RATIO AND PROPORTION WORKSHEET

1. The average age of three boys is 25 years and their ages are in the proportion 3 : 5 : 7. Find the age of the youngest boy.

2. If the angles of a triangle are in the ratio 2:7:11, then find the angles.

3. Two numbers are respectively 20% and 50% are more than a third number, Find the ratio of the two numbers.

4. If $782 is divided among three persons A, B and C in the ratio 1/2 : 2/3 : 3/4, then  find the share of A.

5. An amount of money is to be divided among P, Q and R in the ratio  3 : 7 : 12. The difference between the shares of P and Q is $2400. What will be the difference between the shares of Q and R ?

6. Carter's SUV requires 8 gallons of gasoline to travel 148 miles. How many gasoline, to the nearest gallon, will he need for 500 mile trip ?

7. If 5x : 3 = (x + 14) : 2, what is the value of x ?

8. 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.

9. John weighs 56.7 kilograms. If he is going to reduce his weight in the ratio 7 : 6, find his new weight.

10. If a : b = c : d = 2.5 : 1.5, what are the values of ad : bc and a + c  :  b + d ?

Detailed Answers

1. Answer :

From the ratio 3 : 5 : 7, the ages of three boys are 3x, 5x and 7x.

Average age of three boys = 25

(3x + 5x + 7x)/3 = 25

15x = 75

x = 5

Age of the first boy = 3x = 3(5) = 15

Age of the first boy = 5x = 5(5) = 25

Age of the first boy = 7x = 7(5) = 105

So, the age of the youngest boy is 15 years.

2. Answer :

From the ratio 2 : 7 : 11, the three angles can be assumed to be

2x, 7x, 11x 

In any triangle, sum of the angles = 180°.

2x + 7x + 11x = 180

20x = 180

x = 9

First angle = 2x = 2 ⋅ 9 = 18°

Second angle = 7x = 7 ⋅ 9 = 63°

Third angle = 11x = 11 ⋅ 9 = 99°

Hence the angles of the triangle are (18°, 63°, 99°).

3. Answer :

Let x be the third number.

First number = (100 + 20)% of x

= 120% of x

= 1.2x

Second number = (100 + 50)% of x

= 150% of x

= 1.5x

Ratio between the first number and second number :

= 1.2x : 1.5x 

= 1.2 : 1.5

= 12 : 15

= 4 : 5

4. Answer :

Given ratio ---> 1/2 : 2/3 : 3/4.

First let us convert the terms of the ratio to integers.

L.C.M of denominators (2, 3, 4) = 12

When we multiply each term of the ratio by 12, we get

(12 ⋅ 1/2) : (12 ⋅ 2/3) : (12 ⋅ 3/4) = 6 : 8 : 9

From the ratio 6 : 8 : 9,

share of A  =  6x

share of B  =  8x

share of C  =  9x

We know that,

share of A + share of B + share of C = 782

6x + 8x + 9x = 782

23x = 782

x = 34

Share of A :

= 6x

= 6 ⋅ 34

= $204

5. Answer :

From the given ratio 3 : 7 : 12,

share of P = 3x

share of Q = 7x

share of R = 12x

Difference between the shares of P and Q is $ 2400.

share of Q - share of P = 2400

7x - 3x = 2400

4x = 2400

x = 600

Difference between the shares of Q and R is

= 12x - 7x

= 5x

= 5 ⋅ 600

= $3000

6. Answer :

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.

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.

7. Answer :

5x : 3 = (x + 14) : 2

Using cross product rule,

2(5x) = 3(x+14)

10x = 3x+42

7x = 42

x = 6

8. Answer :

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.

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.

9. Answer :

Original weight of John : 56.7 kg.

Weight is reduced in the ratio ----> 7 : 6.

Let x be the weight after having reduced.

56.7 : x = 7 : 6

7x = 6(56.7)

Divide each side by 7.

x = 48.6

John's new weight is 48.6 kg.

10. Answer :

In the given proportion a : b and c : d, applying cross product rule, we get

ad = bc

Dividing by bc on both sides, we get

ad/bc = 1

ad/bc = 1/1

ad : bc = 1 : 1

Given : a : b = c : d = 2.5 : 1.5 -----(1)

In the given proportion a : b and c : d, applying the property addendo, we get

a : b = c : d = (a + b) : (c + d) ----(2)

From (1) and (2), we get

(a + b) : (c + d) = 2.5 : 1.5

= (2.5 x 10) : (1.5 x 10)

= 25 : 15

= (25/5) : (15/5)

= 5 : 3