Question

Find which ratios form a proportion. Also, write the middle terms where the ratios form a proportion.
1. 7 : 91 ∷ 14 : 196, middle term is 91 and 14
2. 17 : 136 ∷ 21 : 168, middle term is 136 and 21
3. 8 : 96 ∷ 5 : 65, middle term is 96 and 5
4. 11 : 131 ∷ 16 : 176, middle term is 131 and 176

Answer 1

Correct Answer - Option 2 : 17 : 136 ∷ 21 : 168, middle term is 136 and 21

Concept used:

If Product of extreme terms = Product of middle terms, then the ratios form a proportions.

If four numbers a, b, c and d are in proportional (i.e., a : b ∷ c : d),

then a and d are known as extreme terms and b and c are called middle terms.

Calculations:

We check option,

Option number 1)

⇒ 7 : 91 ∷ 14 : 196

⇒ Product of extreme terms = 7 × 196

⇒ Product of extreme terms = 1372

⇒ Product of middle terms = 91 × 14

⇒ Product of middle terms = 1274

Product of extreme terms ≠ Product of middle terms

∴ The ratio 7 : 91 ∷ 14 : 196 Do not form a proportion.

Option number 2)

1) 17 : 136 ∷ 21 : 168

⇒ Product of extreme terms = 17 × 168

⇒ Product of extreme terms = 2856

⇒ Product of middle terms = 136 × 21

⇒ Product of middle terms = 2856

Product of extreme terms = product of middle terms

Middle terms = 136 and 21

∴ The ratios 17 : 136 ∷ 21 : 168 form a proportion and middle terms are 136 and 21.