Decimal Fraction - Aptitude MCQ Questions and Solutions with Explanations

41

The rational number for the recurring decimal 0.125125..... is :

A) $$\frac{{63}}{{487}}$$ B) $$\frac{{119}}{{993}}$$ C) $$\frac{{125}}{{999}}$$ D) None of these

Discuss

Answer & Solution

Answer: Option C

Solution:

$$\eqalign{ & 0.125125.... \cr & = 0.\overline {125} \cr & = \frac{{125}}{{999}} \cr} $$

42

Which of the following fractions lies between $$\frac{2}{3}$$ and $$\frac{3}{5}$$ = ?

A) $$\frac{2}{5}$$ B) $$\frac{1}{3}$$ C) $$\frac{1}{15}$$ D) $$\frac{31}{50}$$

Discuss

Answer & Solution

Answer: Option D

Solution:

$$\eqalign{ & \frac{2}{3} = 0.666 \cr & \frac{3}{5} = 0.6 \cr & \frac{2}{5} = 0.4 \cr & \frac{1}{3} = 0.333 \cr & \frac{1}{{15}} = 0.066 \cr & \frac{{31}}{{50}} = 0.62 \cr} $$
Clearly, 0.62 lies between 0.6 and 0.666
So, $$\frac{31}{50}$$ lies between $$\frac{2}{3}$$ and $$\frac{3}{5}$$

43

$$\frac{5}{9}$$ of a number is equal to twenty five percent of second number. Second number is equal to $$\frac{1}{4}$$ of third number. The value of third number is 2960. What is 30% of first number ?

A) 99.9 B) 88.8 C) 77.7 D) None of these

Discuss

Answer & Solution

Answer: Option A

Solution:

Let the third number be 2960
∵ Second number = $$\frac{1}{4}$$ of the third number = $$\frac{1}{4}$$ × 2960 = 740
$$\frac{5}{9}$$ of first number = 25% of second number
$$\frac{5}{9}$$ first number = $$\frac{25 × 740}{100}$$ = 185
⇒ First number = $$\frac{185 × 9}{5}$$ = 333
∴ 30% of 333 = $$\frac{30}{100}$$ × 333 = 99.9

44

Solve this, $$\frac{3.5 × 1.4}{0.7}$$ = ?

A) 0.7 B) 2.4 C) 3.5 D) 7.1 E) None of these

Discuss

Answer & Solution

Answer: Option E

Solution:

Given expression
= $$\frac{35 × 1.4}{7}$$
= 5 × 1.4
= 7

45

Express $$\frac{1999}{2111}$$ in decimal :

A) 0.893 B) 0.904 C) 0.946 D) 0.986

Discuss

Answer & Solution

Answer: Option C

Solution:

$$\therefore \frac{{1999}}{{2111}} = 0.946$$

46

The value of $$\left( {\frac{{0.943 \times 0.943 - 0.943 \times 0.057 + 0.057 \times 0.057}}{{0.943 \times 0.943 \times 0.943 + 0.057 \times 0.057 \times 0.057}}} \right)$$ is :

A) 0.32 B) 0.886 C) 1.1286 D) None of these

Discuss

Answer & Solution

Answer: Option D

Solution:

Given expression :
$$\eqalign{ & = \frac{{{{\left( {0.943} \right)}^2} - \left( {0.943 \times 0.057} \right) + {{\left( {0.057} \right)}^2}}}{{{{\left( {0.943} \right)}^3} + {{\left( {0.057} \right)}^3}}} \cr & = \frac{{{a^2} - ab + {b^2}}}{{{a^3} + {b^3}}} \cr & = \frac{1}{{a + b}} \cr & = \frac{1}{{0.943 + 0.057}} \cr & = 1 \cr} $$

47

[(?)² + (18)²] ÷ 125 = 3.56

A) 11 B) 12 C) 14 D) 15 E) None of these

Discuss

Answer & Solution

Answer: Option A

Solution:

Let, $$\frac{{{x^2} + {{\left( {18} \right)}^2}}}{{125}} = 3.56$$
Then,
$$\eqalign{ & {x^2} + 324 = 125 \times 3.56 = 445 \cr & \Rightarrow {x^2} = 121 \cr & \Rightarrow x = 11 \cr} $$

48

534.596 + 61.472 - 496.708 = ? + 27.271

A) 62.069 B) 72.089 C) 126.631 D) 132.788 E) None of these

Discuss

Answer & Solution

Answer: Option B

Solution:

Let 534.596 + 61.472 - 496.708 = x + 27.271
Then, x = (534.596 + 61.472) - (496.708 + 27.271)
= 596.068 - 523.979
= 72.089

49

Solve $${\left( {\frac{{18}}{4}} \right)^2} \times $$ $$\left( {\frac{{455}}{{19}}} \right) \div $$ $$\left( {\frac{{61}}{{799}}} \right) = ?$$

A) 6320 B) 6400 C) 6350 D) 6430 E) 6490

Discuss

Answer & Solution

Answer: Option C

Solution:

$$\eqalign{ & {\left( {\frac{{18}}{4}} \right)^2} \times \left( {\frac{{455}}{{19}}} \right) \div \left( {\frac{{61}}{{799}}} \right) \cr & = \frac{{324}}{{16}} \times \frac{{455}}{{19}} \times \frac{{799}}{{61}} \cr & = 6350 \cr} $$

50

Solve $$\frac{294 ÷ 14 × 5 + 11}{?}$$ = 8² ÷ 5 + 1.7

A) 8 B) 6 C) 12 D) 5 E) 10

Discuss

Answer & Solution

Answer: Option A

Solution:

Let the missing number be x
$$\eqalign{ & \frac{{294 \div 14 \times 5 + 11}}{x} = {8^2} \div 5 + 1.7 \cr & \Rightarrow \frac{{\frac{{294}}{{14}} \times 5 + 11}}{x} = \frac{{64}}{5} + 1.7 \cr & \Rightarrow \frac{{21 \times 5 + 11}}{x} = 12.8 + 1.7 \cr & \Rightarrow \frac{{105 + 11}}{x} = 12.8 + 1.7 \cr & \Rightarrow \frac{{116}}{x} = 14.5 \cr & \Rightarrow x = \frac{{116}}{{14.5}} \cr & \Rightarrow x = \frac{{116 \times 10}}{{145}} \cr & \Rightarrow x = 8 \cr} $$
Hence, the number is 8