Tutor MathsGuru: Ask me for your burning Maths questions!

[Vanilla Cake]

Hifive:

Hi VC's mum


Thanks for your explanation and help!

Regards

Hi Hifive,

You are welcome.Your Q18 from RGS P5 2009 SA2 Paper 2 was also discussed http://www.onsponge.com/forum/35-thinkingmathonsponge/4659-external-changed-total-change-percentage.html.

Source : RGS P5 2009 SA2 PAPER 2
Q18. Mr Muhamad has 3 cubical fish tanks of different size. The length of Tank A is twice the length of Tank B and the length of Tank B is twice the length of Tank C. Mr Muhamad filled 20% of Tank A, 35% of Tank B and 40% of Tank C with water at first. He then decided to pour all the water from Tank B and Tank C into Tank A. What percentage of Tank A is filled with water?

VC's mum

[beauty queen]

There are more pupils in School A than School B. 30% of the pupils in School A is 45 more than 40% of the pupils in School B, If 10% of the pupils in School A leaves to join School B, there will be 200 more pupils in School A than School B.

(a) How many pupils are there in School B?

(b) How many percent less pupils are there in School B than School A? Leave your answer as fraction in the simplest form

please help

[YLH88]

Vanilla Cake:

YLH88:

2) RGPS 2010 P6 Prelim paper 2 qn 18
There are more pupils in School A than School B.
30% of the pupils in School A is 45 more than 40% of the pupils in School B.If 10% of the pupils in School A leaves to join School B, there will be 200 more pupils in School A than School B.
(a) How many pupils are there in School B ? (ans : 1200)
(b) How many percent less pupils are there in School B than School A ? Leave your answer as fraction in the simplest form. (ans : 31 3/7)

30% of A = 40% of B+45
100% of A = 40/30x100% of B + 45/30x100 = 400/3% of B + 150

Remaining pupils in School A:
90% of 400/3 % of B + 90% of 150
120% of B + 135

New number of pupils in School B:
10% of (400/3%of B + 150) + 100% of B
340/3% of B + 15

120% of B + 135 = 340/3% of B + 15 + 200
20/3% of B = 80
100% of B = 80x3/20x100 = 1200

(a) Number of pupils in School B = 1200

School A -> 400/3% of B + 150 = (400/3x1200)/100 + 150 = 1750
Difference = 1750-1200 = 550
550/1750x100% = 31 and 3/7%

(b) The percent less pupils in School B than School A = 31 and 3/7%

Pls wait for Uncle Dharma/Uncle Tianzhu and others for better methods to solve this question.
Thanks.

Hi beauty queen,

The solution is posted by Vanilla Cake as per above.

Regards

[Herbie]

Hi i hv one qn. Alan has some money. After spending $10 on 3 exercise bk and 7 pencils, he is short of $0.40 if he were to buy aöther exercise bk. However, if he were to buy one more pencil, he will still hv $0.60 left. How much does an exercise bk cost? How much money does alan have? Tx

[beauty queen]

Herbie:

Hi i hv one qn. Alan has some money. After spending $10 on 3 exercise bk and 7 pencils, he is short of $0.40 if he were to buy aöther exercise bk. However, if he were to buy one more pencil, he will still hv $0.60 left. How much does an exercise bk cost? How much money does alan have? Tx

since he is short he would need $0.40 more to buy a excercise book with his remaining money. .in his remaining money if he buys a pencil he will have 0.60 left. Thus $0.60+$0.40=$1. This is the difference between the pencil and excersise book. so

$10-$3/10 = $0.70 (cost of pencil)

$0.70 + $1 = $1.70 (cost of excercise book)

$10 + $1.70 -$0.40 = $11.30 (the amount of money he has)

[firebird]

Dear maths guru


Please help me on the following maths:

1) John had $180 more than Raymond at first. Both bought a different printer with some of their money. In the end Rayamond was left with $20 more than John. If John’s printer cost 50% more than Raymond’s printer, how much does John’s printer cost?

2) At 9am John was cycling from Point A to Point B. At the same time, Mary was cycling from point B to point A using the same route as John. Cycliing at a speed of 4km/h faster than Mary, they would pass each other 300 meter away from the mid point.

a) What time did they pass each other?

b) If John took another 3 minutes to reach Point B, what time would Mary reach Poin A?

