Question

The ratio of two numbers is 4:3. If the
product of these numbers is 432, then find
the difference of two numbers.
1. 24
2.18
3. 6
4. 42​

Answer 1

$\large{\underline{\boxed{\red{\sf{ \: Option (3): 6}}}}}$

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${\underline{\underline{\sf{ \dag \: Assumption :}}}}$

• Let ratio be in x form.
• So, two numbers are 4x and 3x.

${\underline{\underline{\sf{ \dag \: Given :}}}}$

• Numbers :- 4x and 3x
• Product of these two numbers is 432.

${\underline{\underline{\sf{ \dag \: To \: find :}}}}$

• Difference of two numbers.

${\underline{\underline{\sf{ \dag \: Solution :}}}}$

● Let, first find value of x.

${\sf{ \ratio \longmapsto{4x \times 3x = 432}}} \\ \\ {\sf{ \ratio \longmapsto{12 {x}^{2} = 432}}} \\ \\ {\sf{ \ratio \longmapsto{ {x}^{2} = \dfrac{432}{12} }}} \\ \\ {\sf{ \ratio \longmapsto{ {x}^{2} = 36}}} \\ \\ {\sf{ \ratio \longmapsto{x = \sqrt{36} }}}\\ \\ { \underline{ \boxed{ \green{\sf{ \ratio \longmapsto{x = 6}}}}}}$

● Now two of these numbers are

${\sf{ (1) \longmapsto{4x = 4(6) = {\boxed{\green{\sf{24}}}}}}} \\ \\ {\sf{ (2) \longmapsto{3x = 3(6) = {\boxed{\green{\sf{18}}}}}}}$

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● Now, Difference between two numbers is :-

$\large{\red{\sf{ \longmapsto{24 - 18 = {\boxed{6}}}}}}$

Difference of two numbers is 6, so option (3) is correct.

Answer 2

Answer:

6 is the correct answer

Step-by-step explanation:

=> 4x × 3x = 432

=> 12x² = 432

=> x² = 36

=> x = 6

Therefore 4x = 4 × 6 = 24

3x = 3 × 6 = 18

[ the difference of two numbers= 24 - 18 => 6]