**Q) The sum of two numbers is 18 and the sum of their reciprocals is 9/40. Find the numbers.**

**Ans: **

Let the numbers be X and Y

**Step 1:** By first condition:

X + Y = 18 ………… (i)

**Step 2:** By second condition:

∴

∴ 40 (Y + X) = 9 X Y

e put value of (X + Y) from equation (i), we get:

∴ 40 (18) = 9 X Y

∴ X Y = 40 x

∴ X Y = 80

∴ X = ……… (ii)

**Step 3:** Next, we substitute value of X in equation (i):

X + Y = 18

∴

∴

∴ 80 + Y2 = 18 Y

∴ Y^{2} – 18 Y + 80 = 0

∴ Y^{2} – 10 Y – 8 Y + 80 = 0

^{∴ Y (Y – 10) – 8 (Y – 10) = 0}

∴ (Y – 10) ( Y – 8) = 0

**∴ Y = 10 or Y = 8**

**Step 4: We put values of Y in equation (i):**

X + Y = 18

∴ X + (10) = 18

∴ X = 18 – 10

∴ X = 8

Similarly, for Y = 8, we get X = 10

**Therefore, the two numbers are 8 and 10.**

**Check: **if numbers are 8 and 10, then 8 + 10 = 18 …. 1st condition satisfied

* …. 2nd condition also satisfied.*

*Since both the given condition are satisfied, hence our answer is correct.*

**Please do press “Heart” button if you liked the solution.**