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In this lesson, we will learn how to solve problems about proportional division.

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.

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.

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?

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.

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 .

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.

Q8:

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

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?

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.

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?

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?

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?

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.

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.

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