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Answer: Daniel is 7 years old and Jessica is 4 years old.

The first half of the question involves Daniel (D) and Alan (A).

Daniel is currently one fifth of Alan's age, so:

A = D x 5 (1)

In 21 years time, Alan will be twice his age, so:

A + 21 = (D + 21) x 2 (2)

Using (1) in (2) gives:

A + 21 = (D + 21) x 2

5D + 21 = (D + 21) x 2

5D + 21 = 2D + 42

3D = 21

D = 7

So Daniel is 7 (and Alan is 35).

The second half of the question involves Jessica (J) and Betty (B).

Betty's is exactly seven times the age of Jessica:

B = J x 7 (3)

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

B + 8 = (J + 8) x 3 (4)

Using (3) in (4) gives:

B + 8 = (J + 8) x 3

7J + 8 = (J + 8) x 3

7J + 8 = 3J + 24

4J = 16

J = 4

So Jessica is 4 (and Betty is 28). QED.

Puzzle 4

Using the BrainTracker grid below, how many words can you find? Each word must contain the central P and no letter can be used twice, however, the letters do not have to be connected. Proper nouns are not allowed, however, plurals are. Can you find the nine letter word?