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Lesson: Proportional Division

Sample Question Videos

Worksheet • 16 Questions • 2 Videos

Q1:

The ratio of Dalia’s, Amira’s and Mariam’s ages is 8 6 7 . There is a 10 year age difference between Dalia and Amira. How old is Mariam?

Q2:

The ratio among the measure of the angles of a triangle is 1 6 1 0 1 9 . Find the measure of the greatest angle of this triangle.

  • A 7 6
  • B 4 0
  • C 1 1 0
  • D 6 4

Q3:

The ratio among the measure of the angles of a triangle is 7 1 7 1 2 . Find the measure of the greatest angle of this triangle.

  • A 8 5
  • B 3 5
  • C 5 2
  • D 6 0

Q4:

A school has 588 LE to spend on decorations. The money will be divided between classes 𝐴 , 𝐵 and 𝐶 in the ratio 2 4 6 . How much money does each class get to spend on decorations?

  • AA=98 LE, B=196 LE, C=294 LE
  • BA=196 LE, B=98 LE, C=294 LE
  • CA=294 LE, B=147 LE, C=98 LE
  • DA=294 LE, B=196 LE, C=98 LE

Q5:

If the ratio between the lengths of two roads is 1 0 7 and the difference between them is 6 km, find their lengths.

  • A 14 km, 20 km
  • B 7 km, 10 km
  • C 42 km, 60 km
  • D 24 km, 30 km
  • E 21 km, 27 km

Q6:

Determine the length and the width of a rectangular piece of land whose perimeter is 1 896 m, given that the ratio between them is 1 2 .

  • A 316 m, 632 m
  • B 474 m, 1 896 m
  • C 316 m, 1 896 m
  • D 474 m, 632 m

Q7:

The total number of students in the fourth, fifth and sixth grades of a primary school is 429. The number of students in the fourth grade equals 3 2 that of the fifth. If the number of students in the fifth grade equals 7 2 that of the sixth, calculate the number of students in each grade.

  • A fourth grade: 231 students, fifth grade: 154 students, sixth grade: 44 students
  • B fourth grade: 33 students, fifth grade: 154 students, sixth grade: 44 students
  • C fourth grade: 33 students, fifth grade: 77 students, sixth grade: 319 students
  • D fourth grade: 231 students, fifth grade: 77 students, sixth grade: 44 students

Q8:

If the ratio of three numbers is 4 9 1 0 , where their sum is 69, find the value of each number.

  • A12, 27, 30
  • B14, 44, 53
  • C21, 47, 49
  • D19, 32, 36

Q9:

For school uniforms at the beginning of the school year, a mother shares 370 LE between her sons Nabil and Adam in the ratio 7 3 . How much money did each son receive?

  • ANabil’s share =259 LE, Adam’s share =111 LE
  • BNabil’s share =259 LE, Adam’s share =42 LE
  • CNabil’s share =44 LE, Adam’s share =111 LE
  • DNabil’s share =124 LE, Adam’s share =246 LE
  • ENabil’s share =44 LE, Adam’s share =40 LE

Q10:

Adel, Sameh, and Sherif opened a grocery store. They invested 14 000 LE, 4 000 LE, and 12 000 LE, respectively. At the end of the year, the profit was 18 900 LE. If 1 9 of the profit was paid as taxes, 1 6 was kept as reserve, and the remainder was shared among them according to the ratio of their investments, determine each person’s profit.

  • AAdel’s share =6 370 LE, Sameh’s share =1 820 LE, Sherif’s share =5 460 LE
  • BAdel’s share =8 820 LE, Sameh’s share =2 520 LE, Sherif’s share =7 560 LE
  • CAdel’s share =9 310 LE, Sameh’s share =2 660 LE, Sherif’s share =7 980 LE
  • DAdel’s share =11 270 LE, Sameh’s share =3 220 LE, Sherif’s share =9 660 LE

Q11:

Adam, Fady and Sherif share some money in the ratio 4 5 8 . Twice Adam’s share exceeds Fady’s share by 12 LE. How much money do Adam, Fady and Sherif each have?

  • AAdam has 16 LE, Fady has 20 LE, Sherif has 32 LE
  • BAdam has 32 LE, Fady has 20 LE, Sherif has 32 LE
  • CAdam has 96 LE, Fady has 60 LE, Sherif has 96 LE
  • DAdam has 48 LE, Fady has 60 LE, Sherif has 96 LE

Q12:

In a village, 3 classes were set up to help people learn to read. 300 people apply for the classes in total. The number of applicants for the first class is 5 4 of the number applying for the second one. The number of applicants for the second class is 8 7 of the number applying for the third one. How many people applied for each class?

  • A first class: 120 people, second class: 96 people, third class: 84 people
  • B first class: 120 people, second class: 96 people, third class: 90 people
  • C first class: 46 people, second class: 123 people, third class: 131 people
  • D first class: 10 people, second class: 8 people, third class: 7 people

Q13:

The ratio between the number of TVs produced by three factories is 2 5 1 5 1 2 . The total number of TVs produced in the first two factories combined is 51 000. How many TVs are produced in each of the factories?

  • A 31 875, 19 125, 15 300
  • B 24 519, 14 711, 11 769
  • C 32 875, 20 125, 16 300
  • D 34 459, 28 333, 22 666

Q14:

The ratio between the weights of 3 girls of different ages is 1 7 1 4 6 . If the weight of the first girl is 34 kg, find the weights of the 2 other girls.

  • A 28 kg, 12 kg
  • B 48 kg, 40 kg
  • C 41 kg, 14 kg
  • D 37 kg, 45 kg

Q15:

The ratio between the side lengths of a triangle is 8 7 6 . If the perimeter of the triangle equals 105 cm, find the length of its longest side.

Q16:

In triangle , the lengths of sides and differ by 10 cm, and the ratio of side lengths is . Calculate the length of each side and the perimeter of the triangle.

  • A , , , perimeter
  • B , , , perimeter
  • C , , , perimeter
  • D , , , perimeter
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