Name : ____________________ Date : _____________
Score : _____________
Write down your correct answer and show your workings:
1) Four boys, Alex,
Bryan, Calvin and Derrick, each have some stamps.
The number of stamps Alex has is 1/2? of the total number of stamps Bryan,
Calvin and Derrick have.
The number of stamps Bryan has is 1/3? of the total number of stamps Alex,
Calvin and Derrick have.
The number of stamps Calvin has is 1/4? of the total number of stamps Alex,
Bryan and Derrick have.
If Derrick has 78 stamps, find the total number of stamps Alex and Bryan
have altogether.
2) Tom's monthly allowance
is $42 more than Eric's.
Eric spends $54 more than Tom every month.
Eric's savings is 1/2 of Tom's savings.
If Tom spends 3/7 of his allowance every month, what is his allowance for
the entire year?
3) Siti paid $8.56 for some
26-cents, 30-cents and 50-cent stamps.
She bought 4 more 30-cents stamps than 50-cent stamps.
There were twice as many 26-cent stamps as 30-cent stamps.
How many 26-cent stamps did she buy?
4) Terry walks to school
at an average speed of 4 km/h every day.
One day, after walking a distance of 1 km, he realised that his watch was
slow.
So, he ran at a constant speed and managed to reach the school just on
time.
Later, he calculated that if he had run at this speed right from the start
of the journey,
he would have reached school 5 minutes earlier.
What was his running speed?
5) Amy took 3 hours to travel
from Town P to Town Q.
Pansy took 2 hours to travel from Town Q to Town P.
Both of them started travelling at 9am.
At what time did they pass each other?
Answers:
1)
You can use ratio to solve this question.
A : B+C+D
= 1: 2
= 20: 40
B: A+C+D
= 1:3
= 15:45
C: A+B+D
=1:4
=12:48
First step is to make all the "total units" equal. So the common multiple of 3 (1+2), 4 (1+3) and 5 (1+4) is 60.
A+B = 20+15 = 35 units.
From C: A+B+D = 12:48
D = 48 - 35 = 13 units.
Since D has 78 stamps,
13 units = 78
1 unit = 6 stamps
A+B = 35 units = 35 *6 = 210 stamps.
2)
3)
4)
Time taken to walk 1 km = 1/4 hr
Let the constant speed he ran be y km/h, remaining distance
be x km
Time taken = x/y hr
Total time taken = (x/y + 1/4)hr
If he runs at this speed from beginning, time taken = (x+1) / y hr. This is 1/12 hr (or 5 min) faster.
(x+1) / y = (x/y+1/4) - 1/12
Solve this equation, the "x" will be eliminated and
y = 6 km/h
5)
In 1 hour, Amy covered 1/3 of distance.
In 1 hour , Pansy covered 1/2 of distance
In 1 hour both covered 1/3 + 1/2 = 5/6 of distance
5/6 of distance ====== 1 hour
6/6 of distance ====== 1 1/5 hour = 1 hour 12 minutes
Therefore , they passed each other at 10.12 am.
Notes:
Why calculation is based on 6/6?
As Amy and Pansy are travelling in the opposite direction, when they meet, they would have covered the total distance from P to Q. That explain the 6/6 - whole distance.