Master Plumber Review – July 2023
Email Add: cgdreview.cebu@gmail.com
Contact number: 0945-280-7131
MODULE 3: PLUMBING ARITHMETIC
Number Problems
His age 7 years hence is x + 7
Total Work done by two people:
Principles in Number Problems
Let x be the first number and y be the second number,
First number is twice the other: x = 2y
First number is five more than thrice the other: x = 3y + 5
First number is six less than half the other: x = y/2 – 6
The sum of their squares is 8: 𝑥 2 + 𝑦 2 = 8
The cube of their difference is 3: (𝑥 − 𝑦)3 = 3
The sum of the two numbers is 15: x + y = 15
 Problem 1
One number is five less than the other number. If their sum
is 135, what are the numbers?
 Problem 2
The difference between two numbers is 24 and their sum is
60. Find the bigger number.
Digit Problems
 Problem 5
Peter’s age 13 years ago was 1/3 of his age 7 years hence.
How old is Peter?
 Problem 9
A pump can pump out a tank in 11 hours. Another pump can
pump out the same tank in 20 hours. How long will it take
both pumps together to pump out the tank?
 Problem 6
A father is three times as old as his son. Four years ago, he
was four times as old as his son was at that time. How old is
his son?
 Problem 10
Mr. Brown can wash his car in 15 minutes, while his son John
takes twice as long to do the same job. If they work together,
how many minutes can they do the washing?
Mixture Problems
Clock Problems
Principles in Mixture Problems
The easiest way to solve a mixture problem is to draw a
rectangle or square which will illustrate the content of the
mixture.
Principles in Clock Problems
Let: x = hundred’s digit; y = ten’s digit; z = unit’s digit
The number is: 100x + 10y +z
The reversed number is: 100z + 10y + x
The sum of the digits is: x + y +z
 Problem 3
In a two – digit number, the unit’s digit is 3 greater than the
ten’s digit. Find the number if its 4 times as large as the sum
of the digits.
 Problem 4
The sum of the digits of a three – digit number is 14. The
hundreds digit being 4 times the units digit. If 594 is
subtracted from the number, the order of the digits will be
reversed. Find the number.
Age Problems
Principles in Age Problems
The difference of the ages of two persons is constant.
If x is the age of Peter now:
His age 5 years ago is x – 5
65%
gasoline
35% alcohol
10 L
15 L
100%
mixture
25 L
 Problem 7
Two thousand (2000) kg of steel containing 8% nickel is to be
made by mixing a steel containing 14% nickel with another
steel containing 6% nickel. How much of the steel containing
14% nickel is needed?
 Problem 8
A 40 – gram alloy containing 35% gold is to be melted with a
20 – gram alloy containing 50% gold. How much percentage
of gold is the resulting alloy?
Work Problems
Principles in Work Problems
Work = Rate x time
𝑅𝑎𝑡𝑒 =
1
𝑡𝑖𝑚𝑒 𝑡𝑜 𝑓𝑖𝑛𝑖𝑠ℎ 𝑡ℎ𝑒 𝑤𝑜𝑟𝑘
Principles in Probability
Probability is the likelihood that an event will occur
expressed as the ratio of the number of favorable outcomes
in the set of outcomes divided by the total number of possible
outcomes.
Single Event
𝑃=
𝑁𝑜. 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑤𝑎𝑦𝑠
𝑇𝑜𝑡𝑎𝑙 𝑁𝑜. 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠.
Probability of success: 𝑝 =
Probability of failure: 𝑝 =
Principles in Digit Problems
For a three – digit number,
 Problem 12
How many minutes after 10:00 o’clock will the hands of the
clock be opposite each other for the first time?
1 1
+ =1
𝑥 𝑦
11
12
30°
10
a.) Dependent Events
Two or more events are said to be dependent if the happening
of one affects the probability of the happening of others.
2
3
9
8
x/12
4
7
6
ℎ+𝑓
Multiple Events:
x
1
ℎ
ℎ+𝑓
𝑓
b.) Independent Events
Two or more events are said to be independent if the
happening of one does not affect the probability of the
happening of the others.
5
If the minute hand moves a distance x, the hour hand moves
a distance of x/12.
In 12 hours, the minute – hand and the hour – hand of the
clock overlap each other for 11 times (not 12 times). So in one
day, they will be together 22 times.
Each five – minute mark subtends an angle of 30° from the
center of the clock.
The probability of happening of two or more independent
events is the product of their individual properties.
𝑃 = 𝑃1 𝑥 𝑃2 𝑥 𝑃3 𝑥 … …
Two or more events are said to be Mutually Exclusive if it is
impossible for more than one of them to happen in a single
trial.
The probability that some one, two or more mutually
exclusive events to happen is the sum of their individual
probabilities.
𝑃 = 𝑃1 + 𝑃2 + 𝑃3 + ⋯
 Problem 11
How many minutes after 2 o’clock will the hands of the clock
be perpendicular for the first time?
Master Plumber Review – July 2023
Email Add: cgdreview.cebu@gmail.com
Contact number: 0945-280-7131
MODULE 3: PLUMBING ARITHMETIC
 Problem 13
For a single question in the board exam, there are four choices
and only one of which is correct. By guessing, what is the
probability that you will get the correct answer?
 Problem 14
A box contains 4 blue chips and 5 red chips:
a.) If one chip is drawn at random, what is the probability that
it is blue?
b.) If two chips are drawn at random, what is the probability
that both are red?
c.) If two chips are drawn at random, what is the probability
that one is blue and the other is red?
