Question

Alan's son Daniel, is exactly one fifth of Alan's age.

In 21 years time, Alan will be exactly twice Daniel's age.

Betty's is exactly seven times the age of her daughter, Jessica.

In 8 years time, Betty will be three times the age of Jessica.

How old are Daniel and Jessica now?

Answer 1

so Daniel is of 7year and Jessica is of 4year

Answer 2

(i) Alan's son age is 1/5th of his age.
Alan is 5 time of Daniel age.

Let the present age of Daniel=x
Then, Alan's age=5x

After 21 years,
Daniel age=x+21
Alan age=5x+21
[Alan is twice of Daniel's age]
(5x+21) is 2(x+21)
5x+21=2x+42
5x-2x=42-21
3x=21--→ x=7
Daniel age= 7 years
Alan age= 5×7= 35 years

(ii) Betty is seven times the age of Jessica
Let the age of Jessica be x
Then, Betty's age=7x

After 8 years,
Jessica age=x+8
Betty age=7x+8
[Betty is thrice of Jessica's age]
(7x+8) is 3(x+8)
7x+8=3x+24
7x-3x=24-8
4x=16--→ x=4
Jessica age= 4 years
Betty age= 7×4= 28 years

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