In the Worksheet on Basic Problems on Proportion, you have questions on proportion, continued proportion, finding mean proportional between the numbers, simple proportions, proportions with decimals, etc. Practice the Questions on Proportion Problems Worksheet on a regular basis and enhance your math skills. Answering the Problems in the Proportion Worksheet with Answers students can develop practical skills that are necessary for day-day-life. Try to solve as much as you can and have a clear understanding of the topics within.

Do refer:

Solving Proportions Worksheets PDF

I. Find the value of x in each of the following proportions:
(i) x : 6 = 3 : 9
(ii) 30 : x = 6 : 2
(iii) 3 : 9 = x : 6
(iv) 3 : 2 = x : 4
(v) 5 : 2 = 15 : x
(vi) 6 : 8 = 3 : x

Solution:

(i)  Given x : 6 = 3 : 9
Convert colon based notation to fractional form
x/6=3/9
By cross multiplying we get,
9x=18
x=18/9
=2
Therefore, x=2.
(ii) Given 30 : x = 6 : 2
By converting colon based notation to fractional form we get,
30/x=6/2
Apply cross multiplication we get
60=6x
x=60/6=10
Therefore, x=10.
(iii) 3 : 9 = x : 6
By converting colon based notation to fractional form we get,
3/9=x/6
Apply cross multiplication we get
18=9x
x=18/9=2
Therefore, x=2.
(iv)3 : 2 = x : 4
First, convert colon based notation to fractional form,
3/2=x/4
By Applying cross multiplication we get
12=2x
x=12/2=6
Therefore, x=6.
(v) 5 : 2 = 15 : x
First, convert colon based notation to fractional form,
5/2=15/x
By Applying cross multiplication we get
5x=30
x=30/5=6
Therefore, x=6.
(vi) 6 : 8 = 3 : x
First, convert colon based notation to fractional form,
6/8=3/x
By Applying cross multiplication we get
6x=24
x=24/6=4
Therefore, x=4.

II. Find the mean proportional between:
(i) 0.5 and 3.8
(ii) 0.7 and 8.5
(iii)  16 and 25

Solution:

(i) Let the mean proportional between 0.5 and 3.8 be m.
By applying the formula b² = ac,
Therefore, m x m = 0.5 x 3.8 = 1.9
m2=1.9
m=$$\sqrt{ 1.9 }$$=1.378
Therefore, the mean of 0.5 and 3.8 is 1.378.
(ii) Let the mean proportional between 0.7 and 8.5 be m.
By applying the formula b² = ac,
Therefore, m x m = 0.7. 8.5=5.95
m=$$\sqrt{ 5.95 }$$=2.439
Therefore, the mean of 0.7 and 8.5 is 2.439.
(iii) Let the mean proportional between 16 and 25 be m.
By applying the formula b² = ac,
Therefore, m x m=16.25=400.
m=$$\sqrt{ 400 }$$=20
Therefore, the mean of 16 and 25 is 20.

III. Check whether the following quantities form a proportion or not:
(i) 45:25=35:15
(ii) 3:7=6:14
(iii) 6:3=8:4

Solution:

(i) 1. To check proportionality, we have to multiply means, multiply extremes.
45.15=675
25.35=875
2. Compare the results.
The results of 675,875 are not equal.
Hence, the fractions are not proportional because the product of means and extremes are not equal.
(ii) 1. To check proportionality, we have to multiply means, multiply extremes.
3.14=42
7.6=48
2. Compare the results.
The results 42,48 are not equal.
Hence, the fractions are not proportional because the product of means and extremes are not equal.
(iii) 1. To check proportionality, we have to multiply means, multiply extremes.
6.4=24
3.8=24
2. Compare the results.
The results are equal.
Hence, the fractions are proportional because the product of means and extremes are equal.

IV. Find the unknown value of the following proportion:
i. 3x+2:7=x+4:3

Solution:

i. Given
3x+2/7=x+4/3
First, convert colon based notation to fractional form,
3x+2/7=x+4/3
By cross multiplying we get,
3(3x+2)=7(x+4)
9x+6=7x+28
9x-7x=28-6
2x=22
x=11
Therefore, x=11.
ii. 2:3=x/20-x
First, convert colon based notation to fractional form,
2/3=x/20-x
2(20-x)=3x
40-2x=3x
40=5x
x=40/5=8
Therefore, x=8.

