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Home > Practice > Arithmetic Aptitude > Ratio and Proportion > Miscellaneous

81. If x = $\frac{1}{3}$ y and y = $\frac{1}{2}$ z, then x : y : z is equal to

A. 1 : 2 : 6

B. 1 : 3 : 6

C. 2 : 4 : 6

D. 3 : 2 : 1

Discuss

Solution:

\begin{aligned} x = \frac{1}{3} y = \frac{1}{3} \times \frac{1}{2} z = \frac{1}{6} z \\ L e t x = \frac{1}{3} y = \frac{1}{6} z = k \\ Then, \\ x = k, y = 3 k, z = 6 k \\ ∴ x : y : z = k : 3 k : 6 k \\ = 1 : 3 : 6 \end{aligned}

82. There are Rs. 225 consisting of one rupee, 50 paise and 25 paise coins. The ratio of their numbers in that order is 8 : 5 : 3. The number of one - rupee coins is = ?

A. 80

B. 112

C. 160

D. 172

Discuss

Solution:

Rs. 1 : 50 paise : 25 paise
Number of coins 8x : 5x : 3x

\begin{aligned} Value of coins \\ = \frac{8 x}{1} : \frac{5 x}{2} : \frac{3 x}{4} \\ ∴ 8 x + \frac{5 x}{2} + \frac{3 x}{4} = Rs . 225, \\ Given \frac{32 x + 10 x + 3 x}{4} = 225 \\ \Rightarrow 45 x = 225 \times 4 \\ \Rightarrow x = \frac{225 \times 4}{45} \\ \Rightarrow x = 5 \times 4 = 20 \end{aligned}

∴ Number of one rupees coins
= 20 × 8 = 160

83. An amount of money is to be distributed among P, Q ans R in the ratio of 2 : 7 : 9. The total of P's and Q's share is equal to R's share. What is the difference between the shares of P and Q ?

A. Rs. 5000

B. Rs. 7500

C. Rs. 9000

D. Information inadequate

Discuss

Solution:

P : Q : R
P + Q = R (given)
2x + 7x = 9x
Hence, we don't have sufficient data to insure the values of A, B and C

84. If a : b = 5 : 7 and c : d = 2a : 3b then ac : bd is = ?

A. 20 : 38

B. 50 : 147

C. 10 : 21

D. 50 : 151

Discuss

Solution:

\begin{aligned} a : b c : d \\ 5 : 7 2 a : 3 b \\ \frac{a}{b} = \frac{5}{7}, \frac{c}{d} = \frac{2 a}{3 b} \\ = \frac{2}{3} \times \frac{5}{7} \\ = \frac{10}{21} \\ ∴ a c : b d \\ = \frac{ac}{bd} \\ = \frac{5}{7} \times \frac{10}{21} \\ = \frac{50}{147} \\ = 50 : 147 \end{aligned}

85. If 2A = 3B = 4C, then A : B : C is equal to -

A. 2 : 3 : 4

B. 3 : 4 : 6

C. 4 : 3 : 2

D. 6 : 4 : 3

Discuss

Solution:

Let 2A = 3B = 4C = k

\begin{aligned} Then, \\ A = \frac{k}{2}, \\ B = \frac{k}{3}, \\ C = \frac{k}{4} \\ ∴ A : B : C = \frac{k}{2} : \frac{k}{3} : \frac{k}{4} \\ = \frac{1}{2} : \frac{1}{3} : \frac{1}{4} (Multiply by 12) \\ = 6 : 4 : 3 \end{aligned}

86. If x² + 4y² = 4xy, then x : y is -

A. 1 : 1

B. 1 : 2

C. 2 : 1

D. 1 : 4

Discuss

Solution:

\begin{aligned} = x^{2} + 4 y^{2} = 4 x y \\ \Rightarrow x^{2} - 4 x y + 4 y^{2} = 0 \\ \Rightarrow (x - 2 y^{2}) = 0 \\ \Rightarrow x = 2 y \\ \Rightarrow \frac{x}{y} = 2 \\ \Rightarrow x : y = 2 : 1 \end{aligned}

