Question

The sum and the difference of the reciprocal of the age of mother and daughter is 5/40 3/40 respectively. Find their ages.​

Answer 1

Let the daughter's age be X and the mother's age be Y

According to question-

since,the sum of the reciprocal of their ages is 5/40

i.e. 1/X+1/Y = 5/40...............(1)

Also,the difference of the reciprocal of their ages is 3/40

i.e. 1/X-1/Y = 3/40 ................(2)

Let 1/X=p and 1/Y=q

so,the equations (1) and (2) can be rewritten as

p+q=5/40 ...............(3)

and, p-q=3/40 ................(4)

Adding equations (3) and (4) ,we get,

2p=8/40

p=8/40×1/2

p=1/10

i.e.1/X =1/10

so,X=10

putting p=1/10 in equation (3),we get ,

1/10+q=5/40

q=1/40

i.e. 1/Y= 1/40

so, Y = 40

Thus, mother's age =Y=40 years

and, daughter's age = X = 10 years