1. From city A, Jamil drives a car at an average speed of 60 km/hour to the city B which is 300 km far. One hour later, Aldo drives a car following the departure of Teguh to city B. determine the average speed of Aldo’s car so he can arrive in city B at the same time as Teguh!
2. A map is made such that a distance of 8 cm represents an actual distance of 120 km. Find :
a. the scale used
b. the actual distance if the distance on the map is 18 cm, and
c. the distance on the map if the actual distance is 675 km.
3. The distance between two cities on a map scaled at 1 : 18,000,000 is 20 cm Find the distance between the two cities on a map scaled at 1: 5,000,000 !
4. A drawing of a land is scaled at 1 : 500. If the measure of the land is 22.5 cm × 12 cm, find :
a. the actual measure of the land, and
b. the ratio of its area on the
5. A square land measures 72 m x 72 m. The lands is drawn to a measure of 12 cm x 12 cm. Determine :
a. the scale used, and
b. the ratio of its area on the drawing to its actual area
6. Simplify the following ratios!
a. 18 : 72
b. 2 ½ : 1¼
c. 25 cm : 1 m
d. 200 gr : 7 kg
e. 35 minutes : 1 ½ hours
7. Find the ratio of the following pricings!
a. Rp250 per unit to Rp3,600 per dozen
b. Rp50,000 per meter to Rp800 per cm
8. An elder sister is 8 year older than her brother. If the ratio of their ages is 5 : 3, find their ages!
9. The number of students in a class is 40 people, including 18 boys. Find the ratio of :
a. the number of female students to the number of male students
b. the number of female students to the number of all students
10. The sun of
11. A factory employee receives a wage of Rp17,500 per day. Later, his wage is increased by 6/5 times the previous wage. Determine the current wage of the employee!
12. Find the values of a and p in the following proportions!
a. a : 5 = 16 : 20
b. 6 : 5 = p : 30
13. The following expressions are direct proportions. Find the values of x and y!
a. 40 : (x + 3) = 5 : 2
b. 7 : 3 = 35 : (y + 5)
14. Determine the ratio a : b : c if a : b = 7 : 4 and b : c = !
15. In the following propositions, a : b is the inverse proportion of p : q. Find the value of x if :
a. a : b = and p : q = (x +10) : 24,
b. a : b : (x + 1) and p : q = (2x + 7) : 18!
16. The ratio of two numbers is 2 : 3. If each number is added by 4, then the new ratio is 3 : 4. Find the two numbers!
17. An employee can type 380 words in 20 minutes. How many words can the employee type in 2 ½ hours?
18. In a party, 36 kg of rice in needed to serve 150 guest. How many kilograms of rice are needed to serve 125 people?
19. The bus ticket price for each 15 km is Rp1,800. What is the bus ticket price for a distance of 50 km?
20. The weight of 40 cm3 of gold is 250 grams. What is the weight of 52 cm3 of gold?
21. The cost of staying in a hotel for 7 days is Rp875,000. What is the cost of staying in the hotel for 4 days?
22. Tanti bakes some breads filled with chocolate and some breads filled with cheese. To make 18 breads filled with chocolate requires 4 kg of wheat and to make 15 breads Filled with cheese requires 3 kg of wheat. How many kg of wheat is needed if Tanti wants to bake 216 breads filled with chocolate and 135 breads filled with cheese?
23. Mr. Hamid can buy 40 books for Rp1,200 each. If by the same amount of money the wants to get 50 books, then what is the price of each book which he should buy?
24. Twenty five workers can complete a job in 54 days. How many days can the job be completed if it is done by 18 workers?
25. A landlord estimates he can provide food for 135 person for 8 days. If the food supply is exhausted in 6 days, then how many additional residents are there ?
