Question

The sum of two numbers is 405 and their ratio
is 8: 7. Find the numbers.​

Answer 1

Given -

• Sum of two numbers = 405

• Ratio of numbers = 8:7

To find -

• Actual numbers.

Solution -

In the question, we are given, with the ratio of two number, and their sum is 405, and we need to find the actual numbers. For that, first we will consider a common ratio x, then we will app, up both the ratios, and will put it equal to, 405, whatever the ratio will come, we will be finding x's, by dividing the number obtained, by 405, from that the value of x, will come, after that we will multiply the given ratios, with that number, which will be obtained. Let's do it!

According to question -

Let the common ratio be x

8 = 8x

7 = 7x

sum = 405

On substituting the values -

$\sf \: 8x \: + 7x = 405$

$\sf \: 15x \: = 405$

$\sf \: x = \cancel \dfrac{405}{15}$

$\sf \: x = 27$

Now -

We have, find the value of x, so now, we will multiply 8x and 7x with 27, to obtain the actual numbers.

$\sf \: 8x = 8 \times 27 = 216$

$\sf \: 7x = 7 \times 27 = 189$

Verification -

For verification, we will add up, both the obtained numbers, and will put it equal to 405.

$\sf \: 216 \: + 189 = 405$

$\sf \: 405 = 405$

$\therefore$ The actual numbers are 216 and 189

__________________________________________________

Answer 2

　　　Question ⬇

　

❥ ​The sum of two numbers is 405 and their ratio

is 8:7. Find the numbers.​

　

　　　Answer ⬇

　

❥ Sum of two numbers - 405

❥Ratio of these numbers - 8:7

　

　

　　　According to the question,

　

❥Let the common ratio be x.

❥So,

8 = 8x

7 = 9x

　

　

❥After changing the values. We get,

　

8x + 7x = 405

15x = 405

x = 405 / 15

x = 27

　

　

　

❥To find the actual numbers, we have to multiply 7x and 8x with 27.

　

7x = 7 × 27 = 189

8x = 8 × 27 = 216

　

　

❥Be confirmed about the answers. To check it let's add both the numbers.

　

189 + 216 = 405

405 = 405

　

　

❥Hence, the actual numbers are 189 and 216.