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.

## Saturday, May 09, 2009

### Rosyth Sch 2006 PSLE Math Prelim Q45

Ali, Billy and Caven had some cards. Ali would have twice as many cards as Billy if Billy gave 28 cards to Ali. Both Billy and Caven would have the same number of cards if Caven gave 84 cards to Billy. Given that Caven had 112 more cards than Ali at the beginning, find the number of cards each of them had at the beginning.

Solution

Ali ----- 2 units – 28 (at first)
Billy ----- 1 unit + 28 (at first)
Caven ----- 1 unit + 28 + 84 + 84 (at first)

At first,
(Caven) – (Ali) ---- 112
(1 unit + 28 + 84 + 84) – (2 units – 28) ----- 112
(1 unit + 196) – (2 units – 28) ----- 112
224 – 1 unit ----- 112
224 – 112 ----- 1 unit
1 unit ---- 112

Ali at first
(2 x 112) – 28 = 196

Billy at first
(112) + 28 = 140

Caven at first
(112) + 28 + 84 + 84 = 308

Anonymous said...

21 scouts crossed a river using a small boat. The boat could carry 3 scouts each time. How many times did the boat cross the river ?

Topic on Speed said...

Mr Observer's car departed from Town A and travelled towards Town B. At the same time, his colleague's car started its journey in the direction of Town A from Town B. The two cars passed each other 64 km away from Town B and carried on with their journeys. Both men made an U-turn upon arriving at their own destinations so as to return to their own towns. They passed each other this time 52 km away from Town A. Find the distance between the two places where they passed each other.

Solution:

Base on observer's reference diagram,

C met L on their first journey.
When C moved from their first meeting point and travelled a certain distance to meet L again.

Thus, C has covered 64 km + 64 km from the first meeting point to the second point.

At the second meeting point, C is 52 km away from A. Thus C has also covered 52 + 52 (double distance).

Therefore, 64 x 2 - 52 x2 = 24 km
from both meeting point.

Anonymous said...

A shopkeeper had some red and blue pens. The number of red pens was 25% of the total number of pens. After selling away 30 red pens and 30 blue pens, the number of red pens became 25% of the number of blue pens left. How many pens did he have at first?

Anonymous said...

24 Jul 09, 09:14