## RS Aggarwal Class 6 Solutions Chapter 10 Ratio, Proportion and Unitary Method Ex 10B

These Solutions are part of RS Aggarwal Solutions Class 6. Here we have given RS Aggarwal Solutions Class 6 Chapter 10 Ratio, Proportion and Unitary Method Ex 10B.

**Other Exercises**

**Question 1.****Solution:**

(i) 4, 6, 8, 12

If it is in proportion, then

If ad = bc if 4 x 12 = 6 x 8

If 48 = 48

Which is true

∴ 4, 6, 8, 12 are in proportion

(ii) 7, 42, 13, 78

7 : 42 :: 13 : 78

If ad = bc if 7 x 78 = 42 x 13

If 546 = 546

Which is true

∴ 7, 42, 13, 78 are in proportion

(iii) 33, 121, 9, 96 or 33 : 121 :: 9 : 96

are in proportion

If ad = bc

If 33 x 96 = 121 x 9

If 3168 = 1089

Which is not true

∴ 33, 121,9, 96 are not in proportion

(iv) 22, 33, 42, 63 or 22 : 33 :: 42 : 63

are in proportion

If ad = bc

If 22 x 63 = 33 x 42

If 1386 = 1386

Which is true

∴ 22, 33, 42, 63 are in proportion

(v) 32, 48, 70, 210 or 32 : 48 :: 70 : 210

are in proportion

If ad = bc

If 32 x 210 = 48 x 70

If 6720 = 3360

Which is not true

∴ 32, 48, 70, 210 are not in proportion

(vi) 150, 200, 250, 300 or

150 : 200 :: 250 : 300 are in proportion

If ad = bc if 150 x 300 = 200 x 250

If 45000 = 50000

Which is not true

∴ 150, 200,250, 300 are not in proportion

**Question 2.****Solution:**

(i) We have 60 : 105 :: 84 : 147

Product of means = 105 x 84 = 8820

Product of extremes = 60 x 147 = 8820

∴ Product of means = Product of extremes

Hence 60 : 105 :: 84 : 147 is verified.

(ii) We have 91 : 104 :: 119 : 136

Product of means = 104 x 119 = 12376

Product of extremes = 91 x 136 = 12376

Product of means = Product of extremes

Hence 91 : 104 :: 119 : 136 is verified.

(iii) We have 108 : 72 :: 129 : 86

Product of means = 72 x 129 = 9288

Product of extremes = 108 x 86 = 9288

Product of means = Product of extremes

Hence 108 : 72 :: 129 : 86 is verified.

(iv) We have 39 : 65 :: 141 : 235

Product of means = 65 x 141 = 9165

Product of extremes = 39 x 235 = 9165

∴ Product of means = Product of extremes

Hence 39 : 65 :: 141 : 235 is verified.

**Question 3.****Solution:**

(i) We have 55 : 11 :: x : 6

Product of means = 11 × x = 11x

Product of extremes = 55 x 6 = 330

**Question 4.****Solution:**

(i) We have, 51 : 68 = (\ frac { 51 }{ 68 })

= (\ frac { 3 }{ 4 })

**Question 5.****Solution:**

(i) 25 cm : 1 m and Rs. 40 : Rs. 160

= (\ frac { 25cm }{ 1000cm }) = (\ frac { 1 }{ 4 }),

(\ frac { Rs.40 }{ Rs.160 }) = (\ frac { 1 }{ 4 })

**Question 6.****Solution:**

Let the third term be x.

Then 51 : 68 :: x : 108

Now, product of means = x × 68

And, product of extremes = 51 × 108

x × 68 = 51 × 108

=> x = (\ frac { 51times 108 }{ 68 })

= 3 × 27 = 81

x = 81

Hence the third term of the given proportion is 81

**Question 7.****Solution:**

1st term =12, third term = 8 and fourth term = 14

Let 2nd term = x, then

**Question 8.****Solution:**

(i) The given numbers 48, 60, 75 are in

continued proportion if 48 : 60 :: 60 : 75.

Now, product of means = 60 x 60 = 3600

And, product of extremes = 48 x 75 = 3600

∴ Product of means = Product of extremes

So, 48 : 60 :: 60 : 75

Hence, the numbers 48, 60, 75 are in continued proportion.

(ii) The given numbers 36, 90, 225 are in

continued proportion of 36 : 90 :: 90 : 225

Now, product of means = 90 x 90 = 8100

And, product of extremes = 36 x 225 = 8100

∴ Product of means = Product of extremes

So, 36 : 90 :: 90 : 225

Hence, the numbers 36, 90, 225 are in continued proportion.

(iii)The given numbers 16, 84, 441 are in

continued proportion if 16 : 84 :: 84 : 441.

Now, product of means = 84 x 84 = 7056

And, product of extremes = 16 x 441 = 7056

Product of means = Product of extremes.

So, 16 : 845 :: 84 : 441

Hence 16, 84, 441 are in continued proportion.

(iv) The given numbers 27, 36, 48 are

in continued proportion if 27 : 36 :: 36 : 48

Now, product of means = 36 x 36 = 1296

And, product of extremes = 27 x 48 = 1296

∴ Product of means = Product of extremes.

So, 27 : 36 :: 36 : 48

Hence, the numbers 27, 36, 48 are in continued proportional.

**Question 9.****Solution:**

It is given that 9, x, x, 49 are in proportion, that is, 9 : x :: x : 49

∴ Product of means = Product of extremes

**Question 10.****Solution:**

Let the height of the pole be x metres.

**Question 11.****Solution:**

5 : 3 :: x : 6

Hope given RS Aggarwal Solutions Class 6 Chapter 10 Ratio, Proportion and Unitary Method Ex 10B are helpful to complete your math homework.

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