Question

Two numbers are such that the ratio between them is 3:5. If each is increased by 10, the
ratio between the new numbers so formed is 5: 7. Find the original numbers

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Answer 1

Step-by-step explanation:

Given:-

• The ratio between two numbers is 3 : 5

• If the numbers are increased by 10, the ratio becomes 5 : 7.

To Find:-

• The original numbers.

Solution:-

The ratio between two numbers is 3 : 5

Let the first number be 3x

And the second number be 5x

If the numbers are increased by 10.

The first number becomes 3x + 10

And the second number becomes 5x + 10

Ratio between the new numbers is 5: 7.

$\implies \sf \dfrac{3x + 10}{5x + 10} = \dfrac{5}{7}$

$\implies \sf 7(3x + 10) = 5(5x + 10)$

$\implies \sf 21x+ 70 = 25x + 50$

$\implies \sf 25x - 21x =70 - 50$

$\implies \sf 4x =20$

$\implies \sf x = \dfrac{20}{4}$

$\implies \sf x = 5$

$\dashrightarrow \sf First \: number = 3x = 3 \times 5 = 15$

$\dashrightarrow \sf Second\: number = 5x = 5 \times 5 = 25$

$\large\underline{\boxed{\therefore \textsf{\textbf{ The \: number \: are \: 15 \: and \: 25}}}}$

Answer 2

Answer:

Given :-

• Two numbers are such that the ratio between them is 3:5.
• Each is increased by 10, the ratio between the new numbers are 5:7.

To Find :-

• What is the original number.

Solution :-

Let, the first number be 3x

And, the second number be 5x

Each number is increased by 10, the ratio between the new numbers are 5:7.

According to the question,

⇒ $\dfrac{3x + 10}{5x + 10}$ = $\dfrac{5}{7}$

By doing cross multiplication we get,

⇒ 7(3x + 10) = 5(5x + 10)

⇒ 21x + 70 = 25x + 50

⇒ 21x - 25x = 50 - 70

⇒ - 4x = - 20

⇒ x = $\dfrac{\cancel{- 20}}{\cancel{- 4}}$

➠ x = 5

Hence, the required number are,

✦ First number = 3x = 3(5) = 15

✦ Second number = 5x = 5(5) = 25

$\therefore$ The number are 15 and 25 .

Let's Verify :-

⇒ 7(3x + 10) = 5(5x + 10)

Put x = 5

⇒ 7(15 + 10) = 5(25 + 10)

⇒ 7(25) = 5(35)

➠ 175 = 175

➥ LHS = RHS

Hence, Verified.