Question

the sum of the reciprocals of Rehman's ages 3yrs ago and 5yrs from now is 1/3 . find his present age ?​

Answer 1

Answer:

Let the present age of Rehman =x

3 years ago Rehman’s age =(x–3) years

5 years later Rehman’s age =(x+5) years.

Now, according to the condition,

(x–3)

1

+

(x+5)

1

=

3

1

(x–3)(x+5)

(x+5+x–3)

=

3

1

(x

2

–3x+5x–15)

(2x+2)

=

3

1

x

2

+2x–15=6x+6

x

2

–4x–21=0

(x+3)(x–7)=0

Either,x+3=0 Or, x–7=0

Thus, x=7 or –3; but age cannot be negative.

Hence the present age of Rehman is 7 years

Answer 2

Step-by-step explanation:

Let the present age of Rehman =x

3 years ago Rehman’s age =(x–3) years

5 years later Rehman’s age =(x+5) years.

Now, according to the condition,

(x–3)

1

+

(x+5)

1

=

3

1

(x–3)(x+5)

(x+5+x–3)

=

3

1

(x

2

–3x+5x–15)

(2x+2)

=

3

1

x

2

+2x–15=6x+6

x

2

–4x–21=0

(x+3)(x–7)=0

Either,x+3=0 Or, x–7=0

Thus, x=7 or –3; but age cannot be negative.

Hence the present age of Rehman is 7 years.