This blog is managed by Song Hock Chye, author of Improve Your Thinking Skills in Maths (P1-P3 series), which is published and distributed by EPH.

## Thursday, July 30, 2009

### Singapore Chinese Girls Sch 2008 PSLE Math Prelim Q40

The number of girls who registered for art class was 20% of the number of boys. On the actual day, 3 more girls and 3 more boys turned up for the class. As a result, there were 1/3 as many girls as boys at the art class. What was the total number of children who came to art class?

Solution

Girls 20% of boys, hence, girls 1/5 of boys

Before

Girls 1 unit
Boys 5 units

After 3 more boys and 3 more girls turned up, there were 1/3 as many girls as boys:

Girls 1 unit + 3 ----- 1 part (x3)
Boys 5 units + 3 ----- 3 parts

Girls 3 units + 9 ----- 3 parts
Boys 5 units + 3 ----- 3 parts

(Boys) 5 units + 3 ----- 3 units + 9 (Girls)
5 units – 3 units ----- 9 – 3
2 units ----- 6
1 unit ----- 3

Total number of students

Girls ---- 3 + 3 = 6
Boys ---- (5 x 3) + 3 = 18

6 + 18 = 24

Anonymous said...

A coin will have an equal chance of getting either a head or a tail when being tossed. James has 5-cents, 10-cents, 20-cents and 50-cents coins. He tossed the coins at the same time. Find the ratio of the possible outcomes of having more heads than tails to the total possible outcomes. [5 marks]

Anonymous said...

Sam went shopping at a department store. He spent 1/5 of his money on a sofa set and \$786 on a washing machine. Later, he spent 1/8 of his remaining amount on a dining table. If the amount of money left was \$86.35 more than half of the amount he had at first, how much money did Sam have at first? (5...any1 noe ans???if gt url,pls send

Car A left Town X for Town Y while Car B left Town Y for Town X and both cars left at the same time. The ratio of their respective speed is 5 : 4 initially. After they passed each other, Car A reduced its speed by 1/5 while Car B increased its speed by 20 %. When Car A reach Town Y, Car B was still 25 km away from Town X. What is the distance between Town X and Town Y?

Mr Pang’s car left Town A for Town B. Mr Freddy’s car left Town B for Town A at the same time. Initially, the ratio of the speed of both cars was 6 : 5. After both cars passed each other, Mr Pang’s car speed was reduced by 1/6 and Mr Freddy’s car speed was reduced by 25 %. When Mr Pang’s car arrived at Town B, Mr Freddy’s car was still 54 km away from Town A. Find the distance between Town A and Town B.

Anonymous said...

Mary bought some files, storybooks and assessment books. Each storybook cost \$17.50. She spent 1/9 of her money on files. The ratio of the amount spent on assessment books to the amount spent on story books is 5 : 7. The ratio of the number of files bought to the number of storybooks bought is 3 : 2. She also bought 1/2 as many storybooks as assessment books. How much did she pay for an assessment book? (5m)

Anonymous said...

Distance travelled by truck= 50 x 4 = 200 km. 4 units = 200. 9 units = 450 km. 450 - 200 = 250 km. Speed of car = 250/2 = 125. 125 - 5 = 120. 200/120 = 1 2/3 hr = 1 hr 40 mins. Thus, 1200 + 1 hr 40 mins = 1340 hr...

Anonymous said...

A car and a lorry were travelling towards Sunshine Park. When the car overtook the lorry, they were 260km away from Sunshine Park.. The car arrived at Sunshine Park 2 1/2h earlier than the lorry. When the car reached Sunshine Park, the lorry was still 100km away. Find their speeds.

Suggested solution: The lorry would need to travel another 100 km and required 2.5 hours. Speed of lorry-> 100/2.5 = 40 km/h. 260-100 = 160 km. The lorry would need 160/40 = 4 hours to travel 160 km. Speed of car-> 260/4 = 65 km/h.

Anonymous said...

When Kumar partners Bala, they take 8 days to paint a house. When Bala partners Hashim, they take 6 days to paint the house. When Hashim partners Muthu, they take 12 days to paint the house. How many days do Kumar and Muthu take to paint the house together?

Solution:

Bala + Kumar = 8 days

Bala + Halim = 6 days

From the above, we have to eliminate one of them which is Bala as Bala appeared twice.

Bala + Kumar - Bala - Halim = 8-6
Kumar - Halim = 2 days

Halim = Kumar - 2

Since Halim + Muthu = 12 days,

Replace Halim to Kumar - 2,

we will have,

Kumar - 2 + Muthu = 12 days

Thus,

Kumar + Muthu = 12 + 2
= 14 days

Anonymous said...

Curious Cat :): Therefore, the answer is 6!!!
14 Aug 09, 19:34
Curious Cat :): Common multiples: 5,10,15,20,25,30
14 Aug 09, 19:34
Curious Cat :): Nathan: 1 1/4, 2 1/2, 3 3/4, 5, 6 1/4, 7 1/2, 8 3/4, 10, 11 1/4, 12 1/2, 13 3/4, 15, 16 1/4, 17 1/2, 18 3/4, 20, 21 1/4, 22 1/2, 23 3/4, 25, 26 1/4, 27 1/2, 28 3/4, 30
14 Aug 09, 19:31
Curious Cat :): James: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30
14 Aug 09, 19:30
Curious Cat :): find the common multiples of 1min and 1 1/4 min below 30.........

Anonymous said...

