Pie Chart — Part 2 MCQs with Explanations

Number of mobile phones sold by A during November $$\eqalign{ & = 45000\times\frac{12}{100}\times\frac{7}{15} \cr & = 2520 \cr} $$ Number of phones sold by A in November without discount $$\eqalign{ & = 2520\times\frac{65}{100} \cr & = 1638 \cr} $$

Mobile phones of B sold during August $$\eqalign{ & = 45000\times\frac{22}{100}\times\frac{5}{9} \cr & = 5500 \cr} $$ Mobile phones of B sold during September $$\eqalign{ & = 45000\times\frac{25}{100}\times\frac{2}{5} \cr & = 4500 \cr} $$ ∴ Required number of phones sold = 5500 + 4500 = 10000

Number of students enrolled in various streams: $$\eqalign{ & \text{IT → } \frac{20}{100}\times3500 = 700 \cr & \text{Arts → } \frac{30}{100}\times3500 = 1050 \cr & \text{Science → } \frac{22}{100}\times3500 = 770 \cr & \text{Commerce → } \frac{12}{100}\times3500 = 420 \cr & \text{Management → } \frac{16}{100}\times3500 = 560 \cr} $$ Number of girls enrolled in various streams: $$\eqalign{ & \text{IT → } \frac{18}{100}\times1500 = 270 \cr & \text{Arts → } \frac{38}{100}\times1500 = 570 \cr & \text{Science → } \frac{11}{100}\times1500 = 165 \cr & \text{Commerce → } \frac{21}{100}\times1500 = 315 \cr & \text{Management → } \frac{12}{100}\times1500 = 180 \cr} $$ (Number of girls enrolled in Arts) : (Number of boys enrolled in Science) = 570 : (770 - 165) = 570 : 605 = 114 : 121

Number of students enrolled in various streams: $$\eqalign{ & \text{IT → } \frac{20}{100}\times3500 = 700 \cr & \text{Arts → } \frac{30}{100}\times3500 = 1050 \cr & \text{Science → } \frac{22}{100}\times3500 = 770 \cr & \text{Commerce → } \frac{12}{100}\times3500 = 420 \cr & \text{Management → } \frac{16}{100}\times3500 = 560 \cr} $$ Number of girls enrolled in various streams: $$\eqalign{ & \text{IT → } \frac{18}{100}\times1500 = 270 \cr & \text{Arts → } \frac{38}{100}\times1500 = 570 \cr & \text{Science → } \frac{11}{100}\times1500 = 165 \cr & \text{Commerce → } \frac{21}{100}\times1500 = 315 \cr & \text{Management → } \frac{12}{100}\times1500 = 180 \cr} $$ Number of girls enrolled in Arts, Science and Commerce = 570 + 165 + 315 = 1050 Required percentage $$\eqalign{ & = \left(\frac{1050}{3500}\times100\right)\% \cr & = 30\% \cr} $$

Number of students enrolled in various streams: $$\eqalign{ & \text{IT → } \frac{20}{100}\times3500 = 700 \cr & \text{Arts → } \frac{30}{100}\times3500 = 1050 \cr & \text{Science → } \frac{22}{100}\times3500 = 770 \cr & \text{Commerce → } \frac{12}{100}\times3500 = 420 \cr & \text{Management → } \frac{16}{100}\times3500 = 560 \cr} $$ Number of girls enrolled in various streams: $$\eqalign{ & \text{IT → } \frac{18}{100}\times1500 = 270 \cr & \text{Arts → } \frac{38}{100}\times1500 = 570 \cr & \text{Science → } \frac{11}{100}\times1500 = 165 \cr & \text{Commerce → } \frac{21}{100}\times1500 = 315 \cr & \text{Management → } \frac{12}{100}\times1500 = 180 \cr} $$ Total number of girls enrolled in Science and Commerce together = 165 + 315 = 480

Number of students enrolled in various streams: $$\eqalign{ & \text{IT → } \frac{20}{100}\times3500 = 700 \cr & \text{Arts → } \frac{30}{100}\times3500 = 1050 \cr & \text{Science → } \frac{22}{100}\times3500 = 770 \cr & \text{Commerce → } \frac{12}{100}\times3500 = 420 \cr & \text{Management → } \frac{16}{100}\times3500 = 560 \cr} $$ Number of girls enrolled in various streams: $$\eqalign{ & \text{IT → } \frac{18}{100}\times1500 = 270 \cr & \text{Arts → } \frac{38}{100}\times1500 = 570 \cr & \text{Science → } \frac{11}{100}\times1500 = 165 \cr & \text{Commerce → } \frac{21}{100}\times1500 = 315 \cr & \text{Management → } \frac{12}{100}\times1500 = 180 \cr} $$ Total number of boys enrolled in Management and IT together = (560 - 180) + (700 - 270) = 380 + 430 = 810

