**Solve proportions word problems worksheet :**

Here we are going to see some example problems of the topic solving proportions word problems.

(1) Crishtina takes 2 hours to travel 35 km. How much distance she will travel in 6 hours?

(2) If a person reads 20 pages from a book in 2 hours, how many pages will he read in 8 hours at the same speed?

(3) If 15 people can repair a road of length 150 meters, how many people are needed to repair a road of length 420 meters.

(4) The cost of 10 kg rice is $400. Find the cost of 3 kg rice?

(5) A car needs 12 litres of petrol to cover a distance of 156 km. How much petrol will be required for the car to cover a distance of 1300 km?

**Example 1 :**

Crishtina takes 2 hours to travel 35 km. How much distance she will travel in 6 hours?

**Solution :**

From the given question, we can find the ratio between number of hours that she traveled to the distance covered by her.

2 : 35

From the given information, we need to find that the distance traveled by her 6 hours.

Let "x" be the distance traveled by her.

6 : x

2 : 35 :: 6 : x

2/35 = 6/x

2 x = 6(35)

2x = 210

Divide by 2 on both sides

2x/2 = 210/2

x = 105

Hence the distance covered by Crishtina is 6 hours is 105 km.

**Example 2 :**

If a person reads 20 pages from a book in 2 hours, how many pages will he read in 8 hours at the same speed?

**Solution :**

From the given question, we can find the ratio between number of pages that she read to the number of hours she takes.

20 : 2

From the given information, we need to find that the number of pages that she read.

Let "x" be the number of hours that she takes.

x : 8

20 : 2 :: x : 8

20/2 = x/8

10 = x/8

Multiply by on both sides, we get

10(8) = (x/8)8

80 = x

Hence a person can read 80 pages in 8 hours.

**Example 3 :**

If 15 people can repair a road of length 150 meters, how many people are needed to repair a road of length 420 meters.

**Solution :**

From the given question, we can find the ratio between number of people who can repair the road to the length of road.

15 : 150

From the given information, we need to find that the number of people can repair the road of length 420 meters

Let "x" be the number of people

x : 420

15 : 150 :: x : 420

15/150 = x/420

15(420) = x(150)

Divide by 150 on both sides, we get

x = 15 (420)/150

x = 42

Hence 42 person can repair the road of length 420 m.

**Example 4 :**

The cost of 10 kg rice is $400. Find the cost of 3 kg rice?

**Solution :**

From the given question, we shall find the ratio between the quantity of rice to the cost of rice.

10 : 400

We need to find the cost of 3 kg rice.

Let "x" be the cost of rice whose wight is 3 kg.

3 : x

10 : 400 :: 3 : x

10/400 = 3/x

10(x) = 3(400)

Divide by 10 on both sides

10x/10 = 1200/10

x = 120

Hence the cost of 3 kg rice is $120.

**Example 5 :**

A car needs 12 litres of petrol to cover a distance of 156 km. How much petrol will be required for the car to cover a distance of 1300 km?

**Solution :**

From the given question, we shall find the ratio between number of liters of petrol to the distance covered by the car.

12 : 156

We need to find the number of liters of petrol

Let "x" be the quantity of petrol consuming by the car is 1300 km

x : 1300

12 : 156 :: x : 1300

12/156 = x/1300

12(1300) = x(156)

15600 = 156x

Divide by 156 on both sides

x = 15600/156

x = 100

Hence the power consumption is 100 liters.

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