Bar Chart — Part 2 MCQs with Explanations

$$\eqalign{ & \text{Speeds of vehicles on Day 1:} \cr & \text{A → } \frac{832}{16}\text{ km/hr}=\text{52 km/hr} \cr & \text{B → } \frac{516}{12}\text{ km/hr}=\text{43 km/hr} \cr & \text{C → } \frac{693}{11}\text{ km/hr}=\text{63 km/hr} \cr & \text{D → } \frac{552}{12}\text{ km/hr}=\text{46 km/hr} \cr & \text{E → } \frac{935}{17}\text{ km/hr}=\text{55 km/hr} \cr & \text{F → } \frac{703}{19}\text{ km/hr}=\text{37 km/hr} \cr & \cr & \text{Speed of vehicles on Day 2:} \cr & \text{A → } \frac{864}{16}\text{ km/hr}=\text{54 km/hr} \cr & \text{B → } \frac{774}{18}\text{ km/hr}=\text{43 km/hr} \cr & \text{C → } \frac{810}{18}\text{ km/hr}=\text{45 km/hr} \cr & \text{D → } \frac{765}{15}\text{ km/hr}=\text{51 km/hr} \cr & \text{E → } \frac{546}{14}\text{ km/hr}=\text{39 km/hr} \cr & \text{F → } \frac{636}{12}\text{ km/hr}=\text{53 km/hr} \cr} $$ $$\eqalign{ & \text{Required ratio} \cr & = \frac{\text{Speed of D on Day 2}}{\text{Speed of E on Day 2}} \cr & = \frac{51}{39} \cr & = \frac{17}{13} \cr & = 17 : 13 \cr} $$

$$\eqalign{ & \text{Speeds of vehicles on Day 1:} \cr & \text{A → } \frac{832}{16}\text{ km/hr}=\text{52 km/hr} \cr & \text{B → } \frac{516}{12}\text{ km/hr}=\text{43 km/hr} \cr & \text{C → } \frac{693}{11}\text{ km/hr}=\text{63 km/hr} \cr & \text{D → } \frac{552}{12}\text{ km/hr}=\text{46 km/hr} \cr & \text{E → } \frac{935}{17}\text{ km/hr}=\text{55 km/hr} \cr & \text{F → } \frac{703}{19}\text{ km/hr}=\text{37 km/hr} \cr & \cr & \text{Speed of vehicles on Day 2:} \cr & \text{A → } \frac{864}{16}\text{ km/hr}=\text{54 km/hr} \cr & \text{B → } \frac{774}{18}\text{ km/hr}=\text{43 km/hr} \cr & \text{C → } \frac{810}{18}\text{ km/hr}=\text{45 km/hr} \cr & \text{D → } \frac{765}{15}\text{ km/hr}=\text{51 km/hr} \cr & \text{E → } \frac{546}{14}\text{ km/hr}=\text{39 km/hr} \cr & \text{F → } \frac{636}{12}\text{ km/hr}=\text{53 km/hr} \cr} $$ Difference between the speed of A on Day 1 and speed of C on Day 1 = (63 - 52) km/hr = 11 km/hr

$$\eqalign{ & \text{Speeds of vehicles on Day 1:} \cr & \text{A → } \frac{832}{16}\text{ km/hr}=\text{52 km/hr} \cr & \text{B → } \frac{516}{12}\text{ km/hr}=\text{43 km/hr} \cr & \text{C → } \frac{693}{11}\text{ km/hr}=\text{63 km/hr} \cr & \text{D → } \frac{552}{12}\text{ km/hr}=\text{46 km/hr} \cr & \text{E → } \frac{935}{17}\text{ km/hr}=\text{55 km/hr} \cr & \text{F → } \frac{703}{19}\text{ km/hr}=\text{37 km/hr} \cr & \cr & \text{Speed of vehicles on Day 2:} \cr & \text{A → } \frac{864}{16}\text{ km/hr}=\text{54 km/hr} \cr & \text{B → } \frac{774}{18}\text{ km/hr}=\text{43 km/hr} \cr & \text{C → } \frac{810}{18}\text{ km/hr}=\text{45 km/hr} \cr & \text{D → } \frac{765}{15}\text{ km/hr}=\text{51 km/hr} \cr & \text{E → } \frac{546}{14}\text{ km/hr}=\text{39 km/hr} \cr & \text{F → } \frac{636}{12}\text{ km/hr}=\text{53 km/hr} \cr} $$ $$\eqalign{ & \text{Required %} \cr & = \left(\frac{636}{703}\times100\right)\% \cr & = \frac{63600}{703}\% \cr & = 90.46\% \cr & \approx 90\% \cr} $$

$$\eqalign{ & \text{From bar diagram} \cr & \text{Profit percent of company Q} \cr & = \frac{40-30}{30}\times100 \cr & = \frac{100}{3} \cr & = 33\frac{1}{3}\% \cr} $$

