Hi <tchtby>,

Following is my worked solution:

*** - for alignment purpose

<Before>

Fc : Fs ***** Rc : Rs

35 : 50 ***** 45 : 10

<F gave some c, s to R>

<After>

Fc : Fs ***** Rc : Rs

40 : 60 ***** 70 : 30

2 : 3 ******** 7 : 3

As this is an internal transfer, the <Unchanged Total> concept can be applied. I.e. total number of c in both F,R candy bags <before> and <after> has to be the same. Likewise , the total number of s.

Let the <After> ratios in F candy bag be part (p) qty , while that in R candy bag be unit (u) qty.

<c>

2p + 7u = 35 + 45

2p + 7u = 80 --- (1)

<s>

3p + 3u = 50 + 10

3p + 3u = 60 --- (2)

Eliminate (u) qty:

(1)x3:

6p + 21u = 240 --- (3)

(2)x7:

21p + 21u = 420 --- (4)

(4)-(3):

21p - 6p = 420 - 240

15p --> 180

1p --> 12

Number of c , s in F candy bag <After>:

= 2p + 3p

= 5p --> 5 × 12 = 60

Number of c , s in F candy bag <before>:

= 35 + 50 = 85

Gave:

85 - 60 = 25

Hence, F gave **25** chocolate bars and sweets altogether to R.

==========

Trust this helps.

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

Cheers,

Edward