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

51. If Rs. 782 be divided into three parts, proportional to $\frac{1}{2}$ : $\frac{2}{3}$ : $\frac{3}{4}$ then the first part is:

A. Rs. 182

B. Rs. 190

C. Rs. 196

D. Rs. 204

Discuss

Solution:

\begin{aligned} (\frac{1}{2} : \frac{2}{3} : \frac{3}{4}) \times 12 \\ \Rightarrow 6 : 8 : 9 \\ ∴ 1^{st} part's share \\ = Rs . (\frac{6}{23} \times 782) \\ = Rs . 6 \times 34 \\ = Rs . 204 \end{aligned}

52. The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?

A. 3 : 3 : 10

B. 10 : 11 : 20

C. 23 : 33 : 60

D. Cannot be determined

Discuss

Solution:

\begin{aligned} Let, \\ A = 2 k \\ B = 3 k and \\ C = 5 k \\ A^{'} s new salary \\ = \frac{115}{100} o f 2 k = \frac{115}{100} \times 2 k = \frac{23 k}{10} \\ B^{'} s new salary \\ = \frac{110}{100} o f 3 k = \frac{110}{100} \times 3 k = \frac{33 k}{10} \\ C^{'} s new salary \\ = \frac{120}{100} o f 5 k = \frac{120}{100} \times 5 k = 6 k \\ ∴ New ratio \\ = \frac{23 k}{10} : \frac{33 k}{10} : 6 k \\ = 23 : 33 : 60 \end{aligned}

53. If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?

A. 2 : 5

B. 3 : 7

C. 5 : 3

D. 7 : 3

Discuss

Solution:

\begin{aligned} Let 40 % of A = \frac{2}{3} B \\ Then, \frac{40 A}{100} = \frac{2 B}{3} \\ \Rightarrow \frac{2 A}{5} = \frac{2 B}{3} \\ \Rightarrow \frac{A}{B} = \frac{2}{3} \times \frac{5}{2} = \frac{5}{3} \\ ∴ A : B = 5 : 3 \end{aligned}

54. The fourth proportional to 5, 8, 15 is:

A. 18

B. 24

C. 19

D. 20

Discuss

Solution:

\begin{aligned} Let the fourth proportional to 5, 8, 15 be x \\ Then, 5 : 8 : 15 : x \\ \Rightarrow 5 x = 8 \times 15 \\ x = \frac{8 \times 15}{5} = 24 \end{aligned}

55. Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:

A. 27

B. 33

C. 49

D. 55

Discuss

Solution:

\begin{aligned} Let the number be 3 x and 5 x \\ Then, \frac{3 x - 9}{5 x - 9} = \frac{12}{23} \\ \Rightarrow 23 (3 x - 9) = 12 (5 x - 9) \\ \Rightarrow 9 x = 99 \\ \Rightarrow x = 11 \\ ∴ The smaller number \\ = 3 \times 11 \\ = 33 \end{aligned}

56. In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?

A. 50

B. 100

C. 150

D. 200

Discuss

Solution:

Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively
Then, sum of their values

\begin{aligned} = R s . (\frac{25 x}{100} + \frac{10 \times 2 x}{100} + \frac{5 \times 3 x}{100}) \\ = R s . \frac{60 x}{100} \\ ∴ \frac{60 x}{100} = 30 \Leftrightarrow x = \frac{30 \times 100}{60} = 50 \\ Hence, the number of 5p coins \\ = (3 \times 50) \\ = 150 \end{aligned}

57. What is the ratio in Rs. 2.80 and 40 paise?

A. 1 : 7

B. 2 : 7

C. 7 : 1

D. 1 : 14

Discuss

Solution:

Rs. 2.80 = 280 paise
∴ Required ration = 280 : 40
= 7 : 1

58. A person spends Rs. 8100 in buying some tables at Rs. 1200 each and some chairs at Rs. 300 each. The ratio of the number of chairs to that of tables when the maximum possible number of tables is purchased,

A. 1 : 2

B. 1 : 4

C. 2 : 1

D. 5 : 7

Discuss

Solution:

Maximum possible number of tables = 6
[∵ 1200 × 6 = 7200]
Number of chairs purchased

\begin{aligned} = \frac{8100 - 7200}{300} = \frac{900}{300} = 3 \\ Hence, \\ Required ratio = 3 : 6 \\ = 1 : 2 \end{aligned}

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

A. 3 : 2 : 1

B. 1 : 2 : 6

C. 1 : 3 : 6

D. 2 : 4 : 6

Discuss

Solution:

\begin{aligned} x = \frac{1}{3} y and y = \frac{1}{2} z \\ \frac{x}{y} = \frac{1}{3} and \frac{y}{z} = \frac{1}{2} \\ x : y = 1 : 3 \\ y : z = 1 : 2 \times 3 (multiply) \\ i . e . y : z = 3 : 6 \\ ∴ x : y : z = 1 : 3 : 6 \end{aligned}

60. If x : y = 3 : 1, then x³ - y³ : x³ + y³ = ?

A. 13 : 14

B. 14 : 13

C. 10 : 11

D. 11 : 10

Discuss

Solution:

\begin{aligned} x : y = 3 : 1 \\ ∴ \frac{x}{y} = \frac{3}{1} \\ ∴ \frac{x^{3} - y^{3}}{x^{3} + y^{3}} \\ \Rightarrow \frac{y^{3} (\frac{x^{3}}{y^{3}} - 1)}{y^{3} (\frac{x^{3}}{y^{3}} + 1)} \\ taking y^{3} common \\ = \frac{\frac{x^{3}}{y^{3}} - 1}{\frac{x^{3}}{y^{3}} + 1} \\ \Rightarrow \frac{27 - 1}{27 + 1} \\ \Rightarrow \frac{26}{28} \\ \Rightarrow \frac{13}{14} \end{aligned}

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