Concept of Ratio
There should be two quantities required to compare them with each other. For example, a : b, they are called terms(a and b). The first term(a) is called antecedent and the second term(b) is called the consequent. Generally, a ratio is expressed in the simplest form.
Two Quantities of Ratio.
The order of the terms in a ratio is important, we can not write a : b to b : a. They are different.
Ratio exists only between quantities of the same kind as well as in the same units.
We can convert them into fractions whenever needed.
Fraction and Ratio.
Types of Ratios
Some of the important ratios are:
Inverse Ratio- The new ratio obtained by reversing the terms of a ratio is called the inverse ratio. For example, the inverse ratio of 2 : 3 will be 3 : 2.
Compound Ratio- The new ratio formed by the product of the previous terms of two or more ratios and the product of the last terms is called a mixed ratio. For example, the mixed ratio of two ratios (a : b) and (c : d) will be (ad : bc). Similarly the mixed ratio of 2 : 3 , 4 : 5 and 6 : 7 will be 2 × 4 × 6 : 3 × 5 × 7 i.e. 48 : 105 or 16 : 35.
Duplicate Ratio- If a new ratio is made by mixing a ratio with the same, then it is called a square ratio. For example, the square ratio of 2 : 3 is 2² : 3³. That is 2 × 2 : 3 × 3 or 4 : 9.
How To Solve Ratio?
When two numbers are divided by each other, the ratio of those numbers is obtained. As a and b are two numbers then a/b will be their ratio. If we want to find the ratio of two numbers 3 and 7, then 3/7 will be their ratio. It will be written as 3:7.
Simple Ratio Problems(Illustrations)
What is the ratio of 2 to 3?
Solution: 2 + 3 = 5. We have 5 parts in the ratio of 2 : 3.
25 cm and 1 m. What is the ratio?
Solution: 1 m = 100 cm.
25 cm and 100 cm ratio of 25/100 = 1 : 4.
The sum of the two numbers is 60 and the difference is 6. What will be the ratio?
Solution: Required ratio of numbers:
(60 + 6) / (60 - 6) = 66/54 = 11/9 or 11 : 9.
What will be the inverse ratio of 5 : 6?
Solution: The inverse ratio of 5 : 6 is 6 : 5.
What will be the duplicate ratio of 3 : 4?
Solution: The duplicate ratio of 3 : 4 = 3² : 4² or 9 : 16
If a quantity is divided in the ratio of 5 : 7, the larger part is 100. Find the quantity.
Solution: Let the quantity be x.
Then the two parts will be 5x / 7 + 5 and 7x / 7 + 5.
Hence, if the larger part is 100, we get 7x / 5 + 7 = 100.
7x / 12 = 100
7x = 100 × 12
7x = 1200
x = 1200 / 7
x = 171.42
Therefore, the quantity is 171.42.
Learning by Doing
Problems On Ratio:
1. Shilpa earns ₹150 in 4 hours and isha ₹300 in 7 hours. What will be the ratio of their earnings?
Ans: Shilpa earning: 150 X 4 = 600.
Isha earning: 300 X 7 = 2100.
Ratio= 600 : 2100
= 2 : 7
2. The ratio between the speeds of two trains is 4:5. If the second train runs 400 kms. in 6 hours. What will be the speed of the first train?
Ans: The speed of train in 1 hours : 400/6 = 66(approx)
Ratio = 4x/5x=y/66
= 4x X 66 = 5x X y
= 264 x = 5xy
The speed of the first train is 52.8 km/hr.
The Ratio refers to the comparison of at least two quantities of each other. If a and b are two quantities of the same kind (in the same units), then the fraction a/b is called the ratio of a to b. It is written as a : b. The quantities a and b are called the terms of the ratio, a is called the first term or antecedent and b is called the second term or consequent. The ratio compounded of the two ratios a : b and c : d is ad : bc. A ratio compounded of itself is called its duplicate ratio. a² : b² is the duplicate ratio of a : b. For any ratio a : b, the inverse ratio is b : a.
FAQs on Ratio Problems
1. Isha weighs 55 kg. If she reduces her weight in the ratio of 5: 4, find his reduced weight.
Let the previous weight be 5x.
5x = 55
x = 11
Therefore, 4 × 11 = 44 kg. The reduced weight is 44 kg.
2. Shubham leaves $ 1000000 behind. According to his wish, the money is to be divided between his wife and sister in the ratio of 3 : 2. Find the sum received by his wife.
We know if a quantity x is divided in the ratio a: b then the two parts are ax / a + b and bx / a + b.
= 3/5 × 1000000
= 3 × 200000
Therefore, the sum received by his wife is $600000.
3. Ishita weighs 56.7 kg. If she reduced her weight in the ratio of 7 : 6, find her new weight.
Original weight of Ishita = 56.7 kg.
She reduces her weight by a ratio of 7 : 6.
Her new weight = (6 × 56.7)/7 = 6 × 8.1 = 48.6.