Line Chart — Part 2 MCQs with Explanations

Average profit of A and B in 2010 $$\eqalign{ & = \frac{1}{2}\times\left[\left(\frac{90}{100}\times25\text{ lakh}\right)+\left(\frac{70}{100}\times25\text{ lakh}\right)\right] \cr & = \frac{1}{2}\times\left(\frac{45}{2}+\frac{35}{2}\right)\text{lakh} \cr & = \frac{80}{4}\text{ lakh} \cr & = \text{20 lakh} \cr} $$

Investment in 2006 = Rs. $$\left(\frac{100}{65}\times812500\right)$$ = Rs. (100 × 12500) = Rs. 1250000 Total income of B in 2006 = Investment + Profit = Rs. (1250000 + 812500) = Rs. 2062500

$$\eqalign{ & \text{Investment of B in 2004 = 12 lakh} \cr & \text{Income of B in 2004} \cr & =\text{Rs.}\left(\frac{155}{100}\times12\text{ lakh}\right) \cr & = \text{Rs. 18.6 lakh} \cr & \text{Profit earned in 2005} \cr & =\text{Rs.}\left(\frac{55}{100}\times18.6\text{ lakh}\right) \cr & =\text{Rs.}\left(\frac{11}{10}\times9.3 \text{ lakh}\right) \cr & =\text{Rs. 10.23 lakh} \cr} $$

Profit percent earned by company B in 2009 = 35% Profit percent earned by company B in 2010 = 50% Expenditure of company B in 2009 = 12 lakhs Expenditure of company B in 2010 = 14.5 lakhs Income of company B in 2009 $$\eqalign{ & 35\% = \frac{I - E}{E}\times100 \cr & \Rightarrow 35 = \frac{I - 12\text{ lakh}}{12\text{ lakh}}\times100 \cr & \Rightarrow \left(35\times12\right)\text{lakh} = 100I-1200\text{ lakh} \cr & \Rightarrow 420\text{ lakh} = 100I - 1200 \text{ lakh} \cr & \Rightarrow I = 16.20 \text{ lakh} \cr & \text{Income of company B in 2009} \cr & 50\% = \frac{I - E}{E}\times100 \cr & \Rightarrow 50 = \frac{I - 14.5\text{ lakh}}{14.5\text{ lakh}}\times100 \cr & \Rightarrow \left(50\times14.5\right)\text{lakh} = 100I-14.50\text{ lakh} \cr & \Rightarrow 2175\text{ lakh} = 100I \text{ lakh} \cr & \Rightarrow I = 21.75 \text{ lakh} \cr} $$ So, Total income of company B in 2009 and 2010 = 16.2 + 21.75 = Rs. 37.95 lakhs

Solution cannot be determined because profit percentage of company A in all the years are not given.

$$\eqalign{ & \text{In 2010, 50} = \frac{2-E_1}{E_1}\times100 \cr & \Rightarrow 50\,E_1= 200-100\,E_1 \cr & \Rightarrow 150\,E_1 = 200 \cr & \Rightarrow E_1 = \frac{4}{3} \cr & \text{In 2011, 45} = \frac{3-E_2}{E_2}\times100 \cr & \Rightarrow 45\,E_2 = 300 - 100\,E_2 \cr & \Rightarrow 145\,E_2=300 \cr & \Rightarrow E_2= \frac{300}{145} \cr & \text{Then, }\frac{E_1}{E_2} = \frac{4}{3}\times\frac{145}{300} \cr & \Rightarrow \frac{E_1}{E_2} = \frac{29}{45} \cr & \Rightarrow E_1:E_2=29:45 \cr} $$

$$\eqalign{ & \text{For company A, In 2012} \cr & P\% = \frac{I-E}{E}\times100 \cr & \Rightarrow 30 = \frac{I-3}{3}\times100 \cr & \Rightarrow 90 = 100I-300\cr & \Rightarrow \frac{390}{100} = I \cr & \Rightarrow I = 3.9 \cr & \text{For company B, In 2012} \cr & P\% = \frac{I-E}{E}\times100 \cr & \Rightarrow 40 = \frac{I-4}{4}\times100 \cr & \Rightarrow 160 = 100I-400 \cr & \Rightarrow \frac{560}{100} = I \cr & \Rightarrow I = 5.6 \cr & \text{Then required ratio} \cr & = \frac{3.9}{5.6} \cr & = \frac{39}{56} \cr & = 39:56 \cr} $$

Let the income of company A in 2013 = $$x$$ Let the income of company B in 2013 = (5.7 - $$x$$) Expenditure of company A = Expenditure of company B $$\eqalign{ & =E\, \frac{40}{100}-\frac{x-E}{E}\times100 \cr & \frac{x}{E} = 1.4\,\, . . . . . \,\left(\text{i}\right) \text{ and} \cr & \frac{45}{100} = \frac{\left(5.7-x\right)-E}{E} \cr & \Rightarrow \frac{5.7-x}{E} = 14.5\,\, . . . . .\, \left(\text{ii}\right) \cr & \text{Divide equation (ii) by (i) we get} \cr & \Rightarrow \frac{5.7-x}{E}\times\frac{E}{x}=\frac{145}{140} \cr & \Rightarrow \frac{5.7x}{x}=\frac{145}{140} \cr & \Rightarrow 5.7\times140-140x=145x \cr & \Rightarrow 798 = 285x \cr & \Rightarrow x = 2.8 \text{ lakhs} \cr & \because \frac{x}{E} = 1.4 \cr & E = 2 \text{ lakhs} \cr & \text{Total expenditure of two companies} \cr & =2+2 \cr & = 4 \text{ lakhs} \cr} $$

