ∴ The constant of variation is 60 and the equation of variation is pq = 60.
ii. …[Given] iii. …[Given] iv. …[Given]
Question 3
Maharashtra Board Solution
The boxes are to be filled with apples in a heap. If 24 apples are put in a box then 27 boxes are needed. If 36 apples are filled in a box how many boxes will be needed?
Solution & Step-by-Step Answer:
Let x represent the number of apples in each box and y represent the total number of boxes required. The number of apples in each box are varying inversely with the total number of boxes. ∴ ∴ where, k is the constant of variation, ∴ x × y = k …(i) If 24 apples are put in a box then 27 boxes are needed. i.e., when x = 24, y = 27 ∴ Substituting x = 24 and y = 27 in (i), we get x × y = k ∴ 24 × 27 = k ∴ k = 648 Substituting k = 648 in (i), we get x × y = k ∴ x × y = 648 …(ii) This is the equation of variation. Now, we have to find number of boxes needed when, 36 apples are filled in each box. i.e., when x = 36,y = ? ∴ Substituting x = 36 in (ii), we get x × y = 648 ∴ 36 × y = 648 ∴ y = ∴ y = 18 ∴ If 36 apples are filled in a box then 18 boxes are required.
Question 4
Maharashtra Board Solution
Write the following statements using symbol of variation. |
Question 5. and when x = 40 then y = 16. If x = 10, find y. Solution: ∴ where, k is the constant of variation. ∴ x × √y = k …(i) When x = 40, y = 16 ∴ Substituting x = 40 andy = 16 in (i), we get x × √y = k ∴ 40 × √16 = k ∴ k = 40 × 4 ∴ k = 160 Substituting k = 160 in (i), we get x × √y = k ∴ x × √y = 160 …(ii) This is the equation of variation. When x = 10,y = ? ∴ Substituting, x = 10 in (ii), we get x × √y = 160 ∴ 10 × √y = 160 ∴ √y = ∴ √y = 16 ∴ y = 256 … [Squaring both sides]
Question 6
Maharashtra Board Solution
x varies inversely as y, when x = 15 then y = 10, if x = 20, then y = ?
Solution & Step-by-Step Answer:
Given that, ∴ where, k is the constant of variation. ∴ x × y = k …(i) When x = 15, y = 10 ∴ Substituting, x = 15 and y = 10 in (i), we get x × y = k ∴ 15 × 10 = k ∴ k = 150 Substituting, k = 150 in (i), we get x × y = k ∴ x × y = 150 …(ii) This is the equation of variation. When x = 20, y = ? ∴ substituting x = 20 in (ii), we get x × y = 150 ∴ 20 × y = 150 ∴ y = ∴ y = 7.5
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