V.  If x : y = 3 : 4 and y : z = 6 : 7, find x : y : z.

Solution:

Given that,
x : y = 3 : 4 and y : z = 6 : 7
Since y is the common term between the two ratios;
Multiply each term in the first ratio by the value of y in the second ratio.
x: y = 3: 4 = 18:24
Also, multiply each term in the second ratio by the value of y in the first ratio.
y: z = 6: 7 = 24: 28
Therefore, the ratio x: y: z = 18:24:28.

VI. If m : n = 2 : 7 and n : s = 3 : 8, find m : s.

Solution:

Given that,
m : n = 2 : 7 and n : s = 3 : 8
Since n is the common term between the two ratios;
Multiply each term in the first ratio by the value of n in the second ratio.
m: n = 2: 7 = 6:21
Also, multiply each term in the second ratio by the value of n in the first ratio.
n: s = 3: 8= 21: 56
Therefore, the ratio m: s= 6:56.

VII. Verify if the ratio 2:4::4:8 is proportion?

Solution:

This is a case of continued proportion, therefore apply the formula a x c =b x b,
In this case, a: b:c =2:4:8, therefore a=2, b=4 and c=8
Multiply the first and third terms
2 × 8 = 16
Square of the middle terms:
(4) ² = 4× 4= 16
Here a x c =b x b is equal.
Therefore, the ratio of 2:4:8 is in proportion.

VIII. If the third proportion of the two numbers is 24. The first number is 6, then find the second number?

Solution:

Given that first number=6,
Third number=24
To find the second number, we can apply the formula a x c =b x b
Here a=6, c=24
b x b=6 .24
=144
b=12
Therefore, the second number is 12.

IX. One piece of pipe 10 meters long is to be cut into two pieces, with the lengths of the pieces being in a 2 : 3 ratio. What are the lengths of the pieces?

Solution:

Given,
Length of one piece of pipe=10 m
The ratio of length of pieces=2:3
Let the length of a short piece of pipe=x
Length of long pipe=10-x
short piece/long piece: 2/3=x/10-x
2(10-x)=3x
20-2x=3x
20=5x
x=20/5=4
Length of the short piece=4m.
Length of the long piece=10-4=6m.

X. The time taken by a vehicle is 2 hours at a speed of 40 miles/hour. What would be the speed taken to cover the same distance at 4 hours?

Solution:

Consider speed as m and time parameter as n.
If the time taken increases, then the speed decreases. This is an inverse proportional relation, hence m ∝ 1/n.
Using the inverse proportion formula,
m = k/ n
m × n = k
At speed of 40 miles/hour, time = 2 hours, from this we get,
k = 40 × 2 = 80
Now, we need to find speed when time, n = 4.
m × n = k
m × 4 = 80
∴ m = 80/4 = 20
Therefore, the speed at 4 hours is 20 miles/hour.

XI. In a construction company, a supervisor claims that 6 men can complete a task in 36 days. In how many days will 15 men finish the same task?

Solution:

Let the number of men is M and the number of days is D.
Given:
M1= 6 ,
D1= 36, and
M2= 15.
This is an inverse proportional relation, as if the number of workers increases, the number of days decreases.
M ∝ 1/D
Considering the first situation,
M1= k/D1
6 = k/36
k = 6 × 36 = 216
Considering the second situation,
M2= k/D2
15 = 216/D2
D2= 216/15 = 14
Therefore, 15 men can complete the same task in 14 days.

XII. Suppose x and y are in an inverse proportion such that when x = 100, y = 3. Find the value of y when x = 150 using the inverse proportion formula?

Solution:

Given: x = 100 when y = 3.
x ∝ 1/y
x = k / y, where k is a constant,
or k = xy
Putting, x = 100 and y = 3, we get;
k = 100 × 3 = 300
Now, when x = 120, then;
150 y = 300
y = 300/150 = 2
That means when x is increased to 150 then y decreases to 2.