Amit, Raju and Ram agree to pay their total electricity bill in the proportion 3 : 4 : 5. Amit pays first day's bill of Rs. 50, Raju pays second day's bill of Rs. 55 and Ram pays third day's bill of Rs. 75. How much amount should Amit pay to settle the accounts
Answers
Answer:
The ratio of two quantities a and b of same units is the fraction x/y, where b ≠ 0
- The fraction x/y can be represented as x:y
Different types of ratios are:
1) Duplicate ratio: It is the ratio of squares of two numbers.
Duplicate ratio of the fraction x is given as: x = x2 or x : y = x2 : y2
y y y2
2) Sub-duplicate ratio: It is the ratio between square roots of two numbers.
Duplicate ratio of the fraction x is given as: x = x or x : y = x : y
y y y
3) Triplicate ratio: It is the ratio of cubes of two numbers.
Triplicate ratio of the fraction x is given as x = x3
y y y3
4) Sub- Triplicate ratio: It is the ratio between cube roots of two numbers
Sub-Triplicate ratio of the fraction x is given as x = x(1/3)
y y y(1/3)
5) Compound ratio: It is the ratio of product of first terms in every ratio to that of product of second term in every ratio.
For example:
Compound ratio of (a : x), (b : y), (c : z) is (abc : xyz)
6) Inverse ratio: The ratio formed by interchanging their old places in the ratio to new
The inverse ratio of 5 : 8 is 8 : 5.
Proportion:
1) Proportion is the equality of two ratios.
When (a : b = x : y) is represented as (a : b :: x : y), then a, b, x, y are said to be in proportion.
In (a : b :: x : y), a and y are called as extremes and b and x are called as mean terms.
Product of means = Product of extremes
2) Mean proportion: Mean proportion between x and y is given as xy
3) Third proportion: If p : q = q : s, then s is called as third proportional to p and q.
4) Fourth proportion: If u : v = x : y, then y is the fourth proportional of u, v and x.
Quick Tips and Tricks
1) Comparison of ratios:
If (x : y) > ( a : b) → x > a
y b