Question

A rope of 40 cm length is divided into two parts such that the sum of their reciprocals is 8/75 find the length of each part

Answer 1

The length of each part is 15 and 25.

Step-by-step explanation:

Given data

Lets consider the two parts as a and (40-a)

Find the length of each part.

$\frac{1}{\text{a}} + \frac{1}{40 -\text{a}} = \frac{8}{75}$

$\frac{40- \text{a} + \text{a}}{\text{a}(40 -\text{a})} = \frac{8}{75}$

$\frac{40}{40\text{a}- \text{a}^2} = \frac{8}{75}$

40 × 75 = 8 (40 a - a² )

3000 = 320 a - 8 a²

8 a² - 320 a + 3000 = 0

a² - 40 + 375 = 0

a² - 25 a - 15 a + 375 = 0

a (a- 25) - 15 ( a - 25) = 0

(a- 25)(a - 15) = 0

a = 25 ; a = 15.

Hence the length of the each part is 25 and 15 cm .

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