# SOLVE PROPORTIONS WORD PROBLEMS WORKSHEET

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

## Solve Proportions Word Problems Worksheet

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 ?

## Solve Proportions Word Problems Worksheet - Solutions

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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