Rates P6 2010 Kong Hwa CA1 Q9

A group of painters is painting the classrooms. If they paint 6 classrooms per day, they will be able to complete 1 day ahead of schedule. If they paint 4 classrooms per day, they will be 2 days behind schedule. How many classrooms are there?


                            6 x 1 (1 day earlier)
                              |   |
[   ][   ][   ][   ][   ][   ]
[   ][   ][   ][   ]       |
                       |       |Number of classrooms
                       4 x 2 (need 2 more days)

2 u  -->  4 x 2  +  6 x 1  =  14

1 u  -->  14 / 2 = 7 days

7  -  1  =  6

6  x  6  =  36 classrooms

[or 7  +  2  =  9
      9  x  4  =  36 classrooms]

There were 36 classrooms.

Decimal P6 2010 Pei Hwa CA1 Q18

7 apples cost $4.00.

9 oranges cost $11.00.
James bought a total of 1000 apples and oranges for $999.00.
How many apples and how many oranges did he buy?


7 A  +  9 O  --> 1000  Use 7 A and 9 O for the number of apples and oranges respectively to avoid handling fractions or decimals

4 A  +  11 O  -->  999

28 A  +  36 O  -->  4 x 1000 = 4000

28 A  +  77 O  -->  7 x 999 = 6993

41 O  -->  6993  -  4000  =  2993

9 O  -->  9/41  x  2993  =  657 oranges

7 A  -->  1000  -  657  =  343 apples


He bought 343 apples and 657 oranges.

Percentage P6

In a primary school, 50 pupils were surveyed on the pets they liked. 80% of the pupils liked dogs, 50% of them liked birds and 34% of them liked rabbits. The survey results were that 1 out of every 5 pupils did not like any of the animals. What is the least number of pupils who liked all 3 types of animals. [Ans : 2]


1/5 x 50 =10 -- did not like pets


100% --> 50

80% --> 80/100 x 50 = 40 -- like dogs

50% --> 50/100 x 50 = 25 -- like birds

34% --> 34/100 x 50 = 17 -- like rabbits

25 + 17 - 40 = 2 pupils   Least overlap between those who like birds and rabbits

The least number of pupils who liked all 3 types of animals is 2.

Whole Number P6

Wilson purchased a certain number of wallets at $6 each. If he had purchased those at $8 each, he would have purchased 20 fewer wallets. How much money did he have? [Ans : $480]


6 : 8 = 3 : 4         Ratio of the number is inversely proportional to the price

1 u --> 20

4 u --> 4 x 20 = 80       Note: 4 u at $6 (3 u at $8) [inverse proportion]

6 x 80 = $480

He had $480. 

Percentage P6

Benny spent 15% of his salary on food and $440 on camera. Then he spent 30% of the remainder on clothes and saved the rest of his salary. He found that the amount he spent on clothes was $120 more than the amount he had spent on food.
(a) How much did he spend on food? Ans: $360
(b) How much did he save? Ans: $1120


30% r --> 15% + $120

70/30 x 15% = 35%

70/30 x 120 = $280

70% r --> 35% + $280

100% - 15% - 15% - 35% = 35%

35% --> 440 + 120 + 280 = $840

15% --> 15/35 x 840 = $360

a) He spent $360 on food.


840 + 280 = $1120

b) He saved $1120.