# 6.2.4. Proportional Division

A man passed away and left behind a piece of land having an area of 80 acres. In his will, he stated that an orphanage is to be built on a part of the land and the remainder is to be distributed between his son and daughter with a ratio of . Given that the area of the orphanage is 8 acres, determine the shares of both the son and the daughter.

- A son's share acres, daughter's share acres
- B son's share acres, daughter's share acres
- C son's share acres, daughter's share acres
- D son's share acres, daughter's share acres

In order to buy school uniforms at the beginning of the school year, a father distributed LE among his sons Alaa and Atef with a ratio of . Determine their shares.

- A Alaa’s share LE, Atef’s share LE
- B Alaa’s share LE, Atef’s share LE
- C Alaa’s share LE, Atef’s share LE
- D Alaa’s share LE, Atef’s share LE

A father distributed LE among his three sons. The first one's share was the third, and the ratio between the share of the second and that of the third is , find the share of each of them.

- A the first's: 286 LE, the second's: 132 LE, the third's: 132 LE
- B the first's: 143 LE, the second's: 198 LE, the third's: 198 LE
- C the first's: 143 LE, the second's: 132 LE, the third's: 154 LE
- D the first's: 286 LE, the second's: 198 LE, the third's: 198 LE

In a village, 3 classes have been opened to end illiteracy; the number of sign ups is 300 people. The number of sign ups in the first class those in the second one. Also, the number of sign ups in the second class those in the third one. Determine the number of sign ups in each class.

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

A school has 287 students. Determine the number of both boys and girls, given that the number of the girls that of the boys.

- A number of boys , number of girls
- B number of boys , number of girls
- C number of boys , number of girls
- D number of boys , number of girls

A man passed away leaving behind a capital of LE to be distributed among his wife, 2 sons, and 5 daughters. The share of the wife is of the capital, and the share of a son is twice as a daughter’s. Calculate the share of each of the wife, a son, and a daughter.

- A The share of the wife is LE, the share of a son is LE, and the share of a daughter is LE.
- B The share of the wife is LE, the share of a son is LE, and the share of a daughter is LE.
- C The share of the wife is LE, the share of a son is LE, and the share of a daughter is LE.
- D The share of the wife is LE, the share of a son is LE, and the share of a daughter is LE.

The ratio between the side lengths of a triangular garden in a school is . Given that the perimeter of the garden is 399 meters, determine the lengths of its sides.

- A first side m, second side m, third side m
- B first side m, second side m, third side m
- C first side m, second side m, third side m
- D first side m, second side m, third side m

Three people opened a restaurant; the first paid LE, the second paid LE, and the third paid LE. At the end of the first year, the restaurant lost LE which was deducted from the capital. Calculate the capital of each person at the beginning of the second year.

- A capital of the first LE, capital of the second LE, capital of the third LE
- B capital of the first LE, capital of the second LE, capital of the third LE
- C capital of the first LE, capital of the second LE, capital of the third LE
- D capital of the first LE, capital of the second LE, capital of the third LE

Ahmed, Khaled, and Mazen started a business in which Ahmed paid LE, Khaled paid LE, and Mazen paid LE. Knowing that at the end of the year the total loss was LE, determine the losses of each one of them.

- A Ahmed: LE, Khaled: LE, Mazen: LE
- B Ahmed: LE, Khaled: LE, Mazen: LE
- C Ahmed: LE, Khaled: LE, Mazen: LE
- D Ahmed: LE, Khaled: LE, Mazen: LE

Three persons invested in a project; the first person paid 8 800LE, the second paid 2 600LE, and the third paid 3 600LE. If by the end of the year the profit of the first person exceeded that of the second one by 961LE, find the profits of the second and third persons.

- A
profit of the second1 364LE, profit of the third558LE
- B profit of the second403LE, profit of the third558LE
- C
profit of the second9 761LE, profit of the third3 561LE
- D
profit of the second403LE, profit of the third1 364LE

If 348 pounds are distributed among Hazem and Ahmed according to the ratio , determine the share of each one of them.

- AHazem’s share is 116 pounds, and Ahmed's share is 232.
- BHazem’s share is 348 pounds, and Ahmed's share is 174.
- CHazem’s share is 174 pounds, and Ahmed's share is 348.
- DHazem’s share is 232 pounds, and Ahmed's share is 116.

Find the share of each of three classes , and if the school has to divide 588 LE between them according to the ratio , respectively, to buy decorations.

- A, ,
- B, ,
- C, ,
- D, ,