RS Aggarwal Class 6 Math Tenth Chapter Ratio, Proportion And Unitary Method Exercise 10B Solution

RS Aggarwal Class 6 Math Tenth Chapter Ratio, Proportion And Unitary Method Exercise 10B Solution

EXERCISE 10B

(1) Determine if the following numbers are in proportion:

(i) 4, 6, 8, 12

Solution: We have,

Hence, 4, 6, 8, 12 are in proportion.

(ii) 7, 42, 13, 78

Solution: We have,

Hence, 7, 42, 13, 78 are in proportion.

(iii) 33, 121, 9, 96

Solution: We have,

Hence, 33, 121, 9, 96 are not in proportion.

(iv) 22, 33, 42, 63

Solution: We have,

Hence, 22, 33, 42, 63 are in proportion.

(v) 32, 48, 70, 210

Solution: We have,

Hence, 32, 48, 70, 210 are not in proportion.

(vi) 150, 200, 250, 300

Solution: We have,

Hence, 150, 200, 250, 300 are not in proportion.

(2) Verify the following:

(i) 60 : 105 : : 84 :147

Solution: We have:

Product of extremes = (60 x 147) = 8820

Product of means = (105 x 84) = 8820

So, Product of extremes = Product of means.

(ii) 91 : 104 : : 119 : 136

Solution: We have,

Product of extremes = (91 x 136) = 12376

Product of means = (104 x 119) = 12376

So, Product of extremes = Product of means.

(iii) 108 : 72 : : 129 : 86

Solution: We have,

Product of extremes = (108 x 86) = 9288

Product of means = (72 x 129) = 9288

So, Product of extremes = Product of means.

(iv) 39 : 65 : : 141 : 235

Solution: We have,

Product of extremes = (39 x 235) = 9165

Product of means = (65 x 141) = 9165

So, Product of extremes = Product of means.

(3) Find the value of x in each of the following proportion:

(i) 55 : 11 : : x : 6

Solution: Clearly, product of means = product of extremes.

(ii) 27 : x : : 63 : 84

Solution: Clearly, product of means = product of extremes.

(iii) 51 : 85 : : 57 : x

Solution: Clearly, product of means = product of extremes.

(iv) x : 92 : : 87 : 116

Solution: Clearly, product of means = product of extremes.

(4) Write (T) for true and (F) for false in case of each of the following:

(i) 51 : 68 : : 85 : 102 = F

Solution: We have,

Product of extremes = (51 x 102) = 5202

Product of means = (68 x 85) = 5780

So, Product of extremes ≠Product of means.

(ii) 36 : 45 : : 80 : 100 = T

Solution: We have,

Product of extremes = (36 x 100) = 3600

Product of means = (45 x 80) = 3600

So, Product of extremes = Product of means.

(iii) 30 bags : 18 bags : : Rs 450 : Rs 270 = T

Solution: We have,

Product of extremes = (30 x 270) = 8100

Product of means = (18 x 450) = 8100

So, Product of extremes = Product of means.

(iv) 81 kg : 45 kg : : 18 men : 10 men = T

Solution: We have,

Product of extremes = (81 x 10) = 810

Product of means = (45 x 18) = 810

So, Product of extremes = Product of means.

(v) 45 km : 60 km : : 12h : 15 h = F

Solution: We have,

Product of extremes = (45 x 15) = 675

Product of means = (60 x 12) = 720

So, Product of extremes≠Product of means.

(vi) 32 kg : Rs 36 : : 8 kg : Rs 9= T

Solution: We have,

Product of extremes = (32 x 9) =288

Product of means = (36 x 8) = 288

So, Product of extremes = Product of means.

(5) Determine if the following ratios form a proportion:

(i) 205 cm : 1 m and Rs 40 : Rs 160

Solution: Here, 1 m =100 cm. We have:

So, the ratios 25 cm : 1 m and Rs 40 : Rs 160 are in proportion.

(ii) 39 litres : 65 litres and 6 bottles : 10 bottles

Solution: We have,

So, the ratios 39 litres : 65 litres and 6 bottles : 10 bottles are in proportion.

(iii) 200 mL : 2.5 L and Rs 4 : Rs 50

Solution: Here 2.5 L = 2500 mL. We have:

So, the ratios 200 mL : 2.5 L and Rs 4 : Rs 50 are in proportion.

(iv) 2 kg : 80 kg and  25 g : 625 kg

Solution: Here, 25 g = 0.025 kg. We have,

So, the ratios 2 kg : 80 kg and 25 g : 625 kg are not in proportion.

(6) In a proportion, the 1st, 2nd and 4th terms are 51, 68 and 108 respectively. Find the 3rd term.

Solution: Let the 3rd term is x.

So, the 3rd term is 81.

(7) The 1st, 3rd and 4th terms of a proportion are 12, 8 and 14 respectively. Find the 2nd term.

Solution: Let the 2nd term is x.

So, the 2nd term is 21.

(8) Show that the following numbers are in continued proportion:

(i) 48, 60, 75

(ii) 36, 90, 225

(iii) 16. 84, 441

(9) If 9, x ,x 49 are in proportion, find the value of x.

Solution: Clearly, Product of means = Product of extremes

Hence, x = 21.

(10) An electric pole casts a shadow of length 20 m at a time when a tree 6 m high casts a shadow of length 8m. Find the height of the pole.

Solution: Let the height of the pole is x m.

So, the height of the pole is 15 m.

(11) Find the value of x if 5 : 3 : : x : 6

Solution:

Hence, the x is 10.