Question

The sum of two natural numbers is 500. If they differ by 100 then find out the greater number?​

Answer 1

➤ Answer

• The greatest number = 300.

➤ Given

• Sum of two natural number is 500 and they differ by 100.

➤ To Find

• The greater number.

➤ Step By Step Explanation

Let us consider the numbers be x and y.

Then,

Sum of two natural number will be x + y = 500 and there difference will be x - y = 100

Now, let x + y = 500 be equation 1 and x - y be equation 2.

Let's solve this pair of linear equation in two variable to find the value of x and y.

➠ Value of x.

$\longmapsto\tt x + y = 500 \\ \\\longmapsto\tt x = 500 - y$

➠ By substituting the value

Let's substitute the value of x in 2nd equation.

$\longmapsto\tt x - y = 100 \\ \\\longmapsto\tt (500 - y) - y = 100 \\ \\\longmapsto\tt 500 - y - y = 100 \\ \\\longmapsto\tt 500 - 2y = 100 \\ \\\longmapsto\tt - 2y = 100 - 500 \\ \\\longmapsto\tt - 2y = - 400 \\ \\\longmapsto\tt y = \cancel\cfrac{ - 400}{ - 2} \\ \\\longmapsto\bf{\green{y = 200}}$

Hence, x = 500 - y => 300.

We can observe that 300 > 200 => x > y

➵ Therefore, the greatest number = 300.

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