Total income of all the five companies = Rs. (35 + 50 + 40 + 40 + 50) crores = Rs. 215 crores Total expenditure of all the five companies = Rs. (45 + 40 + 45 + 30 + 45) crores = Rs. 205 crores $$\eqalign{ & \therefore \text{ Profit percent}\cr & = \frac{\text{Income - Expenditure}}{\text{Expenditure}}\times100 \cr & = \frac{215 - 205}{205}\times100 \cr & = \frac{1000}{205} \cr & = 4.88\% \cr} $$

Expenditure of company R in 2000 $$\eqalign{ & = \frac{45\times100}{120} \cr & = \text{Rs. 37.5 crores} \cr }$$ Let the income of company in 2000 be Rs. $$x$$ crores $$\eqalign{ & \therefore 10 = \frac{x-37.5}{37.5}\times100 \cr & \Rightarrow x - 37.5 = \frac{37.5\times10}{100} \cr & \Rightarrow x - 37.5 = 3.75 \cr & \Rightarrow x = 37.5+3.75 \cr & \Rightarrow x = \text{Rs. 41.25 crores} \cr} $$

$$\eqalign{ & \text{Income of company Q in 2000} \cr & = \frac{100}{110}\times140 \cr & = \frac{400}{11}\text{ crores} \cr & \text{If expenditure in 2000 be Rs. x crores} \cr & \text{Profit %} \cr & \Rightarrow \frac{\text{Income - Expenditure}}{\text{Expenditure}}\times100=\frac{\frac{400}{11}-x}{x} \cr & \Rightarrow \frac{20}{100} = \frac{400-11x}{11x} \cr & \Rightarrow \frac{1}{5} = \frac{400-11x}{11x} \cr & \Rightarrow 5\times400-55x=11x \cr & \Rightarrow 66x = 2000 \cr & \Rightarrow x = \frac{2000}{66} \cr & \Rightarrow x = \text{Rs. 30.30 crores} \cr} $$

Total income of companies M and N = Rs. (35 + 50) crores = Rs. 85 crores Total expenditure = Rs. (45 + 40) crores = Rs. 85 crores Hence, the companies M and N had no loss and no profit.

Total monthly salary of Arun in all the years = 14000 + 18000 + 23000 + 21000 + 27000 + 25000 = Rs. 128000 Monthly salary of Suman in the year 2007 = Rs. 15000 Difference between their Salary = 128000 - 15000 = Rs. 1.13 lakh

Year Arun's income Jyoti's income Difference 2005 14000 9000 5000 2006 18000 11000 7000 2007 23000 18000 5000 2008 21000 27000 6000 2009 27000 26000 1000 2010 25000 35000 10000 In 2006 difference between Jyoti's monthly income and Arun's monthly income second highest.

Jyoti's income in 2008 = Rs. 27000 Jyoti's income in 2007 = Rs. 18000 ∴ Increase percentage $$\eqalign{ & = \frac{2700-1800}{18000}\times100 \cr & = \frac{9000}{18000}\times100 \cr & = 50\% \cr} $$

In year 2006 Arun's salary In year 2007 Suman's salary In year 2005 Jyoti's salary 18000 15000 9000 18 15 9 6 5 3

Monthly income of Suman in year 2009 = Rs. 29000 Monthly income of Jyoti in year 2010 = Rs. 35000 $$\eqalign{ & = \frac{29000}{35000}\times100 \cr & = 82.85 \cr & \approx 83\% \cr} $$

Production of company D = 2700 Production of company A = 1500 $$\eqalign{ & h = \frac{\text{Production of company D}}{\text{Production of company A}} \cr & h = \frac{2700}{1500} \cr & h = \frac{9}{5} \cr & h = 1.8 \cr} $$

Number of companies having more demand than production = 3 Number of companies having more production than demand = 2 ∴ Required ratio = 3 : 2

Difference between demand and production of company A = 3000 - 1500 = 1500 Difference between production and demand of company D = 2700 - 1200 = 1500

Total production of the five companies = 1500 + 1800 +1000 + 2700 + 2200 = 9200 Total demand of the five companies = 3000 + 600 + 2500 + 1200 + 3300 = 10600 ∴ Required difference $$\eqalign{ & = \frac{1}{5}\left(10600-9200\right) \cr & = \frac{1}{5}\times1400 \cr & = 280 \cr} $$

