Question

The ratio of two numbers is 4:3. If their product is 432, the difference between the number is

Answer 1

Given: The ratio of two numbers is 4 : 3. & The product of these two numbers is 432.

Need to find: The Difference b/w two numbers?

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❍ Let's say, that the first number be 4x and second number be 3x respectively.

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$\underline{\bigstar\:\boldsymbol{According\;to\; the\; Question\! :}}$⠀⠀

• It is Given that, the product of these two numbers is 432.

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$:\implies\sf First~number\times Second~number= Product\\\\\\:\implies\sf4x \times 3x = 432 \\\\\\:\implies\sf 12x^2 = 432 \\\\\\:\implies\sf x^2 = \cancel\dfrac{432}{12} \\\\\\:\implies\sf x^2 = 36 \\\\\\:\implies\sf x = \sqrt{36} \\\\\\:\implies{\underline{\boxed{\pmb{\frak{\red{x = 6}}}}}}\;\bigstar$

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Therefore,

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• First number, 4x = 4(6) = 24
• Second number, 3x = 3(6) = 18
• Difference b/w numbers = 24 – 18 = 6

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∴ Hence, the two Difference b/w these numbers is 6.

Answer 2

Answer:

Given :-

• The ratio of two numbers is 4 : 3.
• Their product is 432.

To Find :-

• What is the difference between the two numbers.

Solution :-

Let,

$\mapsto \bf First\: Number =\: 4a$

$\mapsto \bf Second\: Number =\: 3a$

According to the question,

$\implies \sf\bold{\pink{1^{st}\: Number \times 2^{nd}\: Number =\: Product\: of\: two\: numbers}}$

$\implies \sf 4a \times 3a =\: 432$

$\implies \sf 12a^2 =\: 432$

$\implies \sf a^2 =\: \dfrac{\cancel{432}}{\cancel{12}}$

$\implies \sf a^2 =\: \dfrac{36}{1}$

$\implies \sf a^2 =\: 36$

$\implies \sf a =\: \sqrt{36}$

$\implies \sf a =\: \sqrt{\underline{6 \times 6}}$

$\implies \sf\bold{\purple{a =\: 6}}$

Hence, the required numbers are :

❒ First Number :

$\longrightarrow \sf First\: Number =\: 4a$

$\longrightarrow \sf First\: Number =\: 4(6)$

$\longrightarrow \sf First\: Number =\: 4 \times 6$

$\longrightarrow \sf\bold{\green{First\:Number =\: 24}}$

❒ Second Number :

$\longrightarrow \sf Second\: Number =\: 3a$

$\longrightarrow \sf Second\: Number =\: 3(6)$

$\longrightarrow \sf Second\: Number =\: 3 \times 6$

$\longrightarrow \sf\bold{\green{Second\: Number =\: 18}}$

Now, we have to find the difference between the two numbers :

$\footnotesize\leadsto \bf Difference\: between\: the\: two\: numbers =\: 1^{st}\: Number - 2^{nd}\: Number$

$\footnotesize\leadsto \sf Different\: between\: two\: numbers=\: 24 - 18$

$\footnotesize\leadsto \sf\bold{\red{Different\: between\: two\: numbers =\: 6}}$

${\footnotesize{\bold{\underline{\therefore\: The\: difference\: between\: the\: two\: numbers\: is\: 6\: .}}}}$

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VERIFICATION :-

$\leadsto \sf 4a \times 3a =\: 432$

By putting a = 6 we get,

$\leadsto \sf (4 \times 6) \times (3 \times 6) =\: 432$

$\leadsto \sf 24 \times 18 =\: 432$

$\leadsto \sf\bold{432 =\: 432}$

Hence, Verified.