Worksheet given in this section will be much useful for the students who would like to practice solving word problems on proportions.

**Problem 1 :**

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

**Problem 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 ?

**Problem 3 :**

If 15 people can repair a road of length 150 meters, at the same rate, how many people are needed to repair a road of length 420 meters ?

**Problem 4 :**

If the cost of 10 kg rice is $400, then find the cost of 3 kg rice.

**Problem 5 :**

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

**Problem 1 :**

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

**Solution :**

The ratio between number of hours and distance traveled is

2 : 35 -----(1)

Let 'x' be the distance traveled by her in 6 hours.

Then,

6 : x -----(2)

From (1) and (2),

2 : 35 = 6 : x

2(x) = 6(35)

Divide each side by 2.

x = 6(35) / 2

x = 3(35)

x = 105

So, the distance covered by Crishtina in 6 hours is 105 km.

**Problem 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 :**

The ratio between number of pages and time taken

= 20 : 2

= 10 : 1 -----(1)

Let 'x' be the number of pages read in 8 hours.

Then,

x : 8 -----(2)

From (1) and (2),

10 : 1 = x : 8

10(8) = 1(x)

80 = x

So, the person can read 80 pages in 8 hours.

**Problem 3 :**

If 15 people can repair a road of length 150 meters, at the same rate, how many people are needed to repair a road of length 420 meters ?

**Solution :**

The ratio between number of people and length of road repaired is

= 15 : 150

= 1 : 10 -----(1)

Let 'x' be the number of people needed to repair a road of length 420 meters.

Then,

x : 420 -----(2)

From (1) and (2),

1 : 10 = x : 420

1(420) = 10(x)

420 = 10x

Divide each side by 10.

42 = x

So, 42 people are needed to repair a road of length 420 meters.

**Problem 4 :**

If the cost of 10 kg rice is $400, then find the cost of 3 kg rice.

**Solution :**

The ratio between the number of kilograms of rice and the cost is

10 : 400 -----(1)

Let 'x' be the cost of 3 kilograms of rice.

Then,

3 : x -----(2)

From (1) and (2),

10 : 400 = 3 : x

10(x) = 3(400)

Divide each side by 10.

x = 3(400) / 10

x = 3(40)

x = 120

So, the cost of 3 kg rice is $120.

**Problem 5 :**

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

**Solution :**

The ratio between the number of liters of petrol and distance covered is

= 12 : 156

= 1 : 13 -----(1)

Let 'x' be the number of liters of petrol required to cover a distance 1300 km.

Then,

x : 1300 -----(2)

From (1) and (2),

1 : 13 = x : 1300

1(1300) = x(13)

1300 = 13x

Divide each side by 13.

100 = x

So, 100 liters of petrol will be required to cover a distance of of 1300 miles.

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