Question

The sum of two numbers is 8. If their
sum is four times their difference,
then the numbers are *
a. 3 & 4
b. 4 & 5
c. 5 & 3
d. 4 & 6​

Answer 1

• Option (c) 5 & 3 is correct.

Given :–

• The sum of two numbers = 8.
• Their sum is four times their difference.

To Find :–

• Both numbers.

Solution :–

Let,

The first number be x.

The second number be y.

Given,

$\mapsto x + y = 8$ ––––(1)

According to the question,

Their sum is four times their difference.

$\mapsto x + y = 4(x - y)$

We have,

• x + y = 8.

So,

$\mapsto 8 = 4(x - y)$

$\mapsto \cancel \dfrac{8}{4} = x - y$

$\mapsto 2 = x - y$

$\mapsto x - y = 2$ ––––(2)

Now, add both the equation,

$\mapsto (x + y) + (x - y) = 8 + 2$

$\mapsto x + y + x - y = 10$

$\mapsto x + x + y - y = 10$

$\mapsto 2x + 0 = 10$

$\mapsto 2x = 10$

$\mapsto x = \cancel\dfrac{10}{2}$

$\mapsto x = 5$

Now,

Substitute the value of x in equation (1),

$\mapsto x + y = 8$

• x = 5

$\mapsto 5 + y = 8$

$\mapsto y = 8 - 5$

$\mapsto y = 3$

Hence,

The numbers are 5 and 3.

So, the option (c) 5 & 3 is correct.