3) Daniel had 40% more stickers than Brandon. Daniel and Brandon each gave 20% of their stickers to Calvin. As a result, Calvin’s stickers increased by 80%. If Daniel has 20 more stickers than Calvin in the end, how many stickers did Brandon have at first?

4) At a conference made up of speakers and participants, there were 20% more men than women. The ratio of male speakers to female speakers was 8:5. There was an equal number of male and female participants.

a) Find the ratio of male speakers to male participants at the conference.

b) Halfway, 40 male participants left the conference and another 60 female participants joined the conference. In the end, there were 3/4 as many male participants remaining behind. How many speakers were there at the conference?

Thank you
Firebird

[Vanilla Cake]

firebird:

Dear maths guru

Please help me on the following maths:

Hi Firebird,
Pls refer to the below workings done by Vanilla Cake, this morning. Due to time constraint, she didn't complete the speed question(she was in a rush to go to school). Sorry, pls wait for others like Dharma etc to help.If you don't mind, could you pls advise the source of these questions? The ones on ratio and speed are interesting and I will let DD2 to practise.
Thks.

VC's mum

firebird:

1) John had $180 more than Raymond at first. Both bought a different printer with some of their money. In the end Rayamond was left with $20 more than John. If John's printer cost 50% more than Raymond's printer, how much does John's printer cost?

John's printer-> 150%
Raymond's printer -> 100%
$(180+20)= $200
50% -> $200
150% -> $600

Cost of John's printer = $600

firebird:

2) At 9am John was cycling from Point A to Point B. At the same time, Mary was cycling from point B to point A using the same route as John. Cycliing at a speed of 4km/h faster than Mary, they would pass each other 300 meter away from the mid point.
a) What time did they pass each other?
b) If John took another 3 minutes to reach Point B, what time would Mary reach Poin A?

0.3/4 = 0.075 h = 4.5 min
Add 4.5 min to 9 am -> 9:04:30
(a) They passed each other at 9:04:30

(b) Not enough time to think and solve, pls wait for others to solve.

firebird:

3) Daniel had 40% more stickers than Brandon. Daniel and Brandon each gave 20% of their stickers to Calvin. As a result, Calvin's stickers increased by 80%. If Daniel has 20 more stickers than Calvin in the end, how many stickers did Brandon have at first?

Before
140%
B: 100%
u

After
112%
B: 80%
u+28%+20% = u+48%

80% increased for C-> 180/100xu = 1.8u

1.8u=u+48%
0.8u=48%
u=60%

60%+48% = 108%
Difference between D and C -> D-C=112%-108% = 4%
4% -> 20
100% -> 20/4x100=500

At first, Brandon had 500 stickers.

firebird:

4) At a conference made up of speakers and participants, there were 20% more men than women. The ratio of male speakers to female speakers was 8:5. There was an equal number of male and female participants.
a) Find the ratio of male speakers to male participants at the conference.
b) Halfway, 40 male participants left the conference and another 60 female participants joined the conference. In the end, there were 3/4 as many male participants remaining behind. How many speakers were there at the conference?

This is a trick question and you have to know the common difference is 3u as the number of male and female participants was the same.

Total
M : W
120 : 100
6 : 5
18: 15

Speakers
M : W
8 : 5
Total speakers = 13u (8u+5u)

Participants
M : W
10 : 10

8: 10
(a) Ratio of male speakers to male participants = 8 : 10 = 4 : 5

I use cross multiplication to solve this, you may wish to use alternative methods to suit you.

(10u-40)/(10u+60)=3/4
30u+180=40u-160
10u=340
u=34
13u=442

Number of speakers at the conference = 442

Check
Speakers
M: 272
W: 170

Participants
M: 340
F: 340

Total
M: 612
W: 510

Phew, done except for speed part (b).Pls check all my calculations, thanks.

[Dharma]

firebird:

Dear maths guru


Please help me on the following maths:

1) John had $180 more than Raymond at first. Both bought a different printer with some of their money. In the end Rayamond was left with $20 more than John. If John's printer cost 50% more than Raymond's printer, how much does John's printer cost?

