PROPERTIES OF PROPORTION WORKSHEET

Problem 1 :

Find the value of x, if 10/3 : x  =  5/2 : 5/4.

Problem 2 :

Find the fourth proportional to 2/3, 3/7, 4.

Problem 3 :

Find the third proportion to 2.4 and 9.6.

Problem 4 :

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

Problem 5 :

If a : 3 = b : 4 = c : 7, then, find the value of (a + b + c) : c.

1. Answer :

10/3 : x  =  5/2 : 5/4.

Using cross product rule, we get, 

(10/3) ⋅ (5/4)  =  x ⋅ (5/2)

25/6  =  5x/2

(25/6) ⋅ (2/5)  =  x

5/3  =  x

So, the value of x is 5/3.

2. Answer :

2/3, 3/7, 4

Let 'a' be the fourth proportional.

Then, we have

2/3 : 3/7  =  4 : a

Using cross product rule, we have

(2/3) ⋅ a  =  4 ⋅ (3/7)

2a/3  =  12/7

a  =  (12/7) ⋅ (3/2)

a  =  18/7

So, the fourth proportional is 18/7. 

3. Answer :

Let 'a' be the third proportional. 

Then, we have 

2.4 : 9.6  =  9.6 : a

Using cross product rule, we have

2.4a  =  9.6 ⋅ 9.6

a  =  92.16/2.4

a  =  38.4

So, third proportion is 3.8.4

4. 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

(a + b) : (c + d)  =  (2.5x10) : (1.5x10)

(a + b) : (c + d)  =  25 : 15

(a + b) : (c + d)  =  (25/5) : (15/5)

(a + b) : (c + d)  =  5 : 3

5. Answer :

In the given proportion a : 3  =  b : 4  =  c : 7, applying the property addendo, we get

a : 3  =  b : 4  =  c : 7  =  (a + b + c) : (3+4+7)

a : 3  =  b : 4  =  c : 7  =  (a + b + c) : 14

Now, all the above four ratios are equal.

Taking the last two ratios, we get

c : 7  =  (a + b + c) : 14

c/7  =   (a + b + c)/14

14/7  =   (a + b + c)/c

2  =   (a + b + c)/c

or

 (a + b + c)/c  =  2/1

(a + b + c) : c  =  2 : 1

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