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
The cost of a diamond is directly proportional to the square of its weight. The cost of a 14 gm diamond is Rs. 2560. This diamond got broken down into two pieces in the ratio of 5 ∶ 9. How much loss percent is incurred due to this breakage ? (Correct to two decimal places)
Atul purchased Bread costing Rs.20 and gave a 100 rupee note to the shopkeeper. The shopkeeper gave the balance money in coins of denomination Rs.2, Rs.5 and Rs.10. If these coins are in the ratio 5 ∶ 4 ∶ 1, then how many Rs.5 coins did the shopkeeper give?
A person divides a certain amount among his three sons in the ratio of 3 ∶ 4 ∶ 5. If he had divided this amount in the ratio of 1/3,1/4,1/5, his son, who had got the lowest share earlier, would get Rs.1,188 more. Find the amount (in Rs).
In a school 3/8 of the number of students are girls and the rest are boys. One-third of the number of boys are below 10 years and 2/3 the number if girls are also below 10 years. If the number of students of age 10 or more years is 260. then the number of boys in the school is:
If a : b : c = \(\frac{1}{4} : \frac{1}{3} : \frac{1}{2}, \) then \( \ \frac{a}{b} : \frac{b}{c} : \frac{c}{a} = ?\)
