Question

20. Find the value of x in the given proportion: - 15 : 20 :: x : 36

Answer 1

Answer :-

• The value of x is 27.

Given :-

• The numbers 15, 20, x and 36 are in proportion.

To find :-

• The value of x.

Step-by-step explanation :-

• In this question, it has been given that 15, 20, x and 36 are in proportion. We have to find the value of x.

Calculations :-

Let's calculate our answer!

We know that, in a proportion :-

$\underline{ \boxed{ \sf Product \: of \: extremes = Product \: of \: means.}}$

Here,

• Extremes = 15 and 36.
• Means = 20 and x.

• So, that means the product of 15 and 36 is equal to the product of 20 and x.

-------------------

$\tt\implies 20 \times x = 15 \times 36$

Multiplying the numbers on both sides,

$\tt\implies 20x = 540$

Transposing 20 from LHS to RHS, changing it's sign,

$\tt\implies x = \dfrac{540}{20}$

Dividing 540 by 20,

$\tt \implies x = 27.$

• So, the value of x is 27.

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Verification :-

• We have the value of x now. So it means that 15, 20, 27 and 36 are in proportion.

• We already know that in a proportion, the product of means is equal to the product of extremes.

Now, we have :-

• Extremes = 15 and 36.
• Means = 20 and 27.

• So, that means the product of 15 and 36 should be equal to the product of 27.

• So, to check our answer, let's find the product of extremes and the product of means. Then we will see whether they are equal or not.

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$\sf Product \: of \: extremes = 15 \times 36 = 540.$

$\sf Product \: of \: means = 20 \times 27 = 540.$

Observation :-

• We see that the product of means is equal to the product of extremes. So, the numbers are in proportion.

Hence verified!

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Answer 2

Answer :

$\large \sf \implies \underline{\boxed{\mathfrak{x=27}}}$

Solution :

Given :

$\sf \: \: \: \: \: 15 : 20 :: x : 36 \bf \: are \: in \: proportional.$

To Find :

• Value of x.

$\bigstar$ ━━━━━━━━━━━━━━━━$\bigstar$

We Know that,

$\red \bigstar \underline{\boxed{\tt Product \: of \: Means \: = \: Product \: of \: extremes}}$

Here,

• Extremes are 15 and 36.
• Means are 20 and x.

• $\sf \frac{15}{20} = \frac{x}{36}$

• So, Product of 20 and x = Product of 15 and 36.

So,

$\large\sf\implies 20 \times x = 15 \times 36 \\ \\ \large\sf\implies 20x = 540$

• Divide both sides by 20

$\\ \sf\implies \frac{\cancel{20}\:x}{\cancel{20}}= \frac{54\cancel{0}}{2\cancel{0}} \\ \\ \large\sf\implies \boxed{\mathfrak{x = 27}}$

Hence,

Value of x is 27.

Verification :

• If Product of means = product of extreme. Then we can say it is in proportion.

➠ Product of extremes = 15 × 36

$\:\:\:\:\:\:\:\:\:\implies \boxed{540}$

➠ Product of means = 20 × 27

$\:\:\:\:\:\:\:\:\:\implies \boxed{540}$

Product of means = Product of extreme

Means it is in Proportion,

Hence verified !!

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