Average - Aptitude MCQ Questions and Solutions with Explanations

Average of first 'n' natural number
$$\eqalign{ & = \frac{{\left( {n + 1} \right)}}{2} \cr & = \frac{{93 + 1}}{2} \cr & = 47 \cr} $$

$$\eqalign{ & {\text{Students in }}A = 50 \cr & {\text{Students in }}B = 40 \cr & {\text{Total students}}:A:B = 9:5:4 \cr & \frac{{{\text{Average of }}A}}{{{\text{Average of }}B}} = \frac{{13x}}{{10x}} \cr & 9 \times 63 = 13x \times 5 + 10x \times 4 \cr & 567 = 65x + 40x \cr & 105x = 567 \cr & x = \frac{{567}}{{105}} \cr & x = \frac{{81}}{{15}} \cr & x = \frac{{27}}{5} \cr & {\text{Average of }}B = 10x \cr & = 10 \times \frac{{27}}{5} \cr & = 54 \cr} $$

$$\eqalign{ & 21,\,22,\,23\,........\,39 \cr & n = \left( {39 - 21} \right) + 1 \cr & n = 18 + 1 \cr & n = 19 \cr & {S_{19}} = \frac{n}{2}\left( {{\text{first}} + {\text{last}}} \right) \cr & = \frac{{19}}{2}\left( {21 + 39} \right) \cr & = \frac{{19}}{2} \times 60 \cr & = 19 \times 30 \cr & {\text{Average}} = \frac{{{\text{sum}}}}{n} \cr & = \frac{{19 \times 30}}{{19}} \cr & = 30 \cr} $$

By using alligation method
Total students = 50
Girls = 22 (Given)
Boys = 50 - 22 = 28

\[\begin{array}{*{20}{c}} {}&{28}&:&{22} \\ {{\text{Ratio}} \Rightarrow }&{14}&:&{11} \end{array}\]
14 units = 7
1 unit = $$\frac{7}{{14}}$$
1 unit = $$\frac{1}{2}$$
11 units = 11 × $$\frac{1}{2}$$ = 5.5
Average marks of boys
x = 42 + 5.5 = 47.5

$$\eqalign{ & {\text{Let numbers be }}a,\,a + 1,\,a + 2,\,a + 3,\,a + 4 \cr & {\text{Next, }}a + 5,\,a + 6,\,a + 7,\,a + 8,\,a + 9 \cr & {\text{Next to Next, }}a + 10,\,a + 11,\,a + 12,\,a + 13,\,a + 14 \cr & {{\text{I}}^{{\text{st}}}}{\text{ condition}} = \frac{{5a + 10}}{5} = x \cr & 5a + 10 = 5x\,......\,\left( {\text{i}} \right) \cr & {\text{I}}{{\text{I}}^{{\text{nd}}}}{\text{ condition}} \cr & = \frac{{a + 10 + a + 11 + a + 12 + a + 13 + a + 14}}{5} \cr & = \frac{{5a + 50 + 10}}{5} \cr & {\text{From equation }}\left( {\text{i}} \right) \cr & = \frac{{5x + 50}}{5} \cr & = x + 10 \cr} $$

$$\eqalign{ & x + x + 1 + \,.......\, + x + 7 = 38.5 \times 8 = 308 \cr & 8x + 28 = 308 \cr & x = \frac{{308 - 28}}{8} \cr & x = \frac{{280}}{8} = 35 \cr & {\text{Lergest number}} = x + 7 \cr & = 35 + 7 \cr & = 42 \cr} $$

$$\eqalign{ & {\text{11 to 80 divisible by 6}} \cr & {\text{12, 18, }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. 78}} \cr & {\text{First term}}\left( a \right) = 12 \cr & {\text{Last term}}\left( l \right) = 78 \cr & {\text{Total number of terms}} \cr & = \frac{{{\text{Last term }} - {\text{ First term}}}}{{{\text{Common difference}}}} + 1 \cr & = \frac{{78 - 12}}{6} + 1 \cr & = 12 \cr & {\text{Average of 12 numbers}} \cr & = \frac{n}{2}\frac{{\left( {a + l} \right)}}{n} \cr & = \frac{{12 + 78}}{2} \cr & = 45 \cr} $$

7 × 5a + 13 × 6a = 20 × 13.56
35a + 78a = 271.2
113a = 271.2
a = 2.4
Average of girls = 5a
= 5 × 2.4
= 12

$$\eqalign{ & A:B:C = 2:5:3 \cr & {\text{Average}} = \frac{{30 \times 2 + 17 \times 5 + 25 \times 3}}{{10}} \cr & = \frac{{60 + 85 + 75}}{{10}} \cr & = 22 \cr} $$

$$66\frac{2}{3}\% \to \frac{{ + 2}}{3}$$
\[\begin{array}{*{20}{c}} {}&{1\,\,\,\,\,\,\,\,\,\,:\,\,\,\,\,\,\,\,\,\,2} \\ {{\text{Average}} \to }&{5a\,\,\,\,\,\,\,\,:\,\,\,\,\,\,\,\,3a} \\ {}&{\overline {\,\,5a + 6a = 3 \times 66\,\,} } \\ {}&{11a = 3 \times 66} \\ {}&{a = 18} \end{array}\]
Average of girls = 3a = 3 × 18 = 54