Algebra
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Q.

The sum of the reciprocals of the ages of two colleagues is five times the difference of the reciprocals of their ages. If the ratio of the products of their ages to the sum of their ages is $14.4 : 1$, the age (in years) of one of the colleagues must be between (both inclusive).

 A.

20 and 23

 B.

23 and 26

 C.

26 and 30

 D.

30 and 35

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Solution:
Option(B) is correct

Suppose that age of the two colleagues be $x$ year and $y$ year

According to question:

\(\dfrac{1}{x}+\dfrac{1}{y}=5\left(\dfrac{1}{x}-\dfrac{1}{y}\right)\)

\(\Rightarrow y=\dfrac{3x}{2}\)--------(i)

Again,

\(\dfrac{xy}{x+y}=\dfrac{14.4}{1}\)

\(5xy=72(x+y)\)

From equation (i):

\(5x\times \left(\dfrac{3x}{2}\right)=72\times \left(x+\dfrac{3x}{2}\right)\)

$\Rightarrow  x= 24$ year

i.e. Age of one of colleagues lies between 23 and 26 year.


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