Hi <Tping>,

Following is my worked solution:

*** - for alignment purpose

Both <If> cases are 'internal transfer' processes; hence, we can apply the <Unchanged Total> concept to the ratios of monies left after the transfer / exchange. I.e. the total units of monies of J, K in the two ratios from the two <If> cases are the same.

<If J gave K $40>

J : K ** Total

1 : 2 **** 3 -- (1)

<if K gave J $40>

J : K ** Total

3 : 1 **** 4 -- (2)

Applying <Unchanged Total> concept, multiply (1) 4x, (2) 3x as shown:

<If J gave K $40>

J : K ** Total

4 : 8 *** 12 -- (3)

<if K gave J $40>

J : K ** Total

9 : 3 *** 12 -- (4)

<Before>

from (3), J = 4u + 40 -- (5)

from (4), J = 9u - 40 -- (6)

As (5)=(6), we can equate these.

4u + 40 = 9u - 40

9u - 4u = 40 + 40

5u --> 80

1u --> 16

from (3), K = 8u - 40

Difference in monies between J, K:

J - K = 4u + 40 - (8u - 40)

= 4u + 40 - 8u + 40 = 80 - 4u

80 - 4u --> 80 - (4 × 16) = 80 - 64

= **$16**

An alternative method that can also be used is the <Simultaneous> method, as shown in my other previous worked solutions.

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Trust this helps.

Do let me know again if there's further clarification.

Cheers,

Edward