Question

Divide 27 into two part such that the sum of their reciprocal is 3 /20

Answer 1

The answer is 12 and 15:

12 + 15 = 27

1/12 + 1/15 is 3/20

A + B = 27

1/A + 1/B = 3/20

To make the denominators equal, multiply 1/A by B/B and 1/B by A/A to get B/AB + A/AB = 3/20

(B+A)/AB = 3/20

We know that B + A is 27, so it becomes 27/AB = 3/20

Multiply both sides of the second fraction by 9 to get

27/AB = 27/180

So, A x B = 180 and A + B = 27

1 + 180 = 180

2 + 90 = 92

3 + 60 = 63

4 + 45 = 49

5 + 36 = 41

6 + 30 = 36

9 + 20 = 29

10 + 18 = 28

12 + 15 = 27

Answer 2

Let number = x

Another number = 27 - x

According to question;

1/x + 1/(27 - x) = 3/20

(27 - x + x)/(27x - x²) = 3/20

Cross-multiply,

20(27) = 3(27x - x²)

540 = 81M - 3x²

x² - 27x + 180 = 0

x² - 15x - 12x + 180 = 0

x(x - 15) -12(x - 15) = 0

(x - 12) (x - 15) = 0

x = 12, 15