CRE 2 - Proportion

Let a = 3x and b = x

a + b = 4x and a – b = 2x

a + b : a – b = 4x : 2x = 2 : 1

Alternately,

Apply Componendo & Dividendo, i.e.

If x/y = p/q, then $\frac{x+y}{x-y}=\frac{p+q}{p-q}$

∴ $\frac{a+b}{a-b}=\frac{3+1}{3-1}=\frac{4}{2}=\frac{2}{1}$

Hence, option (a).

$\frac{a+b}{a-b}=\frac{5}{4}$

⇒ 4a+4b = 5a-5b

⇒  a = 9b

⇒ a/b = 9/1

⇒ a : b = 9 ∶ 1

Alternately, 

Apply Componendo & Dividendo, i.e.

If x/y = p/q, then (x+y)/(x-y) = (p+q)/(p-q)

Hence, (a+b)/(a-b) = 5/4

⇒ $\frac{(a+b)+(a-b)}{(a+b)-(a-b)}=\frac{5+4}{5-4}$

⇒ 2a/2b = 9/1

⇒ a/b = 9/1

Hence, option (a).

Let the third proportional number be x.

Then, 1 : 2 :: 2 : x

⇒ 1/2 = 2/x

⇒ x = 4

∴ Third proportional number = 4

Hence, option (c).

Let the fourth proportional number be x. Then, 12 : 14 :: 18 : x 

⇒ $\frac{12}{14}=\frac{18}{x}$

⇒ x = $\frac{14\times 18}{12}$ = 21

Hence, option (a).

Let mean proportion of 4 and 9 be x.

⇒ $\frac{4}{x}=\frac{x}{9}$

∴ Mean proportional = $\sqrt{4 \times 9}$ = 2 × 3 = 6.

[Remember: Mean proportion of 2 numbers a and b is always $\sqrt{a\times b}$]

Hence, option (c).

Mean proportional of p, q is √pq

⇒ Mean proportional of 64, 4 is $\sqrt{64\times 4}$ = 16

Hence, option (b).

Compounded ratio is : $\frac{2\times 6\times 1\times 1}{3\times 7\times 3\times 8}=\frac{1}{42}$

Hence, option (b).

Inverse ratio would be, $\frac{1}{3}:\frac{1}{2}:\frac{1}{1}$ or $\frac{6}{3}:\frac{6}{2}:\frac{6}{1}$ or 2 : 3 : 6

Hence, option (d).

Duplicate ratio of p : q is p² : q²

⇒ Duplicate ratio of 4 : 9 is 4² : 9² = 16 : 81

Hence, option (d).

Triplicate ratio of p : r is p³ : r³

⇒ Triplicate ratio of 3 : 4 is 3³ : 4³ = 27 : 64.

Hence, option (c).

Sub-duplicate ratio of p : q is √p : √q

⇒ Sub-duplicate ratio of 25 : 16 is √25 : √16 = 5 ∶ 4

Hence, option (a).

Sub-tuplicate ratio of p : q is ∛p : ∛q

⇒ Sub-duplicate ratio of 8 : 125 is ∛8 : ∛125 = 2 ∶ 5.

Hence, option (b).