# 4. (A). It takes 3 liters of paint to cover an area of 24 square meters. What percentage increase in the quantity of paint would be required to cover an area of 50.4 square meters? (B). An automobile travels 3 km towards south, 4 km towards west, 5 km towards north and 2 km towards south-east. How far is it from its starting position?

## (C). Tahir started a business with a capital of Rs. 15,000. After 5 months Umar also joined him with an investment of Rs. 30,000. At the start of 9th month, Usman joined them by investing Rs. 45,000. At the end of the year they earned a profit of Rs. 406,000. Find the share of each one. (D). A man left his property of Rs. 640,000. A debt of Rs. 40,000 was due to him and Rs. 5,000 was spent on his burial. Distribute the amount between his widow, one daughter and two sons according to the Islamic Law.

**A. To cover an area of 50.4 square meters, the quantity of paint required would be**:

Quantity of paint required for 24 square meters = 3 liters Quantity of paint required for 1 square meter = 3/24 = 0.125 liters

Quantity of paint required for 50.4 square meters = 0.125 x 50.4 = 6.3 liters

The percentage increase in the quantity of paint required would be:

Increase in quantity of paint required = 6.3 – 3 = 3.3 liters Percentage increase = (Increase/original) x 100 Percentage increase = (3.3/3) x 100 Percentage increase = 110%

Therefore, a 110% increase in the quantity of paint is required to cover an area of 50.4 square meters.

**B. To find the distance from the starting position, we can use Pythagoras’ theorem**.

The automobile travels 3 km towards south, 4 km towards west, 5 km towards north and 2 km towards south-east. Let’s break this down into its components:

South: -3 km West: -4 km North: +5 km South-east: -2 km towards south and +2 km towards east, which can be broken down into -1.4 km towards south and +1.4 km towards east (using Pythagoras’ theorem)

Total distance travelled towards south = -3 km – 2 km = -5 km Total distance travelled towards west = -4 km Total distance travelled towards north = +5 km Total distance travelled towards east = +1.4 km

Using Pythagoras’ theorem, the distance from the starting position is:

Distance = √((-5)^2 + (-4)^2 + 5^2 + 1.4^2) Distance = √(25 + 16 + 25 + 1.96) Distance = √67.96 Distance ≈ 8.24 km

Therefore, the automobile is about 8.24 km from its starting position.

**C. To find the share of each person, we need to calculate the total profit and then divide it among the partners based on their investment and the duration of their investment**.

Total investment = 15000 x 12 + 30000 x 7 + 45000 x 4 = 654000 Tahir’s share = 15000 x 12 / 654000 x 406000 = Rs. 93,120 Umar’s share = 30000 x 7 / 654000 x 406000 = Rs. 81,960 Usman’s share = 45000 x 4 / 654000 x 406000 = Rs. 97,920

Therefore, Tahir’s share is Rs. 93,120, Umar’s share is Rs. 81,960, and Usman’s share is Rs. 97,920.

**D. According to Islamic Law, the distribution of the inheritance is as follows**:

Widow = 1/8 of the total amount Daughter = 2/3 of the remaining amount after the widow’s share Each son = 1/3 of the remaining amount after the widow’s share

Total amount = Rs. 640,000 Amount due to the debt = Rs. 40,000 Amount spent on burial = Rs. 5,000 Amount available for distribution = Rs. 595,000

Widow’s share = 1/8 x 595,000 = Rs. 74,375 Remaining amount = 595,000 – 74,375 = Rs.