Number of students enrolled in various streams: $$\eqalign{ & \text{IT → } \frac{20}{100}\times3500 = 700 \cr & \text{Arts → } \frac{30}{100}\times3500 = 1050 \cr & \text{Science → } \frac{22}{100}\times3500 = 770 \cr & \text{Commerce → } \frac{12}{100}\times3500 = 420 \cr & \text{Management → } \frac{16}{100}\times3500 = 560 \cr} $$ Number of girls enrolled in various streams: $$\eqalign{ & \text{IT → } \frac{18}{100}\times1500 = 270 \cr & \text{Arts → } \frac{38}{100}\times1500 = 570 \cr & \text{Science → } \frac{11}{100}\times1500 = 165 \cr & \text{Commerce → } \frac{21}{100}\times1500 = 315 \cr & \text{Management → } \frac{12}{100}\times1500 = 180 \cr} $$ Number of Management students already enrolled = 560 New required number $$\eqalign{ & = 560 + \left(\frac{20}{100}\times165\right) \cr & = 560+33 \cr & = 593 \cr} $$

Number of students in various specialisations: $$\eqalign{ & \text{IB → } \frac{19}{100}\times8000 = 1520 \cr & \text{IR → } \frac{16}{100}\times8000 = 1280 \cr & \text{Finance → } \frac{12}{100}\times8000 = 960 \cr & \text{Marketing → } \frac{22}{100}\times8000 = 1760 \cr & \text{IT → } \frac{17}{100}\times8000 = 1360 \cr & \text{HR → } \frac{14}{100}\times8000 = 1120 \cr} $$ $$\eqalign{ & \text{Required percentage} \cr & = \left(\frac{1520}{1760}\times100\right)\% \cr & = \frac{950}{11}\% \cr & = 86.36\% \cr & \approx 86\% \cr} $$

Number of students in various specialisations: $$\eqalign{ & \text{IB → } \frac{19}{100}\times8000 = 1520 \cr & \text{IR → } \frac{16}{100}\times8000 = 1280 \cr & \text{Finance → } \frac{12}{100}\times8000 = 960 \cr & \text{Marketing → } \frac{22}{100}\times8000 = 1760 \cr & \text{IT → } \frac{17}{100}\times8000 = 1360 \cr & \text{HR → } \frac{14}{100}\times8000 = 1120 \cr} $$ $$\eqalign{ & \text{Required percentage} \cr & = \left(\frac{1280}{1120}\times100\right)\% \cr & = \frac{800}{7}\% \cr & = 114.28\% \cr & \approx 114\% \cr} $$

Number of students in various specialisations: $$\eqalign{ & \text{IB → } \frac{19}{100}\times8000 = 1520 \cr & \text{IR → } \frac{16}{100}\times8000 = 1280 \cr & \text{Finance → } \frac{12}{100}\times8000 = 960 \cr & \text{Marketing → } \frac{22}{100}\times8000 = 1760 \cr & \text{IT → } \frac{17}{100}\times8000 = 1360 \cr & \text{HR → } \frac{14}{100}\times8000 = 1120 \cr} $$ Number of those having IB as specialisation = 1520

Number of students in various specialisations: $$\eqalign{ & \text{IB → } \frac{19}{100}\times8000 = 1520 \cr & \text{IR → } \frac{16}{100}\times8000 = 1280 \cr & \text{Finance → } \frac{12}{100}\times8000 = 960 \cr & \text{Marketing → } \frac{22}{100}\times8000 = 1760 \cr & \text{IT → } \frac{17}{100}\times8000 = 1360 \cr & \text{HR → } \frac{14}{100}\times8000 = 1120 \cr} $$ Required number of students = 1280 + 1760 + 1360 = 4400

