**Q) Sum of two numbers is 105 and their difference is 45. Find the numbers.**

**Ans: **

Let the numbers be X and Y

**Step 1:** By first condition: X + Y = 105 ………… (i)

By second condition: X – Y = 45 ………. (ii)

**Step 2:** By adding these two equations, we get:

(X + Y) + (X – Y) = 105 + 45

∴ 2 X = 150

∴ X =

**∴ X = 75**

**Step 3:** By substituting this value of X in equation (i), we get:

X + Y = 105

∴ 75 + Y = 105

∴ Y = 105 – 75

**∴ Y = 30**

**Therefore, the numbers are 75 and 30.**

**Check:** If numbers are 75 and 30, then *sum of the numbers = 75 + 30 = 105 … (matched with value in question)*

*Difference of the numbers = 75 – 30 = 45 … (matched with value in question)*

*Since both the values match with the given values, hence our answer is correct.*

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