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
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