87. If W₁ : W₂ = 2 : 3 and W₁ : W₃ = 1 : 2, then W₂ : W₃ is -

A. 3 : 4

B. 4 : 3

C. 2 : 3

D. 4 : 5

Discuss

Solution:

\begin{aligned} = \frac{W_{2}}{W_{1}} = \frac{3}{2} and \frac{W_{1}}{W_{3}} = \frac{1}{2} \\ \Rightarrow \frac{W_{2}}{W_{3}} = (\frac{W_{2}}{W_{1}} \times \frac{W_{1}}{W_{3}}) \\ = \frac{3}{2} \times \frac{1}{2} = \frac{3}{4} \\ \Rightarrow W_{2} : W_{3} = 3 : 4 \end{aligned}

88. If a : b = b : c, then a⁴ : b⁴ is equal to = ?

A. ac : b²

B. a² : c²

C. c² : a²

D. b² : ac

Discuss

Solution:

\begin{aligned} a : b = b : c \\ \frac{a}{b} = \frac{b}{c} \\ b^{2} = a c \\ b^{4} = a^{2} c^{2} \\ ∴ a^{4} : b^{4} = \frac{a^{4}}{b^{4}} \\ = \frac{a^{4}}{a^{2} c^{2}} \\ = \frac{a^{2}}{c^{2}} \\ = a^{2} : c^{2} \end{aligned}

89. If $A$ : $B$ = $\frac{1}{2}$ : $\frac{3}{8},$ $B$ : $C$ = $\frac{1}{3}$ : $\frac{5}{9}$ and $C$ : $D$ = $\frac{5}{6}$ : $\frac{3}{4},$ Then the ratio of A : B : C : D is ?

A. 6 : 4 : 8 : 10

B. 6 : 8 : 9 : 10

C. 8 : 6 : 10 : 9

D. 4 : 6 : 8 : 10

Discuss

Solution:

\begin{aligned} A : B = \frac{1}{2} : \frac{3}{8}, \\ \frac{A}{B} = \frac{4}{3} \\ B : C = \frac{1}{3} : \frac{5}{9}, \\ \frac{B}{C} = \frac{1}{3} \times \frac{9}{5} = \frac{3}{5} \\ C : D = \frac{5}{6} : \frac{3}{4}, \\ \frac{C}{D} = \frac{5 \times 4}{6 \times 3} = \frac{10}{9} \\ A : B : C : D \\ 4 : 3 \\ 3 : 5 \\ 10 : 9 \\ \Rightarrow A : B : C : D \\ 8 : 6 : 10 : 9 \end{aligned}

90. If A : B : C = 2 : 3 : 4, then ratio $\frac{A}{B}$ : $\frac{B}{C}$ : $\frac{C}{A}$ is equal to?

A. 8 : 9 : 16

B. 8 : 9 : 12

C. 8 : 9 : 24

D. 4 : 9 : 12

Discuss

Solution:

\begin{aligned} A : B : C = 2 : 3 : 4 \\ Let \\ A = 2 x, B = 3 x, C = 4 x \\ ∴ \frac{A}{B} : \frac{B}{C} : \frac{C}{A} = \frac{2 x}{3 x} : \frac{3 x}{4 x} : \frac{4 x}{2 x} \\ \Rightarrow \frac{2}{3} : \frac{3}{4} : \frac{2}{1} \end{aligned}

Multiply by the L.C.M of denominator to remove fraction

\begin{aligned} So, \\ L .C .M of (3, 4, 1) = 12 \\ ∴ \frac{A}{B} : \frac{B}{C} : \frac{C}{A} \\ \frac{2}{3} \times 12 : \frac{3}{4} \times 12 : \frac{2}{1} \times 12 \\ 8 : 9 : 24 \end{aligned}

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