Question

The difference between two postive intrgers is 50 and the ratio of these integers is 1 : 3 . Find these integers

Answer 1

Integers are the numbers which includes negative numbers, postive numbers and also zero.


Now let's come to the question,


Let the numbers in the ratio, i.e, 1 : 3 be 1x and 3x

Given, their difference is 50


According to the question,

3x - 1x = 50

2x = 50

x = $\dfrac{50}{2}$

x = 25


1st integer = 1x = 1 × 25 = 25

2nd integer = 3x = 3 × 25 = 75



$\therefore{}$ The two positive integers are 25 and 75 respectively

Answer 2

Let the required two positive numbers are x and y respectively.

According to the question the difference of the numbers is 50.

∴ x - y = 50

⇒ x = 50 + y

As the value of x is equal to 50 + y, we can say that required two positive numbers are 50 + y and y respectively.

Also given that the ratio of the same integers is 1 : 3.

∴ y : ( y + 50 ) = 1 : 3

⇒$\dfrac{y}{y+50} = \dfrac{1}{3}$

⇒ 3y = y + 50

⇒ 3y - y = 50

⇒ 2y = 50

⇒$y=\dfrac{50}{2}$

⇒ y = 25

Substitute the value of y in x = y + 50

⇒ x = y + 50

⇒ x = 25 + 50

⇒ x = 75

Therefore, required positive numbers are x and y i.e. 75 and 25 respectively.

Required numbers : 75 and 25.