Question

Two numbers are in th ratio 5:8. If 12 be added to each they become in the ratio 3:4 . The product of the number.​

Answer 1

Given :-

• Two numbers are in th ratio 5:8. If 12 be added to each they become in the ratio 3:4.

To find :-

• Product of numbers

Solution :-

• Two numbers are in th ratio 5:8.

Let the number be 5x and 8x

• According to question

If 12 be added to each they become in the ratio 3:4

→ 5x + 12/8x + 12 = ¾

• Cross multiplication

→ 4(5x + 12) = 3(8x + 12)

→ 20x + 48 = 24x + 36

→ 48 - 36 = 24x - 20x

→ 12 = 4x

→ x = 12/4

→ x = 3

Hence,

• x = 3

• Required numbers
• 5x = 5 × 3 = 15
• 8x = 8 × 3 = 24

Therefore,

• Product of numbers = 15 × 24 = 360

Answer 2

Given:

• Two numbers are in ratio= 5:8
• If 1w is added to each the ratio becomes = 3:4

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Need to find:

• Product of the numbers =?

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Let

The the common ratio of numbers be y

Then, the numbers are :

• 5y and
• 8y

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Given,

$\dfrac{5y + 12}{8y + 12} = \dfrac{3}{4}$

$\implies \: 20y + 48 = 24y + 36$

$\implies \: 24y - 20y = 48 - 36$

$\implies \: 4y = 12$

$\purple{\bold{\implies y=3}}$

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Now the numbers are:

• 5y = 15
• 8y = 24

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The product :

= 5y × 8y

= $\red{\bold{\boxed{\large{360}}}}$