Question

Divide the no. 20 into two parts such that their ratio is 9:1 also find the no.Which is mean proportional between these two parts

Answer 1

Answer:

no. are 18 and 20

mean prpoportional = 6

Step-by-step explanation:

ratio = 9:1

let, 'x' be the common multiple

so, the numbers are 9x and x

according to the condition,

9x + x =20

10x=20

x=2

Thus, the numbers are,

9x= 9×2 = 18

&

x =2

let, mean proportional be 'a'

a^2=18×2

a^×=36

a=6

Answer 2

The numbers are 2 and 18 and their mean proportional is 6.

• Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another. Two quantities are compared using division in a ratio. In this case, the dividend is referred to as the "antecedent" and the divisor as the "consequent."
• For instance, out of a group of 30, 17 prefer to walk and 13 prefer to cycle in the morning. We write this information as 17: 13 to express it as a ratio. The letter ":" in this context means "is to." Therefore, "17 is to 13" represents the proportion of those who prefer to walk to those who prefer to cycle.
• Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.

Here, according to the given information, we are given that,

The amount to be divided is 20.

Let the divisions be 9x and x.

Then, we get,

$9x+x=20.$

Or, $10x=20.$

Or, $x = 2.$

Then, 9x = $9.(2)=18.$

Now, the mean proportional is found out by taking square root of the product of the two given numbers. Then, we get,

Product of 2 and 18 = 36.

Mean proportional = $\sqrt{36} =6.$

Hence, the numbers are 2 and 18 and their mean proportional is 6.

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