Question

Date
Page
Q. Divide 32 into the two parts such
that the sum of their Reciprocal
is 1/6. The two parts are ______and _______​

Answer 1

Answer:

8 and 24

Step-by-step explanation:

Given:

• The sum of reciprocal

To Find:

• The two numbers

Solution:

Let first part be x

Other part=32-x

ACQ,

$\therefore \: \tt \leadsto \frac{1}{x} + \frac{1}{32 - x} = \frac{1}{6} \\ \sf \: \\ \sf LCM \: of \: x,32 - x,6 \\ \longrightarrow \sf \: ( x)(32 - x)(6) \\ \\ \tt \leadsto \: \frac{ \cancel{(x)} {(32 - x)}(6)}{ \cancel{x}} + \frac{(x)\cancel{(32 - x)}(6)}{ \cancel{32 - x} } = \frac{(x)(32 - x) \cancel{(6)}} { \cancel{6}} \\ \tt \leadsto \: 6(32 - x) + 6x = x(32 - x) \\ \tt \leadsto192 - 6x + 6x = 32x - {x}^{2} \\ \tt \leadsto \: {x }^{2} - 32x + 192 = 0 \\ \tt \leadsto {x }^{2} - 8x- 24x + 192 = 0 \\ \tt \leadsto \: x(x - 8) - 24(x - 8) = 0 \\ \tt \leadsto(x - 8)(x - 24) = 0$

If x-8=0

x=8

If x-24=0

x=24

Both x are correct

First part= 8

Other part=32-x=32-8=24

Answer 2

Answer:

8 and 24

Step-by-step explanation:

Given:

The sum of reciprocal

To Find:

The two numbers

Solution:

Let first part be x

Other part=32-x

ACQ,

\begin{gathered} \therefore \: \tt \leadsto \frac{1}{x} + \frac{1}{32 - x} = \frac{1}{6} \\ \sf \: \\ \sf LCM \: of \: x,32 - x,6 \\ \longrightarrow \sf \: ( x)(32 - x)(6) \\ \\ \tt \leadsto \: \frac{ \cancel{(x)} {(32 - x)}(6)}{ \cancel{x}} + \frac{(x)\cancel{(32 - x)}(6)}{ \cancel{32 - x} } = \frac{(x)(32 - x) \cancel{(6)}} { \cancel{6}} \\ \tt \leadsto \: 6(32 - x) + 6x = x(32 - x) \\ \tt \leadsto192 - 6x + 6x = 32x - {x}^{2} \\ \tt \leadsto \: {x }^{2} - 32x + 192 = 0 \\ \tt \leadsto {x }^{2} - 8x- 24x + 192 = 0 \\ \tt \leadsto \: x(x - 8) - 24(x - 8) = 0 \\ \tt \leadsto(x - 8)(x - 24) = 0\end{gathered}

∴⇝

x

1

+

32−x

1

=

6

1

LCMofx,32−x,6

⟶(x)(32−x)(6)

⇝

x

(x)

(32−x)(6)

+

32−x

(x)

(32−x)

(6)

=

6

(x)(32−x)

(6)

⇝6(32−x)+6x=x(32−x)

⇝192−6x+6x=32x−x

2

⇝x

2

−32x+192=0

⇝x

2

−8x−24x+192=0

⇝x(x−8)−24(x−8)=0

⇝(x−8)(x−24)=0

If x-8=0

x=8

If x-24=0

x=24

Both x are correct

First part= 8

Other part=32-x=32-8=24