Question

The difference between two positive integer is 75. The ratio of these integers is 7 : 4. Find the integers.

Answer 1

Answer :

The two positive integers are 175 and 100.

Step-by-step explanation :

Given,

• The difference between two positive integer is 75

• The ratio of these integers is 7 : 4

To find,

• The integers

Solution,

⇒  The ratio of the two integers = 7 : 4

Let the two positive integers be 7x and 4x

The larger number = 7x

The smaller number = 4x

⇒  The difference between them = 75

      7x - 4x = 75

        3x = 75

        x = 75/3

         x = 25

=> 7x = 7(25) = 175

=> 4x = 4(25) = 100

Therefore, the two positive integers are 175 and 100

Verification :

• The two positive integers are 175 and 100

[I] The difference between two positive integer is 75

            175 - 100 = 75

                75 = 75

               LHS = RHS

[II] The ratio of these integers is 7 : 4

          175 : 100 = 7 : 4

       25(7) : 25(4) = 7 : 4

           7 : 4 = 7 : 4

           LHS = RHS

Hence verified!!

Answer 2

$\huge\sf\orange{SoLuTiOn}$

Given that Difference between Two positive intergers is 75

Given ratio of Numbers is 7:4

So ATQ ratio We have to take Numbers are 7x,4x

Difference of 7x and 4x is 75

So,

$\sf\purple{7x - 4x = 75}$

$\sf\purple{3x = 75}$

x = $\frac{75}{3}$

So, x = 25

Numbers are 7x = 7(25) = 175

4x = 4(15) = 60

Required numbers are $\sf\red{175,60}$