hey Rohana,

Following pls find my worked solutions:

Q1

<1 B stands up>

<seated>

B : G

4 : 5

<1 G stands up>

<seated>

B : G

7 : 8

In both cases, the number of B and G seated remains the same. Applying <unchanged total> concept for these two ratios, we have ...

B : G Total

4 : 5 9 -- (1)

B : G Total

7 : 8 15 -- (2)

Lowest common multiple is 45. Hence, Multiply (1) 5x, and (2) 3x. We have ...

B : G Total

20 : 25 45 -- (3)

B : G Total

21 : 24 45 -- (4)

Hence, number of B and G in class = 45 + 1 = **46**

==============

Q2

F |-----|-----|-----|-----|-----|

G |-----|-----|-----|-----|

E |-------|

Total: 320

<process>

E, F each lost 1/2 of their marbles.

Split the 5 parts of F into 10 equal units(u) (i.e.each part of F = 2u ).

Likewise, the 4 parts that G had = 8u.

Of these 10u that F had, 5u were lost.

Lost = 5u of F + (1/2)p of E = 100 {320 - 220}

Hence, the <after> model ...

<After>

F |--|--|--|--|--|

G |--|--|--|--|--|--|--|--|

E |---|

Total: 220

<after>:

5u of F and (1/2)p of E = 100 {same as Lost qty}

So, 8u (G) --> 220 - 100 = 120

1u --> 15

F + G (after) = 13u --> 13 × 15 = 195

Hence, E (after) = 220 - 195 = 25

E (at first) = 25 × 2 = **50**

============

Trust the above helps.

Do let me know again if these are different from your Answerkey or if there's further clarification.

Cheers,

Edward