Practice Problems
1.) China, the United States, and Russia are the countries
with the most cellular subscribers in the world. Together,
the three countries have 34.8% of the world cellular
subscribers. If the percent of the world subscribers in China
is 3.1% less than 4 times the percent of the world
subscribers in Russia, and the percent of the world
subscribers in The United States is 4.3% more than the
percent of the world subscribers in Russia, find the percent
of world subscribers for each country.
Answer: Russa = 5.6%, China = 19.3%, USA = 9.9%
2.) If 3 is subtracted from the numerator of a certain
fraction, the value of the fraction becomes 3/5. If one is
subtracted from the denominator of the same fraction, the
value of the fraction becomes 2/3. Find the original fraction.
Answer: 36/55
3.) The sum of three numbers is 51. If the first number is
divided by the second, the quotient is 2 and the remainder is
5, but if the second number is divided by the third, the
quotient is 3 and the remainder is 2. Find the smallest of the
three numbers.
Answer: 4
4.) The larger of the two numbers is 5/2 the smaller. If twice
the smaller is subtracted from twice the larger, the
difference is 12. Find the smaller integer.
Answer: 4
5.) The numerator of a fraction is 3 less than the
denominator. If the numerator and denominator are
increased by 1, the value of the fraction is ¾. What is the
original fraction?
Answer: 8/11
6.) The sum of Kim’s and Kevin’s ages is 18. In 3 years, Kim
will be twice as old as Kevin. What are their ages now?
Answer: Kevin = 5 yrs. old, Kim = 13 yrs. old
Answer: 47
7.) JJ is three times as old as Jan – Jan. Three years ago, JJ was
four times as old as Jan – Jan. The sum of their ages is _____.
Answer: 36
16.) A tank can be filled in 9 hours by one pipe, 12 hours by a
second pipe and can be drained when full by a third pipe in
15 hours. How long will it take to fill an empty tank with all
pipes in operation?
Answer: 7 hours & 50 minutes
8.) Six years ago, Nilda was five times as old as Riza. In five
years, Nilda will be three times as old as Riza. What is the
present age of Riza?
Answer: 17 yrs. old
17.) Mike, Loui and Joy can mow the lawn in 4, 6 and 7 hours
respectively. What fraction of the yard can they mow in 1
hour if they work together?
Answer: 47/84
9.) A father tells his son, “I was your age now when you were
born.” If the father is now 38 years old, how old was his son
2 years ago?
Answer: 17 yrs. old
18.) A and B working together can finish painting a house in
6 days. A working alone can finish it in 5 days less than B.
How long will it take for each of them to finish the work
alone?
Answer: A = 10 days, B = 15 days
10.) Ten liters of 25% salt solution and 15 liters of 35% salt
solution are poured into a drum originally containing 30
liters of 10% salt solution. What is the percent concentration
of salt in the mixture?
Answer: 19.55%
11.) A chemist of a distillery experimented on two alcohol
solutions of different strength, 35% alcohol and 50%
alcohol, respectively. How many cubic meters of each
strength must he use in order to produce a mixture of 60
cubic meters that contains 40% alcohol?
Answer; 40 m^3 of solution with 35% alcohol, 20 m^3 of
solution with 50% alcohol
12.) A goldsmith has two alloys of gold, the first being 70%
pure and the second being 60% pure. How many ounces of
the 60% pure gold must be used to make 100 ounces of an
alloy which will be 66% gold?
Answer: 40 ounces
13.) The tens digit of a certain 2 digit number exceeds the
units digit by four and is one less than twice the units digit.
Find the units digit.
Answer: 5
14.) A number is expressed by 3 digits, which are in
arithmetical progression. If the number is divided by the
sum of the digits, the quotient will be 26 and if 198 be added
to the number, the digits will be reversed. Find the ten’s
digit.
Answer: 3
15.) The ten’s digit of a number is 3 less than the unit’s digit.
If the number is divided by the sum of the digits, the
quotient is 4 and the remainder is 3. What is the original
number?
19.) It takes Myline twice as long as Jeana to do a certain
piece of work. Working together, they can finish the work in
6 hours. How long would it take Jeana to do it alone?
Answer: 9 hours
20.) A farmer can plow the field in 8 days. After working for
3 days, his son joins him and together they plow the field in
3 more days. How many days will it require for the son to
plow the field alone?
Answer: 12 days
21.) In how many minutes after 2 o’clock will the hands of
the clock extend in opposite directions for the first time?
Answer: 43.6 minutes
22.) In how many minutes after 7 o’clock will the hands of
the clock be directly opposite each other for the first time?
Answer: 5.45 minutes
23.) What time after 3 o’clock will the hands of the clock be
together for the first time?
Answer: 3:16.36’
24.) At what time after 12:00 noon will the hour hand and
minute hand of the clock first form an angle of 120°?
Answer: 12:21.818’
25.) From the time 6:15 PM to the time 7:45 PM of the same
day, the minute hand of a standard clock describe an arc of
____.
Answer: 540°
26.) Roll a pair of dice. What is the probability that the sum
of the two numbers is 11?
Answer: 1/18
27.) Roll two dice once. What is the probability that the sum
is 7?
Answer: 1/6
28.) In a throw of two dice, the probability of obtaining a
total of 10 or 12 is _______.
Answer: 1/9
29.) Determine the probability of drawing either a king or a
diamond in a single draw from a pack of 52 playing cards.
Answer: 4/13
30.) A card is drawn from a deck of 52 playing cards. Find
the probability of drawing a king or a red card.
Answer: 0.5385
Master Plumber Review – July 2023
MODULE 3: PLUMBING ARITHMETIC
Email Add: cgdreview.cebu@gmail.com
Contact number: 0945-280-7131