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Worksheet: Proportional Division

Q1:

The ratio of Mariana’s, Vanessa’s and Maria’s ages is 8 6 7 . There is a 10 year age difference between Mariana and Vanessa. How old is Maria?

Q2:

The ratio among the size of the angles of a triangle is . Find the size of the greatest angle of this triangle.

  • A
  • B
  • C
  • D

Q3:

The ratio among the size of the angles of a triangle is . Find the size of the greatest angle of this triangle.

  • A
  • B
  • C
  • D

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=294 LE, B=196 LE, C=98 LE
  • BA=196 LE, B=98 LE, C=294 LE
  • CA=294 LE, B=147 LE, C=98 LE
  • DA=98 LE, B=196 LE, C=294 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 21 km, 27 km
  • B 42 km, 60 km
  • C 24 km, 30 km
  • D 14 km, 20 km
  • E 7 km, 10 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 474 m, 632 m
  • B 474 m, 1 896 m
  • C 316 m, 1 896 m
  • D 316 m, 632 m

Q7:

The total number of students in the fourth, fifth and sixth grades of an elementary school is 429. The number of students in the fourth grade equals that of the fifth. If the number of students in the fifth grade equals that of the sixth, calculate the number of students in each grade.

  • A fourth grade: 231 students, fifth grade: 77 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: 154 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.

  • A19, 32, 36
  • B14, 44, 53
  • C21, 47, 49
  • D12, 27, 30

Q9:

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

  • AWilliam’s share =44 LE, Daniel’s share =40 LE
  • BWilliam’s share =44 LE, Daniel’s share =111 LE
  • CWilliam’s share =124 LE, Daniel’s share =246 LE
  • DWilliam’s share =259 LE, Daniel’s share =111 LE
  • EWilliam’s share =259 LE, Daniel’s share =42 LE

Q10:

Noah, Matthew, and Ethan opened a grocery shop. 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 of the profit was paid as taxes, was kept as reserve, and the remainder was shared among them according to the ratio of their investments, determine each person’s profit.

  • ANoah’s share =11 270 LE, Matthew’s share =3 220 LE, Ethan’s share =9 660 LE
  • BNoah’s share =8 820 LE, Matthew’s share =2 520 LE, Ethan’s share =7 560 LE
  • CNoah’s share =9 310 LE, Matthew’s share =2 660 LE, Ethan’s share =7 980 LE
  • DNoah’s share =6 370 LE, Matthew’s share =1 820 LE, Ethan’s share =5 460 LE

Q11:

Daniel, Michael and Ethan share some money in the ratio . Twice Daniel’s share exceeds Michael’s share by 12 LE. How much money do Daniel, Michael and Ethan each have?

  • ADaniel has 48 LE, Michael has 60 LE, Ethan has 96 LE
  • BDaniel has 32 LE, Michael has 20 LE, Ethan has 32 LE
  • CDaniel has 96 LE, Michael has 60 LE, Ethan has 96 LE
  • DDaniel has 16 LE, Michael has 20 LE, Ethan has 32 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: 10 people, second class: 8 people, third class: 7 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: 120 people, second class: 96 people, third class: 84 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 34 459, 28 333, 22 666
  • B 24 519, 14 711, 11 769
  • C 32 875, 20 125, 16 300
  • D 31 875, 19 125, 15 300

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