Question

The sum and difference of the reciprocal of the age of the son and father are respectively 5/40 and3/40

Answer 1

then let x and 1/y taken then

1/x+1/y= 5/40 ........(1)

1/x-1/y= 3/40..........(2)

the values are x = 10 and y= 40

Answer 2

The age of father is 40 years and age of son is 10 years

Step-by-step explanation:

Let the age of son be x and let the age of father be y

The sum of reciprocals of ages is 5/40

$\frac{1}{x}+\frac{1}{y}=\frac{5}{40}\\\frac{1}{x}=\frac{5}{40}-\frac{1}{y}$

The difference of reciprocals of ages is 3/40

$\frac{1}{x}-\frac{1}{y}=\frac{3}{40}\\ \frac{5}{40}-\frac{1}{y}-\frac{1}{y}=\frac{3}{40}\\ \frac{5}{40}-\frac{2}{y}=\frac{3}{40}\\\frac{2}{40}=\frac{2}{y}$

y=40

$\frac{1}{x}=\frac{5}{40}-\frac{1}{y}\\\frac{1}{x}=\frac{5}{40}-\frac{1}{40}\\\frac{1}{x}=\frac{4}{40}$

x=10

Hence the age of father is 40 years and age of son is 10 years

#Learn more:

The sum and product of two numbers are 13 and 40 respectively. The sum of their reciprocal is

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