Question

Two no. Arein ratio 3:5. If each is increased by 10 the ratio of new no is 5 :7

Answer 1

$\mathbb {Question}$ :- Two numbers are in the ratio 3 : 5. If each is increased by 10, the ratio of new numbers becomes 5 : 7. Find the numbers.

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$\mathbb {Solution}$ :-

Step 1 : Define x

Given, two numbers are in the ratio 3 : 5

So, let the two numbers be 3x and 5x

Each number is increased by 10, so the two numbers becomes 3x + 10 and 5x + 10

After the numbers are increased, the ratio of the two numbers becomes 5 : 7

Step 2 : Find the value of x

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

➾ 7(3x + 10) = 5(5x + 10)

➾ 21x + 70 = 25x + 50

➾ 25x - 21x = 70 - 50

➾ 4x = 20

➾ x = $\dfrac{20}{4}$

➾ x = 5

Step 3 : Find the numbers

1st number ➾ 3x

➾ 3 × 5

➾ $\boxed {15}$

2nd number ➾ 5x

➾ 5 × 5

➾ $\boxed {25}$

Answer 2

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Ratio of two number 3 : 5

Let the common multiple as x

so , the numbers are 3x and 5x

By the given condition, each number is increased by 10

Then, the new numbers be (3x + 10) and (5x + 10)

By the given condition,

(3x + 10) ratio (5x + 10) = 5 : 7

(3x + 10)/(5x + 10) = 5/7

7 (3x + 10) = 5 (5x + 10)

21x + 70 = 25x + 50

25x - 21x = 70 - 50

4x = 20

x = 20/4,
x = 5
Socommon multiple = 5

Therefore, the sum of the numbers

= (3x + 5x)

= 8x

= (8 × 5)

= 40