P6 students: can anyone help me with one maths question? here it is:A rectangular tank is filled completely with sand.when 3/5 of it is poured into a container,the container is half full.The capacity of the container is 1.5m3 more than that of the tank. (a) Find the Height of the tank if it is 3m long and 2m wide. (b) If the remaining sand in the tank is poured out at a rate of 6m3 per minute, how long will it take to empty the tank?

Cool said...

Nicholas and Oliver started driving from the same point but in the opposite directions round a 15 km circular track. Nicholas took 10minutes to complete each round. The two drivers met each other after 6 minutes.
a) At what speed were Nicholas and Oliver driving at ? Give your answer in km/h.
(b) How many rounds would each driver have completed when they met each other at the starting point for the second time ?

Solution

(a)

10 mins = 10/60
= 1/6 hr
1/6 hr -----> 15 km
1 hr -----> 15 x 6 = 90 km

Speed of Nicholas
= 90 km/h

6 mins = 6/60
= 1/10 hr

Distance covered by Nicholas in 1/10 hr
= 90 km/h x 1/10 hr
= 9 km

Distance covered by Oliver in 1/10 hr
= 15 – 9
= 6 km

Speed of Oliver = 6 km / (1/10 hr)
= 60 km/h

Thus, Speed of Nicholas and Oliver are 90 km/h and 60 km/h respectively.

(b)

Time Nicolas Oliver
6 9 6
12 18 12
18 27 18
24 36 24
30 45 30

Number of rounds for Nicholas
= 45/15
= 3 rounds

Number of rounds for Oliver
= 30/15
= 2 rounds

From the above, we can see that Nicholas has covered 3 rounds while Oliver covered 2 rounds in order to meet the second time.

Anonymous said...

Buffet Dinner: Andy and Jackie each has some money. If Andy spends \$80 per day and Jackie spends \$40 per day, Andy will have \$550 left when Jackie has spent all his money. If Andy spends \$40 per day and Jackie spends \$80 per day, Andy will have \$1100 left when Jackie has spent all his money. Find the number of days Jackie will take to spend all his money if he spends \$40 per day. -----It's rather sad that people are taking things for granted.They couldn't be bothered to lift their fingers to search through the archives for similar types of questions but chose to wait for someone to feed them by bringing food to their mouths.Same types of questions are posted again and again.

Anonymous said...

Bad news: Good News: Ericlm's solution much more easier to understand than Observer/Dharma's method. Hooray ! ----- Is Good News another Worried Soul helping to chase away problem solvers

Anonymous said...

Bad news: Good News: Ericlm's solution much more easier to understand than Observer/Dharma's method. Hooray ! ----- Is Good News another Worried Soul helping to chase away problem solvers

Anonymous said...

Time for Change: Agreed. Time for Curious Cat and Cool to come out and help to solve Maths problem sums. Let the regulars like Observer aka Tang, Tianzhu aka Bluesky, Dharma take a break. You certainly don't enjoy eating the same old chicken rice for your lunch for 5 days a week, right ?

Cool said...

A five-digits number, A397B, is divisible by 72. A and B are different digits. Find A.

Solution

72 = 9 X 8

The number A397B can be divided by 9 and 8.

To find A, we must first find the value of B.

To be divisible by 8, choose the last 3 digits, whhich is 978. Thus, the number A397B can be re-written as follow:

A397B = A3000 + 97B

B must be 6.

To be divisible by 9, the sum of the digits number must be multiple of 9.

A + 3 + 9 + 7 + 6 = A + 25
A + 25 = 27
A = 2

Cool said...

It is a dark and stormy night. Four people must evacuate from an island to the mainland. The only link is a narrow bridge which allows passage of two people at a time. Moreover, the bridge must be illuminated, and the four people have only one lantern among them. After each passage to the mainland, if there are still people on the island, someone must bring the lantern back. Crossing the bridge individually, the four people take 2, 4, 8 and 16 minutes respectively. Crossing the bridge in pairs, the slower speed is used. What is the minimum time for the whole evacuation?

Solution

For simplicity, we can name the four people as follow,
A, B, C and D and their time,
2, 4, 8 and 16 respectively.

A = 2, B = 4, C = 8, D = 16

To have the smallest amount of time,
we let the fastest of the pair to go first.
When two persons crossed at the same time, always choose the slowest time. For instance, A + B,
2 and 4, choose 4 mins (slowest).

A + B ------> 4 mins

A -----> 2 mins

The slowest pair will go next.(Always choose the slowest time)

C + D -----> 16 mins

B -----> 4 mins

(Always choose the slowest time)

A + B -----> 4 mins

Thus,
minimum time taken
= 4 + 2 + 16 + 4 + 4
= 30 minutes

Anonymous said...

If Ahmad and Ben work together, they can complete a job in 12 days. If Ahmad and Ben worked together for 3 days, followed by Ben who worked alone for the next 5 days, they can finish of the job. How many days will each of them need to complete the job if they were to work alone?

A certain number of chairs can be arranged such that there are exactly 13 chairs per row. If the same number of chairs is arranged in rows of 10 chairs each, there will be 5 more rows and 4 chairs left over. How many chairs are there altogether?

Anonymous said...

HELP NEEDED!!! URGENT!: Tommy and Wilson jog on a hexagon track (6 equal sides) at 8am. Tommy starts at Point C while Wilson starts at point F. Both jog in the direction as shown by the arrows. Tommy's speed is 1.5 times Wilson's. (a) At which point will they meet? (b) If they meet at 8.20am, find Tommy's speed.