NCERT Solutions Class 8 Maths Chapter 7 — Direct & Inverse Proportions

Solution:

Step 1: Step 1: Understand direct proportion. Two quantities are directly proportional if an increase in one leads to a proportional increase in the other, and a decrease in one leads to a proportional decrease in the other.

Step 2: Step 2: The defining characteristic of direct proportion is that their ratio (x/y) is always constant. This constant is called the constant of proportionality. [x/y = k (where k is the constant of proportionality)]

Solution:

Step 1: Step 1: Analyze each option. A) As speed increases, time decreases (Inverse). B) As workers increase, time decreases (Inverse). C) As the amount of petrol increases, the distance covered increases proportionally (Direct). D) This relationship is not necessarily proportional in a simple direct or inverse way; discount per article might stay constant or change in a complex way.

Step 2: Step 2: Identify the scenario where an increase in one quantity leads to a proportional increase in the other.

Solution:

Step 1: Step 1: Let the number of notebooks be N and the cost be C. Since they are directly proportional, the ratio N/C remains constant. [N1/C1 = N2/C2]

Step 2: Step 2: Given N1 = 5, C1 = ₹125, N2 = 8. We need to find C2.

Step 3: Step 3: Substitute the values: 5/125 = 8/C2.

Step 4: Step 4: Solve for C2: 5 × C2 = 8 × 125 => C2 = (8 × 125) / 5 = 8 × 25 = ₹200.

Solution:

Step 1: Step 1: Identify the relationship: x and y are directly proportional.

Step 2: Step 2: Recall the formula for direct proportion: x1/y1 = x2/y2.

Step 3: Step 3: Recall the formula for inverse proportion: x1y1 = x2y2. Rohan used the inverse proportion formula.

Step 4: Step 4: Therefore, Rohan incorrectly assumed the relationship was inverse proportion instead of direct proportion. The correct setup for direct proportion would be 4/10 = 12/y.

Solution:

Step 1: Step 1: Understand inverse proportion. Two quantities are inversely proportional if an increase in one leads to a proportional decrease in the other, and vice versa.

Step 2: Step 2: The defining characteristic of inverse proportion is that their product (P × Q) is always constant. This constant is called the constant of proportionality. [P × Q = k (where k is the constant of proportionality)]