Finding Third Proportional of 8 and 20
This question requires calculating the third proportional of two given numbers, 8 and 20.
Third Proportional Concept
If three numbers $a$, $b$, and $c$ are in continued proportion, then the ratio of the first to the second is equal to the ratio of the second to the third. This is written as:
$ a : b :: b : c $
This implies the relationship:
$ \frac{a}{b} = \frac{b}{c} $
In this relationship, $c$ is the third proportional to $a$ and $b$.
Calculating the Third Proportional (x)
Given numbers are $a=8$ and $b=20$. We need to find the third proportional, $x$.
Setting up the proportion:
$ 8 : 20 :: 20 : x $
Using the cross-product rule (product of extremes equals product of means):
$ \frac{8}{20} = \frac{20}{x} $
Cross-multiplying gives:
$ 8 \times x = 20 \times 20 $
Calculate the product on the right side:
$ 8x = 400 $
To find the value of $x$, divide both sides by 8:
$ x = \frac{400}{8} $
$ x = 50 $
Result
The value of x, which is the third proportional of 8 and 20, is 50.
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Important Questions from Ratio and Proportion
In a mixture of 156 litres, the ratio of milk and water is 7 : 6. How much water should be added to make the ratio 14 : 13?
If the ratio of the first to second number is 3 : 4 and that of the second to the third number is 8 : 5, and sum of three numbers is 190 then the third number is:
The third proportional to 9 and 15 is:
The average age of 3 persons is 30 years.If their ages are in the ratio of 3 : 5 : 7 respectively, then the age of the eldest person is:
The income of A and B are in the ratio 5 : 3. The expenses of A, B and C are in the ratio of 8 : 5 : 2. If C spends 2000 and B saves ₹ 700, then A saves:
