Answer:

32, 48, 140, 210; (II) 6, 9, 10 and 16

Solution:

(i) 32, 48, 140, 210

32 : 48 = 32/48 = 2/3 = 2 : 3

140 : 210 = 140/210 = 2/3 = 2 : 3

So, 32 : 48 = 140 : 210

Therefore, 32, 48, 140, 210 are in proportion.

i.e., 32 : 48 :: 140 : 210

Step-by-step explanation:

(ii) 6, 9, 10 and 16

6 : 9 = 6/9 = 2/3 = 2 : 3

10 : 16 = 10/16 = 5/8 = 5 : 8

Since, 6 : 9 ≠ 10 : 16 therefore, 6, 9, 10 and 16 are not in proportion.

2. The numbers 8, x, 9 and 36 are in proportion. Find x.

Solution:

The numbers 8, x, 9 and 36 are in proportion

⇒ 8 : x = 9 : 36

⇒ x × 9 = 8 × 36, [Since, the PRODUCT of the means = the product of the extremes]

⇒ x = (8 × 36)/9

⇒ x = 32

3. If x : 15 = 8 : 12; find the VALUE of x.

Solution:

⇒ x × 12 = 15 × 8, [Since, the product of the extremes = the product of the means]

⇒ x = (15 × 8)/12

⇒ x = 10

4. If 4, x, 32 and 40 are in proportion, find the value of x.

Solution:

4, x, 32 and 40 are in proportion, i.e., 4 : x :: 32 : 40

Now, product of extremes = 4 × 40 = 160

And product of means = x × 32

We know that in a proportion product of extremes = product of means

i.e., 160 = x × 32

If we multiply 32 by 5, we get 160

i.e., 5 × 32 = 160

So, x = 5