Are you looking for complete, step-by-step verified solutions for DAV Class 8 Maths Chapter 13 Enrichment Questions (Introduction to Graphs)? At NCERTBooksPDF, we provide complete, graph-verified solutions covering Cartesian coordinates, linear relations, Simple Interest graphs, and Distance-Time motion analysis.
Key Principles of Coordinate Graphs & Linear Relations
| Graph Type | Independent Variable (X-axis) | Dependent Variable (Y-axis) | Mathematical Relation |
|---|---|---|---|
| Simple Interest Graph | Principal Deposit (Rs P) | Annual Interest (Rs I) | I = (P × R × T) / 100 (Passes through origin) |
| Distance – Time Graph | Time elapsed (hours) | Distance travelled (km) | Slope of line = Speed (v = d / t) |
Chapter 13 Enrichment Questions: Complete Solutions
Question 1: Simple Interest vs Principal Linear Graph
Problem: A bank offers 10% Simple Interest per annum on fixed deposits. Draw a linear graph showing the relation between the amount deposited (Principal) and the annual interest earned. Use the graph to find:
(a) The annual interest earned on an investment of Rs 250.
(b) The amount one must deposit to earn an annual interest of Rs 70.
Solution:
Given: Rate of interest R = 10% p.a., Time T = 1 year.
Simple Interest formula: I = (P × R × T) / 100 = (P × 10 × 1) / 100 = P / 10.
| Deposit (Principal Rs P) on X-axis | 100 | 200 | 300 | 500 | 1000 |
|---|---|---|---|---|---|
| Annual Interest (Rs I) on Y-axis | 10 | 20 | 30 | 50 | 100 |
Plot the points (100, 10), (200, 20), (300, 30), (500, 50) and join them with a straight line starting from the origin (0, 0).
(a) Finding annual interest on deposit of Rs 250:
Locate x = 250 on the horizontal axis. Move vertically to meet the graph line, and read the corresponding value on the Y-axis:
y = 250 / 10 = Rs 25.
(b) Finding deposit needed to earn Rs 70 interest:
Locate y = 70 on the vertical axis. Move horizontally to intersect the graph line, and read down to the X-axis:
x = 70 × 10 = Rs 700.
Question 2: Distance – Time Uniform Speed Graph
Problem: An express bus travels along a national highway at a constant uniform speed of 60 km/h.
(a) Prepare a table for time and distance, and plot the distance-time graph.
(b) How far does the bus travel in 2.5 hours?
(c) How much time does it take to cover a distance of 210 km?
Solution:
Distance d = Speed × Time = 60 × t.
| Time (t in hours) | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Distance (d in km) | 60 | 120 | 180 | 240 |
(b) Distance covered in 2.5 hours:
From graph (or relation): d = 60 × 2.5 = 150 km.
(c) Time taken to cover 210 km:
t = Distance / Speed = 210 / 60 = 3.5 hours (3 hours 30 minutes).
Question 3: Collinear Points in Cartesian Plane
Problem: Plot the points A(1, 1), B(2, 3), and C(3, 5) on a graph sheet. Check whether they lie on a straight line.
Solution:
To determine if three points lie on the same line, compare the slope between pairs of points:
• Slope of AB = (y2 – y1) / (x2 – x1) = (3 – 1) / (2 – 1) = 2 / 1 = 2.
• Slope of BC = (y3 – y2) / (x3 – x2) = (5 – 3) / (3 – 2) = 2 / 1 = 2.
Since Slope(AB) = Slope(BC) and point B is common to both segments, the points A, B, and C lie on the exact same straight line (they are collinear).
Equation of the line: y = 2x – 1.
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