Given $$x$$% of demand for company C = Demand for company B $$\eqalign{ & \Rightarrow \frac{2500\times x}{100} = 600 \cr & \Rightarrow 25x = 600 \cr & \Rightarrow x = \frac{600}{25} \cr & \Rightarrow x = 24 \cr} $$

Total sales of branch B6 for both years = 70 + 80 = 150 Total sales of branch B3 for both years = 95 + 110 = 205 ∴ Required percentage = $$\frac{150}{205} × 100$$ = 73.17%

Total sales of branches B1, B3 and B5 for both the years (in thousands numbers) = (80 + 105) + (95 + 110) + (75 + 95) = 560

Required ratio $$=\frac{\text{Total sales of branch B2 for both years}}{\text{Total sales of branch B4 for both years}}$$ $$\eqalign{ & = \frac{75+65}{85+95} \cr & = \frac{140}{180} \cr & = \frac{7}{9} \cr & = 7:9 \cr} $$

Total sales (in thousand numbers) of branches B1, B3 and B6 in 2000 = 80 + 95 + 70 = 245 Average sales (in thousands number) of branches B1, B3 and B6 in 2000 = $$\frac{245}{3}$$ Total sales (in thousands number) of branches B1, B2 and B3 in 2001 = 105 + 65 + 110 = 280 Average sales (in thousand number) of branches B1, B2 and B3 in 2001 $$\eqalign{ & = \frac{280}{3} \cr & \text{So,Required percentage} \cr & = \frac{\frac{245}{3}}{\frac{280}{3}}\times100\% \cr & = \frac{245}{280}\times100 \cr & = 87.5\% \cr} $$

Total sales of all the six branches (in thousand numbers) for the year 2000 = 80 + 75 + 95 + 85 + 75 + 70 = 480 Average sales of all the six branches (in thousand numbers) for the year 2000 $$\eqalign{ & = \frac{480}{6} \cr & = 80 \cr} $$

In 2007, we have: Total number of students = 455030 Number of those choosing the given three subjects = 15000 + 10000 + 15000 = 40000 ∴ Required percentage $$\eqalign{ & = \left(\frac{40000}{455030}\times100\right)\% \cr & = 8.79\% \cr & \approx 9\% \cr} $$

Ratio of the number who opted for English in 2006 and 2008 to the number who opted for Hindi in 2005 and 2009 = (25 + 30) : (5 + 20) = 55 : 25 = 11 : 5

Number of students who opted Hindi and Mathematics in 2006, 2007 and 2009 = {(5 + 35) + (15 + 15) + (20 + 5)} thousands = 95000

Number of students who opted for the given three subjects in the year 2009 is = 20000 + 20000 + 5000 = 45000 Number of girls = 38% of 45000 = 45000 × $$\frac{38}{100}$$ = 17100 Out of these, the number of boys who opted for Mathematics cannot be found.

Number of students opting Mathematics in 2005 and 2008 = 15000 + 30000 = 45000 Number of students opting for these three subjects in 2005 and 2008 = {(5 + 35 + 15) + (25 + 30 + 30)} thousands = 55000 + 85000 = 140000 $$\eqalign{ & \text{Required %} \cr & = \left(\frac{45000}{140000}\times100\right)\% \cr & = \frac{225}{7}\% \cr & = 32.14\% \cr & \approx 32\% \cr} $$

$$\eqalign{ & \text{Total number of teachers in:} \cr & \text{A → } \frac{14}{100}\times4500 = 630\cr & \text{B → } \frac{16}{100}\times4500 = 720\cr & \text{C → } \frac{28}{100}\times4500 = 1260\cr & \text{D → } \frac{15}{100}\times4500 = 675\cr & \text{E → } \frac{21}{100}\times4500 = 945\cr & \text{F → } \frac{6}{100}\times4500 = 270\cr} $$ A B C D E F Males 200 400 600 100 500 100 Females 430 320 660 575 445 170 Total number of male teacher in F, female teacher in C and female teacher in B = 100 + 660 + 320 = 1080

$$\eqalign{ & \text{Total number of teachers in:} \cr & \text{A → } \frac{14}{100}\times4500 = 630\cr & \text{B → } \frac{16}{100}\times4500 = 720\cr & \text{C → } \frac{28}{100}\times4500 = 1260\cr & \text{D → } \frac{15}{100}\times4500 = 675\cr & \text{E → } \frac{21}{100}\times4500 = 945\cr & \text{F → } \frac{6}{100}\times4500 = 270\cr} $$ A B C D E F Males 200 400 600 100 500 100 Females 430 320 660 575 445 170 Clearly, the number of male teachers is more than the number of female teachers in B and E.

