Decimal Fraction - Aptitude MCQ Questions and Solutions with Explanations

= 3899 ÷ 11.99 - 2379 ÷ 13.97
= 3899 ÷ 12 - 2380 ÷ 14
≈ 325 - 170
= 155

Let the missing number be x
Given, $$1\frac{1}{2}$$ + $$2\frac{2}{7}$$ = $$3\frac{1}{2}$$ + x
x = $$1\frac{1}{2}$$ + $$2\frac{2}{7}$$ - $$3\frac{1}{2}$$
x = $$\frac{3}{2}$$ + $$\frac{16}{7}$$ - $$\frac{7}{2}$$
x = $$\frac{21 + 32 - 49}{14}$$
x = $$\frac{4}{14}$$
x = $$\frac{2}{7}$$
Hence, the number is $$\frac{2}{7}$$

= $$\frac{0.0203 × 2.92}{0.0073 × 14.5 × 0.7}$$
= $$\frac{203 × 292}{73 × 145 × 7}$$
= $$\frac{4}{5}$$
= 0.8

$$\eqalign{ & = \frac{{{{\left( {2.3} \right)}^3} - 0.027}}{{{{\left( {2.3} \right)}^2} + 0.69 + 0.09}} \cr & = \frac{{{{\left( {2.3} \right)}^3} - {{\left( {0.03} \right)}^3}}}{{{{\left( {2.3} \right)}^2} + \left( {2.3 \times 0.3} \right) + {{\left( {0.3} \right)}^2}}} \cr & = \left[ {\frac{{{a^3} - {b^3}}}{{{a^2} + ab + {b^2}}}} \right] \cr & = \left( {a - b} \right) \cr & = \left( {2.3 - 0.3} \right) \cr & = 2 \cr} $$

Given expression :
= (100 - 0.25)² - 2250.0625
= (100)² + (0.25)² - 2 × 100 × 0.25 - 2250.0625
= 10000.0625 - 50 - 2250.0625
= 10000.0625 - 2300.0625
= 7700

Given expression :
= $$\frac{0.2 (0.2 + 0.02)}{0.044}$$
= $$\frac{0.2 ×0.22}{0.044}$$
= $$\frac{0.044}{0.044}$$
= 1

$$\eqalign{ & 2\frac{{1.5}}{5} + 2\frac{1}{6} - 1\frac{{3.5}}{{15}} = \frac{{{x^{\frac{1}{3}}}}}{4} + 1\frac{7}{{30}} \cr & \Rightarrow \frac{{11.5}}{5} + \frac{{13}}{6} - \frac{{18.5}}{{15}} = \frac{{{x^{\frac{1}{3}}}}}{4} + \frac{{37}}{{30}} \cr} $$
⇒ L.C.M. of 5, 6 and 15 is 30
$$\eqalign{ & \Rightarrow \frac{{69 + 65 - 37}}{{30}} = \frac{{{x^{\frac{1}{3}}}}}{4} + \frac{{37}}{{30}} \cr & \Rightarrow \frac{{97}}{{30}} = \frac{{{x^{\frac{1}{3}}}}}{4} + \frac{{37}}{{30}} \cr & \Rightarrow \frac{{{x^{\frac{1}{3}}}}}{4} = \frac{{97}}{{30}} - \frac{{37}}{{30}} \cr & \Rightarrow {x^{\frac{1}{3}}} = \frac{{60}}{{30}} \times 4 \cr & \Rightarrow {x^{\frac{1}{3}}} = 8 \cr & \Rightarrow x = {\left( 8 \right)^3} \cr & \Rightarrow x = 512 \cr} $$
Hence, the number is 512

Given expression :
= $$\frac{441 × 16}{21 × 16 × 21}$$
= $$\frac{{7056}}{{7056}}$$
= 1

Given expression :
[(0.98)³ + (0.02)³ + 3 × 0.98 × 0.02 (0.98 + 0.02)] - 1
= (0.98 + 0.02)³ - 1
= (1)³ - 1
= 0

{(41.99)² - (18.04)²} ÷ ? = (13.11)² - 138.99
⇒ {(42)² - (18)²} ÷ ? = (13)² - 139 {∵ a² - b² = (a + b) (a - b)}
⇒ {(42 + 18) (42 - 18)} ÷ ? = 169 - 139
⇒ 60 × 24 ÷ ? = 30
⇒ ? = $$\frac{60 × 24}{30}$$
⇒ ? = 48