COMPETENCY TEST CHAPTER 5
(RATIO AND PROPORTIONS)
I. For each problem numbered 1 to 5 choose the right answer!
1. The Patroness towers in
a. 0.0452 m
b. 0.452 m
c. 4.52 m
d. 45.2 m
2. A map of
a. 10 km
b. 18 km
c. 100 km
d. 180 km
3. If 2 U.S. dollars is worth the same as Rp21,000, then Rp525,000 is worth the same as …
a. 50 dollars
b. 51 dollars
c. 52 dollars
d. 53 dollars
4. Let fuel consumption of a car is 2 liters for a 25 km distance. If the distance between
a. 4 ½ liters
b. 9 liters
c. 12 ½ liters
d. 18 liters
5. If the price of 1 dozen T-shirts is Rp120,000, then the price of 1 score of T-shirt is …
6. By using a car, the distance between two cities can be traveled in 10 hours at an average speed of 60 km/hr. the time needed to travel that distance if the average speed is 75 km/hr is…
a. 7 hours
b. 8 hours
c. 9 hours
d. 10 hours
7. A job is estimated to be completed by 12 people in 1 week. If the job must be completed in 4 days, then the number of additional workers required is …
a. 3 person
b. 6 person
c. 9 person
d. 12 person
8. A poultry man has food supply for 1,000 chickens for 2 week. If the adds 400 more chickens, the food supply will be exhausted in …
a. 9 days
b. 10 days
c. 11 days
d. 12 days
9. To make 75 cakes, it requires 0.75 kg of sugar. The amount of sugar required to make 100 cakes is …
a. 1 kg
b. 1,5 kg
c. 10 kg
d. 15 kg
10. A diskette can hold 1.4 MB of data, a data CD can hold up to 700 MB. The number of diskettes that is needed the match the capacity of a CD is …
a. 500 diskettes
b. 450 diskettes
c. 50 diskettes
d. 45 diskettes
11. In 2004 Mr. Dani earned Rp2,000,000. In 2005, his salary increased by 10%. The ratio of Mr. Dani’s salary in 2004 to that in 2005 is …
a. 2 : 2,1
b. 2 : 2,2
c. 1 : 2,1
d. 1 : 2,2
12. Users of the 5 km long toll road TMI – Cawang is charged Rp1,000. The ideal toll for Cipularang toll road which is 40 km long is …
13. The sum of Hasan’s and Husen’s saving is Rp3,500,000. If the ratio of Hasan ‘s to Husen’s saving is 3 : 2, then the amount of Hasan saving is …
14. The number of students in Nusantara Junior High School is 1,500 with the ratio of the number of male students to the number of female students is 3 : 2. The number of female students who have to be added so that the number of male students equals the number of female students is …
a. 200 people
b. 250 people
c. 300 people
d. 350 people
15. A drawing of a rectangular land measures 16 cm x 10 cm. If the drawing is made to a scale of 1 : 500, then the actual area of the land is ….
a. 400 m2
b. 800 m2
c. 4,000 m2
d. 8,000 m2
II. Do the following problems in detail!
1. A dormitory has food supply for 60 people for 25 days. If its residents increased by 5 persons, then in how many days will the food supply be exhausted?
2. Based on an observation on some circles whose radial are different in length, the area of each is found as follows.
a. Find the ratio of the area to the square of radius of each circle.
b. Is the value of the ratio for a circle equal to that for another circle? Do you familiar with that value?
c. Now make a conclusion of what you know about the number p (pi)!
3. Dewi made 2 types of bread, i.e.., the bread filed with banana and the bread filled with meat. To make 20 breads filled with banana she needs 5 ounces of wheat, and to make 15 breads filled with meat she needs 4 ounces of wheat. How many ounces of wheat Dewi needs to make :
a. 140 breads filled with banana?
b. 45 breads filled with meat?
4. In a ropewalking, a female participant walked at a speed of 6 km/hr so that she could reach the finish line in 5 hours. After 2 hours of walking, she paused for 30 minutes since she suffered from a muscular spasm. In order to reach the finish line according to her initial plan, at what speed did she had to walk?
5. A contractor estimates that he can have a building construction completed in 40 days by employing 15 workers. After 12 days of works, the works is paused for 1 week since he runs out of the building materials. How many workers must he add so that the building constructions can be completed in time?