Number of students in various specialisations: $$\eqalign{ & \text{IB → } \frac{19}{100}\times8000 = 1520 \cr & \text{IR → } \frac{16}{100}\times8000 = 1280 \cr & \text{Finance → } \frac{12}{100}\times8000 = 960 \cr & \text{Marketing → } \frac{22}{100}\times8000 = 1760 \cr & \text{IT → } \frac{17}{100}\times8000 = 1360 \cr & \text{HR → } \frac{14}{100}\times8000 = 1120 \cr} $$ $$\eqalign{ & \text{Required ratio} \cr & = \text{Finance : HR} \cr & = \frac{960}{1120} \cr & = \frac{6}{7} \cr & = 6:7\cr} $$

Percentage Break-up of expenditure is: $$\eqalign{ & \text{Investments →} \left(\frac{54}{360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 15\% \cr & \text{Commuting →} \left(\frac{79.2}{360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 22\% \cr & \text{Shopping →} \left(\frac{68.4}{360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 19\% \cr & \text{Groceries →} \left(\frac{82.8}{360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 23\% \cr & \text{Medicines →} \left(\frac{39.6}{360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 11\% \cr & \text{Entertainment →} \left(\frac{36} {360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10\% \cr} $$ Amount spent on Entertainment and Shopping $$\eqalign{ & = \text{Rs.}\left(45800\times\frac{10+19}{100}\right) \cr & = \text{Rs.}\left(45800\times\frac{29}{100}\right) \cr & = \text{Rs. 13282}\cr} $$

Percentage Break-up of expenditure is: $$\eqalign{ & \text{Investments →} \left(\frac{54}{360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 15\% \cr & \text{Commuting →} \left(\frac{79.2}{360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 22\% \cr & \text{Shopping →} \left(\frac{68.4}{360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 19\% \cr & \text{Groceries →} \left(\frac{82.8}{360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 23\% \cr & \text{Medicines →} \left(\frac{39.6}{360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 11\% \cr & \text{Entertainment →} \left(\frac{36} {360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10\% \cr} $$ $$\eqalign{ & \text{Amount spent on commuting} \cr & = \text{Rs.}\left(45800\times\frac{22}{100}\right) \cr & = \text{Rs. 10076} \cr} $$

Percentage Break-up of expenditure is: $$\eqalign{ & \text{Investments →} \left(\frac{54}{360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 15\% \cr & \text{Commuting →} \left(\frac{79.2}{360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 22\% \cr & \text{Shopping →} \left(\frac{68.4}{360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 19\% \cr & \text{Groceries →} \left(\frac{82.8}{360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 23\% \cr & \text{Medicines →} \left(\frac{39.6}{360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 11\% \cr & \text{Entertainment →} \left(\frac{36} {360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10\% \cr} $$ Amount spent on Groceries, Entertainment and Investments $$\eqalign{ & = 45800\times\frac{23+10+15}{100} \cr & = 45800\times\frac{48}{100} \cr & \text{Amount spent on Commuting} \cr & = 45800\times\frac{22}{100} \cr & \text{Required %} \cr & = \left(\frac{45800\times\frac{48}{100}}{45800\times\frac{22}{100}}\times100\right)\% \cr & = \frac{2400}{11}\% \cr & = 218.18\% \cr & \approx 218\% \cr} $$

Percentage Break-up of expenditure is: $$\eqalign{ & \text{Investments →} \left(\frac{54}{360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 15\% \cr & \text{Commuting →} \left(\frac{79.2}{360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 22\% \cr & \text{Shopping →} \left(\frac{68.4}{360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 19\% \cr & \text{Groceries →} \left(\frac{82.8}{360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 23\% \cr & \text{Medicines →} \left(\frac{39.6}{360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 11\% \cr & \text{Entertainment →} \left(\frac{36} {360}\times100\right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10\% \cr} $$ (Amount spent on medicine) : (Amount spent on groceries) $$\eqalign{ & = \left(45800\times\frac{11}{100}\right):\left(45800\times\frac{23}{100}\right) \cr & = 11:23 \cr} $$

$$\eqalign{ & \text{Expenditure on grocery} \cr & = \frac{25000 \times 14}{100} \cr & = \text{Rs. } 3500 \cr & \text{Expenditure on electricity} \cr & = \frac{25000 \times 9}{100} \cr & = \text{Rs. } 2250 \cr } $$

$$\eqalign{ & \text{Expenditure on education in April} \cr & = 24000 \times \frac{47}{100} \cr & = \text{Rs. }11280 \cr & \text{Expenditure on education in May} \cr & = 25000 \times \frac{50}{100} \cr & = \text{Rs. }12500 \cr & \text{Percentage increase} \cr & = \frac{12500 - 11280}{11280} \times 100 \cr & = 10.82\% \cr }$$

