If 'a' is inversely proportional to 'b' and 'b' inversely proportional to 'c', then
'a' is directly proportional to 'c'
To solve this question, we need to understand the relationship between the variables a, b, and c based on their proportionality.
- We are given that a is inversely proportional to b. This can be mathematically expressed as:
\(a = \frac{k}{b}\), where \(k\) is a constant.
- We are also given that b is inversely proportional to c. This means:
\(b = \frac{m}{c}\), where \(m\) is another constant.
- Let's substitute the equation for b in the equation for a:
\(a = \frac{k}{b} = \frac{k}{\frac{m}{c}} = \frac{k \cdot c}{m}\)
- From this expression, we see that a is directly proportional to c, as a can be expressed as a constant times c:
\(a = \left(\frac{k}{m}\right) c\)
- Thus, the correct statement is that a is directly proportional to c. This matches with the given correct answer option.
Hence, the correct option is: 'a' is directly proportional to 'c'.
Important Questions from Direct or Indirect Proportion
If 3A = 4B = 5C, then A : B : C is equal to:
The monthly incomes of A and B are in the ration 3 : 5 and the ratio of their savings is 2 : 3 If the income of B is equal to three times the savings of A, then what is the ratio of the expenditures of A and B?
If an amount of Rs. 990 is divided among A, B and C in the ratio of 3 : 4 : 2, then B will get:
The ratio of boys and girls in a group is 7 : 6. If 4 more boys join the group and 3 girls leave the group, then the ratio of boys to girls becomes 4 : 3. What is the total number of boys and girls initially in the group?
The ratio of the number of boys to the number of girls in a school of 640 students, is 5 : 3. If 30 more girls are admitted in the school, then how many more boys should be admitted so that the ratio of boys to that of the girls, becomes 14 : 9.
