Red Swastika Sch 2011 PSLE Math Prelim Paper 2 Q10

Katelyn had some green, red and blue ribbons. She had 25% more green ribbons than red ribbons and 20% less blue ribbons than red ones.

a) What is the ratio of red ribbons to green ribbons to blue ribbons?

b) Katelyn exchanges all her blue ribbons for some red and green ribbons. She now has an equal number of red and green ribbons. How many more green than red ribbons did she have at first if she has 244 red ribbons now?

Solution

(a)
Red ----- 100%
Green ----- 25% more than 100% = 125%
Blue ----- 20% less than 100% = 80%

Red : Green : Blue
100 : 125 : 80
20 : 25 : 16

Answer: 20 : 25 : 16

(b)
Before Katelyn exchanges,
Red : Green : Blue
20 : 25 : 16

Blue exchanged for green and red will mean that 16 units of blue will be given up. Since Katelyn finally has an equal of number red and green, 5 units of the 16 units of blue will be exchanged for red first, with the remaining 11 units divided equally between red and green.  

Red will receive ----- 5 units + (11 units divided by 2) = 10.5 units
Green will receive ----- 11 units divided by 2 = 5.5 units

Red ribbons now ----- 20 units + 10.5 units = 30.5 units
30.5 units ----- 244
1 unit ---- 244 divided by 30.5 = 8

In the beginning,
Green - Red
25 units - 20 units = 5 units
5 units ----- 5 x 8 = 40

Answer: 40 red ribbons 
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Red Swastika Sch 2011 PSLE Math Prelim Paper 2 Q8

The ratio of the number of apples in Box A to the number of apples in Box B is 3 : 2. All the apples in Box B are green. The ratio of the number of green to the number of red apples in Box A is 4 : 5. There are 20 more green apples in Box B than in Box A. How many red apples are there?

Solution

* 4 units of green apples + 5 units of red ---- 9 units in Box A
** 3 units in Box A (x 3) ---- 9 units, hence 2 units in Box B (x 3) will give 6 units.  

Green Apples
Box B - Box A ----- 20
6 units - 4 units ----- 20
2 units ----- 20
1 unit ----- 20 divided by 2 = 10

Red Apples
5 units ----- 5 x 10 = 50

Answer: 50 red apples

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Maths Q from a reader

A reader emailed me this question and I am too busy to solve it for him. Could readers please help him by posting the solution in the comments section. Thank you.

Mr Lim spent 885 on honey stars and pies. He spent 471 more on pies than on honey stars. The ratio of the number of packets of pies to the number of honey stars is 8:3. Each packet of pie is 0.45 more than honey stars. How many packets of honey stars did he buy?

Rosyth School 2011 CA1 Math Paper 2 Q17

Farmer Dan harvested some apples. He sold to Adam 3/4 of the apples and another 105 apples. He sold to Geraldine 3/4 of the remainder but took back 55 apples. Farmer Dan had 890 apples left.

a) How many apples did Geraldine have after returning 55 apples to Farmer Dan?

b) How many apples did Farmer Dan harvest?

Solution

1/4 of remaining ----- 890 – 55 = 835

3/4 of remaining ----- 3 x 835 = 2505

a) Geraldine ----- 2505 - 55 = 2450

b) 1 unit ----- 4/4 of remaining + 105

4/4 of remaining ----- 835 x 4 = 3340

1 unit ----- 3340 + 105 = 3445

(Total harvested) 4 units ----- 4 x 3445 = 13 780

Answer: a) 2450 apples b) 13 780 apples.

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