Quote by: echeewhHello Tping,

Following pls find my worked solution:

Q1

Given that apples and oranges were moved from Box B to Box A, this infers an <Internal Transfer - Unchanged Total> concept. In other words, total number of Apples (A) in boxes A,B are the same before and after. Likewise, the total number of Oranges (Or).

<Before>

Total Apples (A) = 225 + 260 = 485

Total Oranges (Or) = 253 + 212 = 465

<process>

A and Or were moved from Box B to Box A.

<After>

Box A:

A : Or

40 : 60

2 : 3

Box B:

A : Or

70 : 30

7 : 3

Apply <Unchanged Total> concept here, we have ...

2p + 7u --> 485 -- (1)

3p + 3u --> 465 -- (2)

Eliminating (p) qty, we do the following:

(1)x3:

6p + 21u --> 1455 -- (3)

(2)x2:

6p + 6u --> 930 -- (4)

(3)-(4):

21u - 6u --> 1455 - 930

15u --> 525

1u --> 35

Box B (after):

7u (A) --> 7 × 35 = 245

3u (Or) --> 3 × 35 = 105

Number of fruits in Box B (before):

260 + 212 = 472

Number of fruits in Box B (after):

245 + 105 = 350

Hence, number of fruits moved from Box B:

472 - 350 = **122**

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Q2

<after>

A : B

60 : 100

3 : 5

<process>

A: -46.5ml

<before>

A: 3p + 46.5

B: 5p

<process1>

B: -35.2ml

<after1>

A: 3p + 46.5

B: 5p - 35.2

Given that volume of water in Beaker B will be 85% that of the water in Beaker A, we have ...

A : B

100 : 85

20 : 17

From these, we have ...

3p + 46.5 = 20u

5p - 35.2 = 17u

Rearranging these,

20u - 3p --> 46.5 -- (1)

5p - 17u --> 35.2 -- (2)

Eliminating (u) qty, multiply (1) 17x; (2) 20x;

(1)x17:

340u - 51p --> 790.5 -- (3)

(2)x20:

100p - 340u --> 704 -- (4)

(3)+(4):

100p - 51p --> 790.5 + 704

49p --> 1494.5

1p --> 30.5

Total volume in A,B (before):

8p + 46.5 --> [8 × 30.5] + 46.5

= **290.5** ml

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Trust you find these useful.

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

Cheers,

Edward