Worksheet on Proportion and Continued Proportion

Practice the questions given in the worksheet on proportion and continued proportion.

1. Check whether the following numbers are in proportion or not:

(i) 3, 5, 6, 10

(ii) 0.25, 0.5, 50, 100

(iii) 3, 4\(\frac{1}{2}\), 6, 9\(\frac{2}{3}\)

(iv) 4\(\frac{1}{2}\), 1\(\frac{1}{3}\), 2\(\frac{1}{4}\), \(\frac{2}{3}\)

2. Verify whether the following numbers are proportional.

(i) 5, 13, 15, 39

(ii) 7, 14, 56, 28

(iii) 0.3, 1.5, 0.06, 0.21

(iv) a, b, a\(^{2}\)b, ab\(^{2}\)

(v) a\(^{2}\) + ab, b\(^{2}\) + ab, ac\(^{2}\) + a\(^{2}\)c, b\(^{2}\)c + bc\(^{2}\)

3. Find x in the following proportions:

(i) 3.5 : 7.0 = x : 20

(ii) 6 : x = 4 : 25

(iii) \(\frac{2}{5}\) : \(\frac{1}{4}\) = x : \(\frac{5}{3}\)

(iv) x : 1\(\frac{1}{2}\) = 2\(\frac{1}{3}\) : 3\(\frac{2}{3}\)

4. Find k in each case so that the numbers are proportional.

(i) k, 25, 80, 16

(ii) 16, k, 38, 57

(iii) 7, 49, k, 112

(iv) 20, 80, 21, x

(v) (a\(^{2}\)b -ab\(^{2}\)), k, (am\(^{2}\) -ap\(^{2}\)), (cm\(^{2}\) - cp\(^{2}\))

5. Find the fourth proportional to:

(i) 25, 125, 3.5

(ii) \(\frac{1}{3}\), \(\frac{3}{7}\), 2\(\frac{3}{4}\)

(iii) 9, 48, 36

(iv) 85, 170, 34

6. Find the fourth proportional of the following sets numbers.

(i) a\(^{2}\)b, b\(^{2}\)c, c\(^{2}\)a

(ii) m - n, m\(^{2}\) - n\(^{2}\), m\(^{2}\) - mn + n\(^{2}\)

(iii) 36, 48, 75

(iv) 0.15, 0.225, 0.64

(v) 2ab, a\(^{2}\), b\(^{2}\)

(vi) a + b, a\(^{2}\) - b\(^{2}\), a\(^{2}\) + ab + b\(^{2}\)

7. Check the following are in continued proportion or not:

(i) 0.4, 3.6, 3.24

(ii) 2.4, 9.6, 38.4

8. Find p in each case so that the numbers are in continued proportion.

(i) p, \(\frac{1}{2}\), 2

(ii) 16, p, 9

(iii) a - b, a(a - b), p

9. Find the third proportional of the following set of numbers:

(i) 7, 14

(ii) 2.5, 3.5

(iii) 1\(\frac{2}{5}\), 5\(\frac{3}{5}\)

(iv) 0.5, 4.5

(v) p\(^{3}\)q\(^{2}\), q\(^{2}\)r

(vi) (x - y)\(^{2}\), (x\(^{2}\) - y\(^{2}\))\(^{2}\)

 10. (i) If m, 10, n, 40 are in continued proportion hen find the positive values of m and n.

(ii) If 4, 16, m, n are in continued proportion then find m and n.

Answers for the worksheet on proportion and continued proportion are given below.

Answers

1. (i) Numbers are in proportion

(ii) Numbers are in proportion

(iii) Numbers are not in proportion

(iv) Numbers are in proportion

2. (i) Yes

(ii) No

(iii) No

(iv) Yes

(v) No

3. (i) 10

(ii) 37\(\frac{1}{2}\)

(iii) 2\(\frac{2}{3}\)

(iv) \(\frac{21}{22}\)

4. (i) 125

(ii) 24

(iii) 16

(iv) 84

(v) bc(a - b)

5. (i) 17.5

(ii) 3\(\frac{15}{28}\)

(iii) 192

(iv) 68

6. (i) \(\frac{bc^{3}}{a}\)

(ii) m\(^{3}\) + n\(^{3}\)

(iii) 100

(iv) 0.96

(v) \(\frac{1}{2}\)ab

(vi) a\(^{3}\) - b\(^{3}\)

7. (i) Numbers are not in continued proportion

(ii) Numbers are in continued proportion

8. (i) \(\frac{1}{8}\)

(ii) 12

(iii) a\(^{2}\)(a - b)

9. (i) 28

(ii) 4.9

(iii) 22\(\frac{2}{5}\)

(iv) 40.5

(v) \(\frac{q^{2}r^{2}}{pq}\)

(vi) (x + y)\(^{4}\)(x - y)\(^{2}\) or, (x + y)\(^{2}\)(x\(^{2}\) - y\(^{2}\))\(^{2}\)

10. (i) m = 5, n = 20

(ii) 64, 256

● Ratio and proportion

• Basic Concept of Ratios
• Important Properties of Ratios
• Ratio in Lowest Term
  
• Types of Ratios
• Comparing Ratios
• Arranging Ratios
  
• Dividing into a Given Ratio
  
• Divide a Number into Three Parts in a Given Ratio
• Dividing a Quantity into Three Parts in a Given Ratio
  
• Problems on Ratio
  
• Worksheet on Ratio in Lowest Term
  
• Worksheet on Types of Ratios
  
• Worksheet on Comparison on Ratios
• Worksheet on Ratio of Two or More Quantities
  
• Worksheet on Dividing a Quantity in a Given Ratio
• Word Problems on Ratio
  
• Proportion
  
• Definition of Continued Proportion
  
• Mean and Third Proportional
  
• Word Problems on Proportion
  
• Worksheet on Proportion and Continued Proportion
  
• Worksheet on Mean Proportional
  
• Properties of Ratio and Proportion

10th Grade Math

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