Question

The product of two numbers is 10000.If one number is 16 times the other numbers ,find the two numbers.​

Answer 1

Given: The Product of two numbers is 10,000. & One number is 16 times the other number.

Need to find: The two numbers?

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❍ Let's say, that the one number be x. Then, other number would be 16x. i.e one number is 16 times the other number.

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

• Product of Both Numbers (x and 16x) is 10000.

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$:\implies\sf x \times 16x = 10000$

$:\implies\sf 16x^2 = 10000$

$:\implies\sf x^2 = \dfrac{10000}{16}$

$:\implies\sf x = \sqrt{\Bigg(\dfrac{10000}{16}\Bigg)}$

$:\implies\sf x = \cancel\dfrac{100}{4}$

$:\implies{\pmb{\boxed{\frak{\red{x = 25}}}}}\;\bigstar$

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Therefore,

• First number, x = 25
• Second number, 16x = 16(25) = 400

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$\therefore{\underline{\textsf{Hence, the numbers are \textbf{25} and \textbf{400} respectively.}}}$

Answer 2

Question:

• The product of two numbers is 10000. If one number is 16 times the other numbers ,find the two numbers.

Answer:

• Both numbers are 25 and 400.

Step By Step Explanation:

Given that:

• The product of two numbers is 10000.
• One number is 16 times the other number.

To Find:

• Both numbers?

Solution:

• Let us consider that one number be n, in question it is stated that other number is 16 times the first number. Therefore, other number is 16n.

❏ According to the Question :

↦ Product of numbers = 10000

↦ n × 16n = 10000

↦ 16n² = 10000

↦ n² = $\sf \dfrac{10000}{16}$

↦ $\sf n = \sqrt{\dfrac{10000}{16}}$

↦ $\sf n = \sqrt{\dfrac{100\:\times\:100}{4\:\times\:4}}$

↦ $\sf n = {\cancel{\dfrac{100}{4}}}$

➦ $\pmb{\underline{\boxed{\bf{\pink{n = 25}}}}}$

Hence,

• 1st number = n = 25
• 2nd number = 16n = 16 × 25 = 400

∴ Hence, both numbers are 25 and 400.

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