Practice Set 7.1 8th Std Maths Answers Chapter 7 Variation
Question 2
Maharashtra Board Solution
Complete the following table considering that the cost of apples and their number are in direct variation.
Solution & Step-by-Step Answer:
The cost of apples (y) and their number (x) are in direct variation.
∴y ∝ x ∴y = kx …(i) where k is the constant of variation i. When, x = 1, y = 8 ii. When,y = 56, x = ? iii. When, x = 12, y = ? iv. When, y = 160, x = ?
Question 3
Maharashtra Board Solution
If m ∝ n and when m = 154, n = 7. Find the value of m, when n = 14.
Solution & Step-by-Step Answer:
Given that, m ∝ n ∴ m = kn …(i) where k is constant of variation. When m = 154, n = 7 ∴ Substituting m = 154 and n = 7 in (i), we get m = kn ∴ 154 = k × 7 ∴ ∴ k = 22 Substituting k = 22 in (i), we get m = kn ∴ m = 22n …(ii) This is the equation of variation. When n = 14, m = ? ∴ Substituting n = 14 in (ii), we get m = 22n ∴ m = 22 × 14 ∴ m = 308
Question 4
Maharashtra Board Solution
If n varies directly as m, complete the following table. |
m | 3 | 5 | 6.5 | __ | 1.25 |
n | 12 | 20 | __ | 28 | __ |
Given, n varies directly as m
∴ n ∝ m
∴ n = km …(i)
where, k is the constant of variation
i. When m = 3, n = 12
∴ Substituting m = 3 and n = 12 in (i), we get
n = km
∴ 12 = k × 3
∴
∴ k = 4
Substituting, k = 4 in (i), we get
n = km
∴ n = 4m …(ii)
This is the equation of variation.
ii. When m = 6.5, n = ?
∴ Substituting, m = 6.5 in (ii), we get
n = 4m
∴ n = 4 × 6.5
∴ n = 26
iii. When n = 28, m = ?
∴ Substituting, n = 28 in (ii), we get
n = 4m
∴ 28 = 4m
∴ 28 = 4m
∴
∴ m = 7
iv. When m = 1.25, n = ?
∴ Substituting m = 1.25 in (ii), we get
n = 4m
∴ n = 4 × 1.25
∴ n = 5
m | 3 | 5 | 6.5 | 7 | 1.25 |
n | 12 | 20 | 26 | 28 | 5
Question 5
Maharashtra Board Solution
y varies directly as square root of x. When x = 16, y = 24. Find the constant of variation and equation of variation.
Solution & Step-by-Step Answer:
Given, y varies directly as square root of x. ∴ y ∝ √4x ∴ y = k √x …(i) where, k is the constant of variation. When x = 16,y = 24. ∴ Substituting, x = 16 and y = 24 in (i), we get y = k√x ∴24 = k√16 ∴24 = 4k ∴ ∴ k = 6 Substituting k = 6 in (i), we get y = k√x ∴ y = 6√x This is the equation of variation ∴ The constant of variation is 6 and the equation of variation is y = 6√x.
Question 6
Maharashtra Board Solution
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 & Step-by-Step Answer:
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. ∴ m ∝ n ∴ m = kn …(i) where, k = constant of variation Remuneration of 4 laborers is Rs 1000. i. e., when n = 4, m = Rs 1000 ∴ Substituting, n = 4 and m = 1000 in (i), we get m = kn ∴ 1000 = k × 4 ∴ ∴ k = 250 Substituting, k = 250 in (i), we get m = kn ∴ m = 250 n …(ii) This is the equation of variation Now, we have to find remuneration of 17 laborers. i. e., when n = 17, m = ? ∴ Substituting n = 17 in (ii), we get m = 250 n ∴ m = 250 × 17 ∴ m = 4250 ∴ The remuneration of 17 laborers is Rs 4250.
Maharashtra Board Class 8 Maths Chapter 7 Variation Practice Set 7.1 Intext Questions and Activities
Question 1
Maharashtra Board Solution
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) |
Number of notebooks (x) | 12 | 3 | 9 | 24 | 50 | 1 |
Cost (In Rupees) (y) | 240 | __ | __ | __ | __ | 20 |
As the number of notebooks increases their cost also increases.
∴ Number of notebooks and cost of notebooks are in direct proportion.
i.
∴ y = 3 × 20
∴ y = 60
ii.
∴ y = 9 × 20
∴ y = 180
iii.
∴ y = 24 × 20
∴ y = 480
iv.
∴ y = 50 × 20
∴ y = 1000
Number of notebooks (x) | 12 | 3 | 9 | 24 | 50 | 1 |
Cost (In Rupees) (y) | 240 | 60 | 180 | 480 | 1000 | 20 |