Question

divide 36 into two parts such that the sum of their reciprocals is 1/8

Answer 1

Answer:

Given:- x+y=50 ……(1)

Reciprocal of x and y are 1/x and 1/y

1/x+1/y=1/12 ……..(2)

Solution:- From eqn. No (2)

1/x+1y=1/12

Multiply both sides by xy, we get

(x+y)=xy/12

Now put (x+y)=50 as given in eqn. No (1) above

50=xy/12

xy=50×12=600

y=600/x Put this value in eqn.(1)

x+y=50

x÷600/x=50

Multiply both side by x ,we get

x2+600=50x

x2−50x+600=0

x2−30x−20x+600=0

x(x-30)-20(x-30)=0

(x-30)(x-20)=0

x=30 and 20

From eqn.(1)

If x=30 then y=20 Answer

and if x=20 then y=30 Answer

Let 50 is divided into x and y, then

x+y=50(1)

1x+1y=112

⟹x+yxy=112⟹xy=12(x+y)=12(50)=600

⟹x=600y

putting the value of x in (1)

600y+y=50⟹600+y2=50y⟹y2−50y+600=0

⟹y2−30y−20y+600=0⟹y(y−30)−20(y−30)=0

⟹(y−30)(y−20)=0⟹y=30∨y=20

when y = 30, x = 20 and when y = 20, x = 30

∴The two parts are 20 and 30

120+130=3+260=560=112