2) At 9am John was cycling from Point A to Point B. At the same time, Mary was cycling from point B to point A using the same route as John. Cycliing at a speed of 4km/h faster than Mary, they would pass each other 300 meter away from the mid point.

a) What time did they pass each other?

b) If John took another 3 minutes to reach Point B, what time would Mary reach Poin A?

3) Daniel had 40% more stickers than Brandon. Daniel and Brandon each gave 20% of their stickers to Calvin. As a result, Calvin's stickers increased by 80%. If Daniel has 20 more stickers than Calvin in the end, how many stickers did Brandon have at first?

4) At a conference made up of speakers and participants, there were 20% more men than women. The ratio of male speakers to female speakers was 8:5. There was an equal number of male and female participants.

a) Find the ratio of male speakers to male participants at the conference.

b) Halfway, 40 male participants left the conference and another 60 female participants joined the conference. In the end, there were 3/4 as many male participants remaining behind. How many speakers were there at the conference?

Thank you
Firebird

Q1)

John : (1u + $180) – (3p)
Raymond : 1u – 2p

1u – 2p = 1u + $180 – 3p + $20
1p = $200
Cost of John’s printer = 3p = $600

Q2)
a) Difference in distance travelled by John and Mary = 4km/h x T
T = 0.3km x 2/(4km/hr) = 3/20 hrs = 9 mins
Time they passed each other => 9.09am

b) For a fixed distance
Time ratio => John : Mary = 3 : 9 = 1 : 3
If John takes 12 mins to travel from A to B; Mary will take 36 mins to travel from B to A.
Mary reaches Pt A at 9.36am

Q3)

Male : Women = 6 : 5
Male speakers : Female speaker = 8 : 5
Male participants : Female participants = 1 : 1
8u + 1p/(5u + 1p) = 6/5
40u + 5p = 30u + 6p
10u = 1p
a)\tMale speakers : Male participants = 8u : 1p = 8u : 10u = 4 : 5
b) Qns is not clear and ambiguous. Kindly check.


However, if I interpret the question as ¾ of the male participants are left at the end; then the 40 participants who left form the ¼ of the male participants who left.
(The info on the 60 female participants who joined in will be redundant)¼ => 40
4/4 => 160
1p = 160
10u = 160
Total number of speakers = 13u = 13 x 16 = 208

[firebird]

Dear Vanilla cake and VC mum


Good morning

Many, many thanks for the solutions.

The speed question was from Catholic High School Prelim 2010, Section C, Question 15.

With best regards
Firebird

[Vanilla Cake]

firebird:

The speed question was from Catholic High School Prelim 2010, Section C, Question 15.

Hi firebird,
On behalf of DD1, Vanilla Cake,sorry for the mistake in the speed question.Pls refer to Dharma solution and http://psle2010a.blogspot.com/2010/09/speed-p6.html.

Dharma:

Q2)
a) Difference in distance travelled by John and Mary = 4km/h x T
T = 0.3km x 2/(4km/hr) = 3/20 hrs = 9 mins
Time they passed each other => 9.09am

b) For a fixed distance
Time ratio => John : Mary = 3 : 9 = 1 : 3
If John takes 12 mins to travel from A to B; Mary will take 36 mins to travel from B to A.
Mary reaches Pt A at 9.36am

Q3)
Male : Women = 6 : 5
Male speakers : Female speaker = 8 : 5
Male participants : Female participants = 1 : 1
8u + 1p/(5u + 1p) = 6/5
40u + 5p = 30u + 6p
10u = 1p
a) Male speakers : Male participants = 8u : 1p = 8u : 10u = 4 : 5
b) Qns is not clear and ambiguous. Kindly check.

However, if I interpret the question as ¾ of the male participants are left at the end; then the 40 participants who left form the ¼ of the male participants who left.
(The info on the 60 female participants who joined in will be redundant)¼ => 40
4/4 => 160
1p = 160
10u = 160
Total number of speakers = 13u = 13 x 16 = 208

As for the conference question, do you know the correct answer for part (b)?
Both Dharma and VC have different interpretations.

Thanks
VC mum.