RATE-RATIO-PROPORTION

PROBLEMS

Question1: If x:y:z=2:3:4 and 4x-2y+5z=44 are given, then

find x.

Question2:

Question3: a-1 is directly proportional to b+2. When a=5, b is 2. Then

find b when a is 9

Question4: a-3 is inversely proportional to b+3. When a is

4 b is 5. Find b when a is 5.

Question5:• The arithmetic mean of a and y is 16. The arithmetic mean of

a and z is 18 and the arithmetic mean of y and z is 24. Find the number z.

Question6:• The geometric mean of x and y is 2. The arithmetic mean of

1/x and 1/y is 3 find the arithmetic mean of x and y.

Question7:• The number of students in three classes are proportional to ½, 1/3 and ¼.

If the total number of students in three classes is 130, find the number of students in each class.

Question8:• If one can paint the wall with area 200 using 5 kg paint, what

can be the area if you use 8 kg paint?

Question9:• 3 equal taps can fill the pool with 40 in 36 hours. Using the

same type of 6 taps, in how many hours can the pool be filled?

Question10:• The sum of age of 28 people in class is 500. If the average ages

of women is 18 and the average ages of men is 20, how many women in this class?

Question11:• The average score of 3 mathematics exams of Ahmet is 80. If

the average of the first two scores is 75, what did Ahmet get in the third exam?

Question12:• If the students in the classroom sit in twos, 6 students cannot sit. If they

sit in threes, 2 desks remain empty. Using these information find the total number of students in the classroom.

Question13:• In the line of ticket office, Emine is the 8th one from the start, and Murat is

the 11th one from the end. There are 5 people between Emine and Murat and Murat is closer to the ticket office than Emine. Therefore, how many people are there in the line?

Question14:• The number of women is 3 times of the number of men. After 4 couples

get off from the bus, the number of women becomes 4 times of the number of men. Then what is the total number of people at first?

Question15:• In the exam there are 40 questions and each question is 6

points. Also, 4 wrong answers erase 1 right answer.

Question16:• The 27kg flour will be divided into packets with 2, 3 and 5 kg. The total

number of packets is 11. If one must use at least one from each packet with 2, 3, and 5 kg, at most how many packets with 2 kg can she use?

AGE PROBLEMS

Remember that:1. In t years, everyone will be t years older.

2. T years ago, everyone was t years younger.

3. The difference between the ages of two people is always constant.

4. The sum of the ages of n people will increase by n.t years in t years.

Question 1:A mother is 38 years old and her daughter is 13 years old. In how many years will the mother be twice as old as her daughter?

Question 2:The sum of the ages of two children is 30. Five years ago, one child was six years older than the other child. Find their ages now.

Question 3:The sum of the ages of three children is 27. In how many years will the sum of their ages be 67?

Question 4:A father has two sons. The father’s age now is ten times the difference of the son’s ages. Three years ago, the father’s age was three times the sum of his son’s ages. If the father is 30 now, how old are his sons?

WORK PROBLEMS

(work rate).(working time)=(amount of work done) OR r.t = w

• REMARK:1. If a number of workers can complete a job in t hours, then the same number of workers can complete of the job in one hour.2. Suppose two workers can complete a job in x and y hours respectively. If they work together, they will complete the job in t hours, where t is given by

+ =

Question 1:Mustafa can paint a house in 18 hours. Murat can paint the same house in 12 hours. If Mustafa works alone for 6 hours and then stops, how long will it take Murat to finish the job?

Question 2:Two pipes can fill a pool in 6 hours. The larger pipe can fill the pool twice as fast as the smaşller one. How long does it take the smaller pipe to fill the pool alone?

Question 3:Two pipes A and B can fill a storage tank in 4 and 6 hours respectively. A drain C can empty the full tank in 3 hours. How long will it take to fill the tank if both pipes and the drain are open?

Question 4:Two pipes A and B can fill an empty pool in 6 and 8 hours respectively. A drain C can empty the full tank in 12 hours. For two hours, the pipes A and B are left open. Then A and B are closed. How long will it take the drain C to empty the water in the pool?

Question 5:Erkin can plough a garden in 20 hours and Asım can do the same job in 32 hours. They work together for 8 hours, then Asım stops working. How long will it take Erkişn to finish the job?

Question 6:In the storage tank , the height of drain C from the base of the tank is 1/3 of the height of the tank. Pipes A and B can fill the tank in 18 hours and 24 hours respectively. Drain C can empty 2/3 of the full tank in 36 hours. If all the pipes and the drain are working, how many hours will it take the pipes to fill the tank?

A B

C

PERCENTAGE PROBLEMS

• REMARK: - b% = - b% of a number x is - If we increase a number x by b%, the result is= - If we decrease a number x by b%, the result is - =

Question 1:

• x% of 40 is 8. Find x.

Question 2: The number of workers in a factory increases from 525 to 550. Find the percentage increases in the number of workers.

Question 3: The price of a car goes up by 3%, which is $420. What is the new price of the car?

Question 4:

80% of the students in a class pass a math exam. If six students failed the exam, find the number of students in the class.

Question 5:

A shopkeeper bought a jacket and a suit from a wholesaler. He then sold the jacket for $55, which was 25% more than the wholesale price.He sold the suit for $64, which was 20% less than the wholesale price. How much money did the shopkeeper lose or earn?

• Profit-loss eklenebilir• Extended kitabında var

SIMPLE AND COMPOUND INTEREST

Simple interest:

Formulas: Annual interest:

Monthly interest:

Daily interest:

Total Amount: A= P + I

Question 1:

Esra’s investment of $950 earned $57 in 3 months. What was the monthly interest rate?

Question 2: A certain amount of money was invested with an annual interest rate of 25%. After one year, the amount increased to $2750. What was the initial principal?

Question 3: Mehmet invested a sum of money. After four years, Mehmet’s investment had doubled. What was the annual simple interest rate?

Compound Interest:

MIXTURE PROBLEMS

Remark:

Consider a solution of sugar in water which has a sugar concentration of 20%.We mean that 100 units of this solution contains 20 units of sugar and 80 units of water

Question 1:A pharmacist has 80 ml of an acid solution which contains 20% acid. How much acid should she add to the solution to make a 60% acid solution?

Question 2:64L of a salt solution contains 25% salt. How much water should be evaporated to make a 32% salt solution?

Question 3:A pharmacist has 20L of a cologne/alcohol solution containing 70% alcohol, and 60L of a cologne/alcohol solution containing 80% alcohol. The solutions are mixed. What is the percentage of alcohol in the new cologne?

Question 4:A chemist has two salt solutions containing 60% salt and 40% salt respectively. She wants to produce 50L of solution containing 46% salt. How much of each original solution should be mix?