# Directly Proportional – Explanation & Examples

## What does Directly Proportional Mean?

Direct proportion is the relationship between two variables whose ratio is equal to a constant value. In other words, direct proportion is a situation where an increase in one quantity causes a corresponding increase in the other quantity, or a decrease in one quantity results in a decrease in the other quantity.

Sometimes, the word proportional is used without the word direct, just know that they have a similar meaning.

## Directly Proportional Formula

Direct proportion is denoted by the proportional symbol (∝). For example, if two variables x and y are directly proportional to each other, then this statement can be represented as x ∝ y. When we replace the proportionality sign (∝) with an equal sign (=), the equation changes to:

x = k * y or x/y = k, where k is called non-zero constant of proportionality

In our day-to-day life, we often encounter situations where a variation in one quantity results in a variation in another quantity. Let’s take a look at some of the real-life examples of directly proportional concept.

• The cost of the food items is directly proportional to the weight.
• Work done is directly proportional to the number of workers. This means that, more workers, more work and les workers, less work accomplished.
• The fuel consumption of a car is proportional to the distance covered.

Example 1

The fuel consumption of a car is 15 liters of diesel per 100 km. What distance can the car cover with 5 liters of diesel?

Solution

• Fuel consumed for every 100 km covered = 15 liters
• Therefore, the car will cover (100/15) km using 1 liter of the fuel

If 1 liter => (100/15) km

• What about 5 liters of diesel

= {(100/15) × 5} km

= 33.3
Therefore, the car can cover 33.3 km using 5 liters of the fuel.

Example 2

The cost of 9 kg of beans is $166.50. How many kgs of beans can be bought for$ 259?

Solution

• $166.50 = > 9 kg of beans • What about$ 1 => 9/166.50 kg
Therefore the amount of beans purchased for $259 = {(9/166.50) × 259} kg • =14 kg Hence, 14 kg of beans can be bought for$259

Example 3

The total wages for 15 men working for 6 days are $9450. What is the total wages for 19 men working for 5 days? Solution Wages of 15 men in 6 days =>$ 9450
The wage in 6 days for 1 worker = >$(9450/15) The wage in 1 day for 1 worker =>$ (9450/15 × 1/6)
Wages of 19 men in a day => $(9450 × 1/6 × 19) The total wages of 19 men in 5 days =$ (9450 × 1/6 × 19 × 5)
= $9975 Therefore, 19 men earn a total of$ 9975 in 5 days.

### Practice Questions

1. If the total daily wages of 7 women or 5 men is $525.What will be the daily wage of 13 and 7 women and men respectively? 2. The fuel consumption of a vehicle is 6.8L/102km. What distance can this vehicle cover in 24 liters of fuel? 3. The cost of ferrying 160 bags of cement for 125 km is Rs. 60. What will be the cost of ferrying 200 bags for 400 km? 4. The wages for 12 men working for 5 days are$7500. Calculate the wages of 17 men working for 6 days.
5. The cost 16 bars of soap each weighing 1.5 kilogram is $672.Calculate the cost of 18 similar bars of soap each weighing 2 kilograms. 6. The drawing scale of a map is represented as 1:20000000. Calculate the actual distance of two regions that are 4 cm apart on the map. 7. A 7-meter flag post casts a shadow of 5 meters. Calculate the height of an electric pole that will cast a shadow of 10 m under the same condition. 8. A train takes 5 hours to cover 200 km. How long will it take to cover 600 km? 9. If the cost of 16 bars of chocolate each weighing 900 g is$84. Find the cost of 27 bars of chocolate each weighing one kilogram.
10. If the daily wages of four women and three men is $480. Calculate the daily wages of seven and eleven men and women respectively. ### Answers Key 1.$ 1710
2. 363 km
3. $240 4.$ 12750
5. $1008 6. 800 km 7. 14 meters 8. 15 hours 9.$ 157.50.
10. \$ 2440.