Question

The sum of reciprocals of Suma' age 2 years ago and 4 years from now is 4/9. Find her present age.

please answer with explanation​

Answer 1

Given :-

• The sum of reciprocals of Suma' age 2 years ago and 4 years from now is 4/9.

To find :-

• Present age

Solution :-

It is given that the sum of reciprocals of Suma' age 2 years ago and 4 years from now is 4/9.

Let the Suma's age be x

Suma's age 2 years ago = (x - 2)

Suma's age 4 years from now = (x + 4)

According to the given condition

→ 1/x - 2 + 1/x + 4 = 4/9

→ (x + 4) + (x - 2)/(x - 2)(x + 4) = 4/9

→ x + 4 + x - 2/x(x + 4) - 2(x + 4) = 4/9

→ 2x - 2/x² + 4x - 2x - 8 = 4/9

→ 2x - 2/x² + 2x - 8 = 4/9

→ 9(2x - 2) = 4(x² + 2x - 8)

→ 18x - 18 = 4x² + 8x - 32

→ 4x² + 8x - 18x - 32 + 18 = 0

→ 4x² - 10x - 14 = 0

Take 2 as a common

→ 2(2x² - 5x - 7) = 0

→ 2x² - 5x - 7 = 0

Splitting middle term

→ 2x² - 7x + 2x - 7 = 0

→ x(2x - 7) + 1(2x - 7) = 0

→ (2x - 7)(x + 1) = 0

Either

→ 2x - 7 = 0

→ 2x = 7

→ x = 7/2

→ x = 3 ½

Or

→ x + 1 = 0

→ x = - 1

Age never in negative

• Therefore, Suma's age is 3 ½ years

Answer 2

☃ Given :-

• The sum of reciprocals of Suma's age 2 years ago and 4 years from now is 4/9.

☃ To Find :-

• Present Ages.

☃ Solution :-

Let,

Suma's Age = x.

Now,

Suma's Age before 2 years = x - 2 years.

Suma's Age after 4 years = x + 4 years.

According To The Question,

↠ 1/x - 2 + 1/x + 4 = 4/9.

↠ (x + 4) + (x-2)/(x - 2)(x + 4) = 4/9.

↠ 2x - 2/x² + 2x - 8 = 4/9.

↠ 9(2x - 2) = 4(x² + 2x - 8).

↠ 18x - 18 = 4x² + 8x - 24.

↠ 4x² - 10x - 14 = 0.

↠ 2(2x² - 5x - 7) = 0.

↠ 2x² - 5x - 7 = 0.

Use Splitting Middle Term.

↠ 2x² - 7x + 2x - 7 = 0.

↠ 2x² + 2x - 7x - 7 = 0.

↠ (2x -7)(x + 1) = 0.

So, Take One Expression.

↠ 2x - 7 = 0.

↠ 2x = 7.

↠ x = 7/2 = 3.5 = 3 ½

Take Another Expression.

↠ x + 1 = 0.

↠ x = -1.

Age Cannot be negative.

So, Suma's Age = 3.5 years.