Question

Mohsin is thinking of two numbers.the first number is smaller than the second number.the sum of the two numbers is 72 and difference between the two numbers is 18.what is the ratio of the first number to the sum of the two numbers?

Answer 1

$\large{\rm{\color{teal}Solution}}$

Remember the condition i.e the first number is smaller than the second number.

Let the two numbers be x and y

Given that, x + y = 72 (Eq 1) also,

y - x = 18 (Eq 2)

From eq (1) and (2),

$\sf y + \cancel x = 72 \\(+)\sf \: y - \cancel x = 18 \\ \cline\rm \: 2y = 90$

y = 45

Substitute the value for y in eq 1

we get, x = 27.

Find

The ratio of the first number to the sum of the two numbers = 27 : 72 = 3 : 8

Therefore, 3 : 8 is the required ratio

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Answer 2

Answer:

The ratio of the first number to the sum of the two numbers = 3 :8

Step-by-step explanation:

Given sum of two numbers = 72

difference  between two numbers = 18

 let the two numbers are $a$ and $b$

                  sum of a and b = 72 ⇒        $a+ b = 72$ _ equation 1

   difference means subtraction ⇒      $a - b = 18$  _ equation 2

     equation 1 - equation 2 ⇒     $a +b - (a-b) = 72-18$

                                                       $a+b -a+b = 54$

                                                      $2b = 54$

                                                       b = 27

     substitute  b= 27 in equation 1 ⇒  $a + 27 = 72$

                                                              a = 72 -27

                                                                a = 45

           the required numbers  are 27 and 45

  ratio of the first number to sum of two numbers = 27 : 72  

                                                                                   = 3 : 8 (divided by 9)