Step-by-step explanation:

product of extreams = product of means

(i) 8, 10, 16, 20

8*20=10*16

160=160

yes

(ii) 42, 54, 63, 81

42*81= 54*63

3402 = 3402

Answer:

i) Yes

ii) Yes

iii) No

iv) No

Step-By-Step Explanation:

i)A group of numbers are said to be in proportion if the product of their extremes is equal to product of their means.

Here,

8 : 10 : : 16 : 20

Extremes = 8 and 20

Product of extremes = 8 × 20 = 160

Means = 10 and 16

Product of means = 10 × 16 = 160

So, we conclude that ;

160 = 160

Therefore, Product of extremes = Product of means.

Hence, the given set of numbers are in

proportion.

ii) Here,

42 : 54 : : 63 : 81

Extremes = 42 and 81

Product of extremes = 42 × 81 = 3402

Means = 54 and 63

Product of means = 54 × 63 = 3402

So, we can conclude that ;

3402 = 3402

Therefore, Product of extremes = Product of means.

Hence, the given set of numbers are in

proportion.

Mark it as

iii) Here,

20 : 30 : : 40 : 50

Product of extremes = 20 × 50 = 1000

Product of means = 30 × 40 = 1200

1000 ≠ 1200

Therefore, Product of extremes ≠ Product of means.

Hence, the given set of numbers are in

proportion.

iv) Here,

3 : 21 : : 14 : 49

Product of extremes = 3 × 49 = 147

Product of means = 21 × 14 = 295

147 ≠ 295

Therefore, Product of extremes ≠ Product of means.

Hence, the given set of numbers are in

proportion.

Mark it as brainliest if you are satisfied ^_^