Number Problems
Work Problems
Twice the larger of two numbers is three more than
five times the smaller, and the sum of four times the
larger and three times the smaller is 71. What are
the numbers?
|NOV2021| An experienced roofer can roof a house
in 26 hours. A beginner roofer needs 39 hours to
complete the same job. Find how long it takes for the
two to do the job together?
The sum of the digits of a number of three digits is
15. If the digits in the hundreds and tens places are
interchanged, the number is increased by 360. The
units digit is ¼ of the sum of the hundreds and tens
places. Find the number.
|MAY2016| A contractor estimates that he could
finish the project in 15 days if he has 20 men. At the
start, he hired 10 men, then after 6 days, 10 more
men are added. How many days was the project
delayed.
Clock Problems
Mixture Problems
At what time between 2 and 3 o'clock will the hands
of the clock make an angle of 45° for the second
time?
Solution A is 50% acid and solution B is 80% acid.
How much of each should be used to make 100 cc
of a solution that is 68% acid?
Age Problems
|MAY2016| A given alloy contains 20% copper and
5% tin. How many pounds of copper and of tin must
be melted with 100 lb of the given alloy to produce
another alloy analyzing 30% copper and 10% tin. All
percentage are by weight.
The present age of Janjan's father is three times that
of Janjan. After 5 years, sum of their ages would be
70 years. Find their present age.
Tonton's father is 5 times older than Tonton and
Tonton is twice as old as his sister Yayang. In two
years' time, the sum of their ages will be 58. How old
is Tonton now?
Money Problems
A businessman increases the price of his goods by
20% due to higher operational costs. However, as
Christmas is approaching, he offers his customers a
20% discount. What percentage discount do the
customers actually received?
Motion Problems
At y am, car A began the journey from a point,
travelling at 40 mph. At 10 am another car B started
travelling from the same point at 60 mph in the same
direction as Car A. At what time will car B pass car
A?
Two pals A and B run at constant speeds along a
circumference track 1350 m in circumference.
Running in opposite directions they meet every 3
minutes, while running in the same direction they are
together every 27 minutes. Determine their speeds
in km/hr.
|NOV2017| A plane flies 465 miles with the wind and
345 miles against the wind in the same length of
time. If the speed of the wind is 20 mph, find the
speed of the plane in still air.
Variation Problems
|NOV2021| The intensity of light (in foot-candle)
varies inversely as the square of x, the distance in
feet from the light source. The intensity of light 2 ft
from the source is 80 ft-candles. How far away is the
source if intensity of light is 5 ft-candles?