$$\eqalign{ & \text{Total number of teachers in:} \cr & \text{A → } \frac{14}{100}\times4500 = 630\cr & \text{B → } \frac{16}{100}\times4500 = 720\cr & \text{C → } \frac{28}{100}\times4500 = 1260\cr & \text{D → } \frac{15}{100}\times4500 = 675\cr & \text{E → } \frac{21}{100}\times4500 = 945\cr & \text{F → } \frac{6}{100}\times4500 = 270\cr} $$ A B C D E F Males 200 400 600 100 500 100 Females 430 320 660 575 445 170 (Number of male teachers in C) : (Number of female teachers in B) = 600 : 320 = 15 : 8

$$\eqalign{ & \text{Total number of teachers in:} \cr & \text{A → } \frac{14}{100}\times4500 = 630\cr & \text{B → } \frac{16}{100}\times4500 = 720\cr & \text{C → } \frac{28}{100}\times4500 = 1260\cr & \text{D → } \frac{15}{100}\times4500 = 675\cr & \text{E → } \frac{21}{100}\times4500 = 945\cr & \text{F → } \frac{6}{100}\times4500 = 270\cr} $$ A B C D E F Males 200 400 600 100 500 100 Females 430 320 660 575 445 170 Female teacher in D = 575 Total number of teacher in A = 200 + 430 = 630 ∴ Required percentage $$\eqalign{ & = \left(\frac{575}{630}\times100\right)\% \cr & = \frac{5750}{63}\% \cr & = 91.2\% \cr & \approx 90\% \cr} $$

$$\eqalign{ & \text{Total number of teachers in:} \cr & \text{A → } \frac{14}{100}\times4500 = 630\cr & \text{B → } \frac{16}{100}\times4500 = 720\cr & \text{C → } \frac{28}{100}\times4500 = 1260\cr & \text{D → } \frac{15}{100}\times4500 = 675\cr & \text{E → } \frac{21}{100}\times4500 = 945\cr & \text{F → } \frac{6}{100}\times4500 = 270\cr} $$ A B C D E F Males 200 400 600 100 500 100 Females 430 320 660 575 445 170 Number of female teachers in F = 170 Total number of teachers in E = 500 + 445 = 945 ∴ Required difference = 945 - 170 = 775

Total accidents = 230 + 150 + 120 + 160 + 40 + 200 + 100 = 1000 Percentage of accidents involving two wheelers = $$\frac{230}{1000}$$ × 100 = 23% Percentage of accidents involving two wheelers and other subjects = $$\frac{770 \times 100}{1000}$$ = 77% ∴ Required difference = 77 - 23 = 54%

Required Percentage $$\eqalign{ & = \left( {\frac{{40 + 200}}{{1000}}} \right) \times 100 \cr & = \frac{{24000}}{{1000}} \cr & = 24\% \cr} $$

Two wheelers + Cars + Buses + Stationary vehicles = 230 + 150 + 120 + 100 = 600 ∴ $$\frac{600}{1000}$$ × 100 = 60%

Required difference = $$\frac{160 - 120}{1000}$$ × 100 = 4%

$$\eqalign{ & \therefore {360^ \circ } = 1000{\text{ Accidents}} \cr & \,\,\,\,\,{1^ \circ } = \frac{{1000}}{{{{360}^ \circ }}} \cr &\,\,\,\,\, {36^ \circ } = \frac{{1000}}{{{{360}^ \circ }}} \times {36^ \circ } \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 100{\text { Accidents}} \cr} $$ It is the accidents of Stationary vehicles

'D' type production in 2007 = 35 × $$\frac{10}{100}$$ 'D' type production in 2008 = 44 × $$\frac{10}{100}$$ Required Answer $$\eqalign{ & = \left( {35 \times \frac{{10}}{{100}} + 44 \times \frac{{10}}{{100}}} \right) \times \frac{{15}}{{100}} \cr & = 118500 \cr} $$

$$\eqalign{ & \text{Required Answer} \cr & = \frac{{35 \times 30}}{{100}} + \frac{{35 \times 15}}{{100}} + \frac{{35 \times 15}}{{100}} \cr & = \frac{{35}}{{100}}\left( {30 + 15 + 15} \right) \cr & = \frac{{35 \times 60}}{{100}} \cr & = 21{\text{ lakhs}} \cr} $$