Question

Raj divided 50 into two parts such that the sum of their reciprocal is 1/12, we get the parts as :

a. 28, 22

b. 24, 36

c. 20, 30

d. 36, 14

Answer 1

Let the the two parts be 'x' and 'y'.

then, x+y= 50

⇒x= 50-y

Also, $\frac{1}{x}+\frac{1}{y}= 1/12$

⇒ $\frac{x+y}{xy}= 1/12$

⇒ 12(x+y)= xy

⇒ 12x+ 12y= xy

Using the first equation we get,

12(50-y) +12y= (50-y)y

⇒600-12y+12y= 50y- y²

⇒600= 50y- y²

⇒y²-50y+600= 0

Now we can find the value of y by using the formula for roots of a quadratic equation.

$\frac{50+ \sqrt{(-50^{2})-4(1)(600)} }{2}$

⇒$\frac{50+10}{2}$

⇒ 30

or

$\frac{50-10}{2}$

⇒20

So, the parts are 30 and 20.

∴ 'c' is the correct option.

Answer 2

Answer:

from option (1/20+1/30) =5/60=1/12, so right answer is c