Question

Two numbers are in ratio 3:5.If each number is increased by 10,the ratio becomes 5:7.The sum of the numbers is

Answer 1

$\bold{Answer :}$

Ratio of the two numbers is 3 : 5

Let us take the common multiple as x

Then, 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) : (5x + 10) = 5 : 7

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

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

or, 21x + 70 = 25x + 50

or, 25x - 21x = 70 - 50

or, 4x = 20

or, x = 20/4

or, x = 5

So, common multiple = 5

Therefore, the sum of the numbers

= (3x + 5x)

= 8x

= (8 × 5)

= $\bold{40}$

#$\bold{MarkAsBrainliest}$

Answer 2

The sum of the numbers is equal to 40.

Given,

Two numbers are in ratio 3:5.

If each number is increased by 10,

the ratio becomes 5:7.

To find,

The sum of the numbers.

Solution,

We can see here, it is given that

the two numbers are initially in the ratio = 3: 5.

Now first, let the two numbers be 3x and 5x.

Further, increasing each number by 10 will mean, on adding 10 to each of the numbers, these numbers become

(3x + 10), and

(5x + 10).

As the new ratio is given to be 5: 7, we can write,

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

Simplifying, by cross-multiplying first,

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

⇒ 21x + 70 = 25x + 50

Rearranging and further simplifying,

25x - 21x = 70 - 50

⇒ 4x = 20

$\implies x = \frac{20}{4}$

⇒ x = 5.

So, the 2 numbers will be,

$3x$ = 3 × 5 = 15, and

$5x$ = 5 × 5 = 25.

And, their sum will be = 15 + 25 = 40.

⇒ the sum of the two numbers = 40.

Therefore, the sum of the numbers is equal to 40.

#SPJ3