Question

The sum of two is 1280. if 3.5% of one number is equal to 4.5% of another number then find the two numbers​

Answer 1

Question:

• The sum of two numbers is 1280. If 3.5% of one number is equal to 4.5% of another number, then find the two numbers.

Answer:

$\large\bold\red{560\;and\;720}$

Step-by-step explanation:

Let the first number be ‘x’

And,

The another number be ‘y’

Now,

According to question,

Sum of two numbers is 1280.

Therefore,

We get,

$= > x + y = 1280 \: \: \: \: \: .........(1)$

Also,

3.5% of first no. equals to 4.5% of another no.

Therefore,

We get,

$= > \frac{3.5}{100} x = \frac{4.5}{100} y \\ \\ = > 3.5x = 4.5y \\ \\ = > 35x = 45y \\ \\ = > x = \frac{45}{35} y \\ \\ = > x = \frac{9}{7} y \: \: \: \: .........(2)$

Substituting this value in eqn (1),

We get,

$= > \frac{9}{7}y + y = 1280 \\ \\ = > \frac{9y + 7y}{7} = 1280 \\ \\ = > \frac{16}{7} y = 1280 \\ \\ = > y = \cancel{1280} \times \frac{7}{ \cancel{16} } \\ \\ = > y = 80 \times 7 \\ \\ = > \large \boxed { \bold{ y = 560}}$

Therefore,

We get,

$= > x = \frac{9}{ \cancel{7}} \times \cancel{ 560} \\ \\ = > x = 9 \times 80 \\ \\ = > \large \boxed{ \bold{ x = 720}}$

Hence,

The required numbers are 560 and 720.

Answer 2

$\bold{\large{\underline{\underline{\sf{StEp\:by\:stEp\:explanation:}}}}}$

Given,

Sum of two numbers = 1280

Let the first number be x and the second number be y.

According to question,

3.5% of x= 4.5% of y

$\frac{x}{y} = \frac{4.5}{3.5}$

$\frac{x}{y} = \frac{9}{7}$

⇒x = 9a, y=7a [where a is a common multiple]

Also , 9a+7a = 1280

16a = 1280

$a =\frac{1280}{16}$

a = 80

So,x = 9 × 80, y=7 × 80

» x= 720

» y=560

Hence,One number is 720 and other number is 560.