Direct and Inverse Proportions
An increase (↑) in one quantity brings about an increase (↑) in the other quantity and similarly a decrease (↓) in one quantity brings about a decrease (↓) in the other quantity, the these two quantities are in
direct proportion or
direct variation.
In direct proportion the ratio of two quantities (say x and y) is a constant called constant of proportionality.
⇒ y/x = k or y = k × x
NCERT Chapter Solutions and other Q & A
NCERT Ex. 13.1
Q1: Following are the car parking charges near a railway station upto
4 hours Rs 60
8 hours Rs 100
12 hours Rs 140
24 hours Rs 180
Check if the parking charges are in direct proportion to the parking time
Answer: Calculating the ratio of parking charging wrt parting time:
No. of Hours (a) | Parking Charges(B) | Ratio (B/A) |
4 | 60 | 60/4 = 15:1 |
8 | 100 | 100/8 =25:2 |
12 | 140 | 140/12 =35:3 |
24 | 180 | 180/24=15:2 |
Since the ratio of various parking charging vs parking time is not the same, the parking charges are NOT in direct proportion to the parking time.
Q2: A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of base.
In the following table, find the parts of base that need to be added.
Parts of red pigment | 1 | 4 | 7 | 12 | 20 |
Parts of base | 8 | ... | ... | ... | ... |