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

71. If x : 7.5 = 7 : 17.5, then the value of x is -

A. 1

B. 2.5

C. 3

D. 3.5

Discuss

Solution:

\begin{aligned} = x : 7.5 = 7 : 17.5 \\ \Rightarrow 17.5 x = 7.5 \times 7 \\ \Rightarrow x = \frac{7.5 \times 7}{17.5} \\ = 3 \end{aligned}

72. The value of $x$ where $x$ : $2 \frac{1}{3}$ :: $21$ : $50$ is -

A. $1 \frac{1}{49}$

B. $1 \frac{1}{50}$

C. $\frac{49}{50}$

D. $\frac{27}{50}$

Discuss

Solution:

\begin{aligned} = x : 2 \frac{1}{3} :: 21 : 50 \\ \Rightarrow 50 x = \frac{7}{3} \times 21 \\ \Rightarrow 50 x = 49 \\ \Rightarrow x = \frac{49}{50} \end{aligned}

73. If $\sqrt{2}$ : $(1 + \sqrt{3})$ :: $\sqrt{6}$ : $x$ , then $x$ is equal to -

A. $\sqrt{3} + 3$

B. $1 - \sqrt{3}$

C. $1 + \sqrt{3}$

D. $\sqrt{3} - 3$

Discuss

Solution:

\begin{aligned} = \sqrt{2} : (1 + \sqrt{3}) :: \sqrt{6} : x \\ \Rightarrow \sqrt{2} x = \sqrt{6} (1 + \sqrt{3}) \\ \Rightarrow x = \frac{\sqrt{6} (1 + \sqrt{3})}{\sqrt{2}} \\ = \sqrt{3} (1 + \sqrt{3}) \\ = \sqrt{3} + 3 \end{aligned}

74. In an alloy, the ratio of copper and zinc is 5 : 2. If 1.250 kg of zinc is mixed in 17 kg 500 gm of alloy, then the ratio of copper and zinc will be = ?

A. 2 : 1

B. 2 : 3

C. 3 : 2

D. 1 : 2

Discuss

Solution:

The ratio of copper and zinc is 5 : 2
i.e 5x : 2x
Quantity of initial mixture = 17.5 kg
∴ 5x + 2x =

\frac{35}{2}

⇒ x =

\frac{5}{2}

Quantity of Copper in initial mixture

\begin{aligned} = \frac{5}{2} \times 5 \\ = \frac{25}{2} k g \end{aligned}

Quantity of Zinc in initial mixture

\begin{aligned} = \frac{5}{2} \times 2 \\ = 5 k g \end{aligned}

Now after adding 1.250 kg of zinc
= 5 + 1.250
= 6.250 kg
=

\frac{25}{4} k g

∴ New Ratio of copper : zinc

\begin{aligned} = \frac{25}{2} : \frac{25}{4} \\ = 2 : 1 \end{aligned}

75. The income of A, B and C are in the ratio 7 : 9 : 12 and their spending are in the ratio 8 : 9 : 15. If A saves $\frac{1}{4}$ th of his income then the savings of A, B and C are in the ratio of = ?

A. 56 : 99 : 69

B. 69 : 56 : 99

C. 99 : 56 : 69

D. 99 : 69 : 56

Discuss

Solution:

Let income of A, B and C are 7x, 9x and 12x respectively
and expenditure of A, B and C are 8y, 9y and 15y respectively

\begin{aligned} \Rightarrow Income of, \\ A \times \frac{1}{4} = Saving of A (given) \\ \Rightarrow 7 x - 8 y = 7 x \times \frac{1}{4} \\ \Rightarrow 28 x - 32 y = 7 x \\ \Rightarrow 21 x = 32 y \\ \Rightarrow x : y = 32 : 21 \end{aligned}

∴ The ratio of savings of A, B and C
⇒ (7x - 8y) : (9x - 9y) : (12x - 15y)
⇒ (7 × 32 - 8 × 21) : (9 × 32 - 9 × 21) : (12 × 32 - 15 × 21)
⇒ (224 - 168) : (288 - 189) : (384 - 315)
⇒ 56 : 99 : 69

76. What will be the simplest form of the ratio 3 hours : 1 day?

A. 1 : 3

B. 1 : 6

C. 1 : 8

D. 1 : 25

Discuss

Solution:

1 day = 24 hours.
∴ Given ration = 3 : 24
= 1 : 8

77. In a proportion the product of 1^st and 4^th terms is 40 and that of 2^nd and 3^rd terms is 2.5x. Then the value of x is.

A. 16

B. 26

C. 75

D. 90

Discuss

Solution:

Product of 1^st and 4^th terms (extremes) = product of 2^nd and 3^rd terms (means)

\begin{aligned} \Rightarrow 2 .5 x = 40 \\ \Rightarrow x = \frac{40}{2.5} = 16 \end{aligned}

78. If 20% of A = 30% of B = $\frac{1}{6}$ of C, then A : B : C is -

A. 2 : 3 : 6

B. 3 : 2 : 16

C. 10 : 15 : 18

D. 15 : 10 : 18

Discuss

Solution:

\begin{aligned} 20 % of A = 30 % of B = \frac{1}{6} of C \\ \Rightarrow \frac{20 A}{100} = \frac{30 B}{100} = \frac{C}{6} \\ \Rightarrow \frac{A}{5} = \frac{3 B}{10} = \frac{C}{6} = k (s a y) \\ \Rightarrow A = 5 K, B = \frac{10 k}{3}, C = 6 k \\ ∴ A : B : C = 5 k : \frac{10 k}{3} : 6 k \\ = 5 : \frac{10}{3} : 6 \\ = 15 : 10 : 18 \end{aligned}

79. Two numbers are in the ratio 17 : 45, One - third of the smaller is less than $\frac{1}{5}$ of the bigger by 15. The smaller number is = ?

A. $25 \frac{1}{2}$

B. $67 \frac{1}{2}$

C. $76 \frac{1}{2}$

D. $86 \frac{1}{2}$

Discuss

Solution:

\begin{aligned} A : B \\ 17 : 45 \\ 17 x : 45 x \\ Given \\ \Rightarrow 17 x \times \frac{1}{3} + 15 = 45 x \times \frac{1}{5} \\ \Rightarrow \frac{17 x + 45}{3} = 9 x \\ \Rightarrow 17 x + 45 = 27 x \\ \Rightarrow 10 x = 45 \\ \Rightarrow x = \frac{45}{10} \\ ∴ Smaller number is \\ = \frac{45}{10} \times 17 \\ = \frac{765}{10} \\ = 76 \frac{1}{2} \end{aligned}

80. 25% of A's income is equal to 35% of B's income. The ratio of the incomes of A and B is -

A. 5 : 7

B. 7 : 5

C. 13 : 15

D. 15 : 13

Discuss

Solution:

\begin{aligned} = 25 % of A = 35 % of B \\ \Rightarrow \frac{25}{100} A = \frac{35}{100} B \\ \Rightarrow \frac{A}{4} = \frac{7 B}{20} \\ \Rightarrow \frac{A}{B} = \frac{7}{20} \times 4 = \frac{7}{5} \\ \Rightarrow A : B = 7 : 5 \end{aligned}

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