Required ratio = $$\frac{24000 \times 18}{100}$$ : $$\frac{25000 \times 2}{100}$$ = 24 ×18 : 25 × 2 = 216 : 25

$$\eqalign{ & {\text{Expenditure on steel}} \cr & {\text{Year }}1991 = \frac{{{{50}^ \circ }}}{{{{360}^ \circ }}} \times 360000 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs. }}50000 \cr & {\text{Year }}2001 = \frac{{864000}}{{360}} \times 60 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs. }}144000 \cr} $$

Required percentage = $$\frac{108°}{360°}$$ × 100 = 30%

$$\eqalign{ & {\text{Expenditure on labourers:}} \cr & {\text{Year }}1991 = \frac{{360000 \times 90°}}{{360°}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs. }}90000 \cr & {\text{Year }}2001 = \frac{{864000 \times 100°}}{{360°}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs. }}240000 \cr & {\text{Percentage increase}} \cr & = \frac{{240000 - 90000}}{{90000}} \times 100 \cr & = 166\frac{2}{3}\% \cr} $$

Number of employees in IT department = 800 × $$\frac{20}{100}$$ = 160 Number of females = 160 - 74 = 86 ∴ Required percentage = $$\frac{86}{800}$$ × 100 = 10.75%

Number of employees in HR department = $$\frac{5}{100}$$ × 800 = 40 Numbers of females = 40 - 12 = 28 ∴ Ration = 28 : 40 → 7 : 10

Total employees in Marketing department = 192 Males = 165 Females = 192 - 165 = 27 ∴ Required ratio = 165 : 27 = 55 : 9

Number of employees in marketing department = $$\frac{24}{100}$$ × 800 = 192 ∴ Required percentage = $$\frac{165}{192}$$ × 100 = 85.93% ≈ 86%

Let the amount permitted to be collected = Rs. x $$\eqalign{ & x = 4910 \times \left( 1 + \frac{10}{100} \right) \cr & x = \left( 4910 \times \frac{110}{100} \right) \cr & x = 491 \times 11 \cr & x = \text{Rs. }5401 \text{ crores} \cr} $$

Total funds = 29952 + 11486 + 5252 + 4910 + 6000 = 57600 57600 = 360° then, 29952 = $$ \frac{29952}{57600} \times 100 $$ = 52°

The amount require for compensation = 11486 - 9695 = Rs. 1791 % increase in market borrowing $$\eqalign{ & = \frac{1791}{29952} \times 100\% \cr & = 5.9\% \cr & \approx 6\% \cr} $$

Corporation tax = x × Excise duty 9 = x × 41 x = $$\frac{9}{41}$$

Excise duty + custom duty : other 41% + 14% : 10% 55% : 10% 11 : 2

Custom duty : Income tax 14 : 26 7 : 13

Excise duty = 41% Total revenue × $$ \frac{41}{100}$$ = 28618 Total revenue = 28618 × $$\frac{100}{41}$$ = Rs. 69,800 crores

Rice + Wheat + Sugar + Tea = 500000 55% + 30% + 10% + 5% = 500000 then rice 55% $$\eqalign{ & = \frac{500000}{100} \times 55 \cr & = 275000 \text{ kg} \cr} $$

Rice + Tea = 55% + 5% = 60% Wheat = 30° = $$\frac{30}{30}$$ × 100 = 100%

100 = 360° 1 = 3.6° 30° = 3.6 × 30 = 108°

(Wheat + Sugar) : (Rice - Tea) (30 + 10) : (55 - 5) 40 : 50 4 : 5

Maximum people in any profession - Minimum people involved in any profession Agriculture = 33.30% Trade = Minimum = 6.70% Difference = 33.30% - 6.70% = 26.60% 100% = 20000 1% = 200 26.6% = 200 × 26.6 = 5320

People in service sector more than trade = 20% - 6.70% = 13.3% = $$\frac{13.3}{100}$$ × 20000 = 2660

Angle made by service sector $$\eqalign{ & = \frac{20}{100} \times 360° \cr & = \frac{360}{5} \cr & = 72° \cr} $$