Total number of calories burnt by A = 185 + 90 + 160 = 435

$$\eqalign{ & \text{Required percentage} \cr & = \frac{60}{75}\times100 \cr & = 80\% \cr} $$

Total number of calories burnt by A and B together on Wednesday = 90 + 125 = 215 Total number of calories burnt by A and B together on Tuesday = 185 + 100 = 285 ∴ Required ratio = 215 : 285 = 43 : 57

Average calories = 125 Total calories = 3 × 125 = 375 Number of calories burnt on Saturday = 375 - 280 = 95

Total number of calories burnt on Saturday $$\eqalign{ & = 180\times \frac{110}{100}+145\times\frac{120}{100} \cr & = 198 + 174 \cr & = 372 \cr} $$

Average number of non-governmental projects handled by company B = 127 Number of Non-Governmental projects handled by company B in 2003 and 2004 is = 127 × 2 = 254 Number of Governmental projects handled by company B in 2003 and 2004 together = 130 + 320 - 254 = 450 - 254 = 196

The number of projects handled by company A in 2003 and 2004 together = 180 + 230 = 410 The number of projects handled by company B in 2005 and 2007 together = 210 + 350 = 560 Required difference = 560 - 410 = 150

Number of projects handled by company B in 2004 = 320 Number of projects handled by company B in 2006 = 190 Required decrease percentage $$\eqalign{ & = \frac{320-190}{320}\times100 \cr & = \frac{130}{320}\times100 \cr & = \frac{1300}{32}\% \cr & = \frac{325}{8}\% \cr & = 40\frac{5}{8}\% \cr} $$

Number of governmental project handled by company A in 2005 and 2006 together = 360 + 250 = 610 Number Governmental projects handled by company A in 2005 and 2006 together = 20% of 610 = $$\frac{20\times610}{100}$$ = 122

Number of projects handled by company A in 2008 = 120% of 300 = $$\frac{120\times300}{100}$$ = 360 Number of projects handled by company A in 2009 = 105% of 360 = $$\frac{105\times360}{100}$$ = 378

The number of watches sold in Town Y in April = 210 The number of watches sold in Town X in April = 150 Required percentage $$\eqalign{ & = \frac{210-150}{150}\times100 \cr & = \frac{60}{150}\times100 \cr & =40\% \cr} $$

Number of watches sold in Town X in the month of May = 180 Number of watches sold in Town X in the month of July = $$\frac{180\times110}{100}$$ = 198 Number of watches sold in Town X in the month of January = 120 ∴ Required ratio $$\eqalign{ & = \frac{198}{120} \cr & = \frac{33}{20} \cr & = 33:20\cr} $$

Total number of watches sold in Town X in January, February, March and June = 120 + 140 + 180 + 240 = 680 = Required average = $$\frac{680}{4}$$ = 170

Number of Watches sold in Town Y in February = 120 Number of Watches sold in Town Y in May = 230 Required percentage increase $$\eqalign{ & = \frac{230-120}{120}\times100 \cr & = \frac{110}{120}\times100 \cr & = \frac{110\times5}{6}\cr & = \frac{275}{3} \cr & = 91\frac{2}{3}\% \cr} $$

Total number of watches sold in both the towns together in the month of June = 240 + 180 = 420 Total number of watches sold in both the towns together in March = 180 + 150 = 330 Required difference = 420 - 330 = 90

$$\eqalign{ & \text{Median} \cr & = \frac{\text{L.V + H.V}}{2} \cr & = \frac{120 + 200}{2} \cr & = \text{Rs. }160 \cr}$$

Wages numbers of workers 120 12 140 26 - 12 = 14 160 34 - 26 = 8 180 40 - 34 = 6 200 50 - 40 = 10 ∴Required percentage = $$\frac{8}{50}$$ × 100 = 16%

It is clear from the graph.

$$\eqalign{ & 2001 : \frac{\text{I}}{\text{E}} = \frac{1}{1} = \frac{4}{4} \cr & 2002 : \frac{\text{I}}{\text{E}} = \frac{75}{100} = \frac{3}{4} \cr & \text{Income} \% = \frac{4 - 3}{4} \times 100 = 25\% \cr}$$

Number of examinees getting more than the average marks = 72 + 48 + 24 + 8 = 152

Number of students who got 40% or less marks = 2 + 4 + 12 + 26 = 44 ∴ Required percentage $$\eqalign{ & = \frac{44}{273} \times 100 \cr & = 16.11\% \cr} $$

Number of students who got above 80% marks = 24 + 8 = 32 ∴ Required percentage $$\eqalign{ & = \frac{32}{273} \times 100 \cr & = 11.72\% \cr}$$

Number of students who got marks above 60% and below 80% = 72 + 48 = 120 ∴ Required percentage $$\eqalign{ & = \frac{120 \times 100}{273} \cr & = 43.95\% \cr} $$

$$\eqalign{ & = \text{Required answer} \cr & = \frac{\text{Production of A}}{\text{Demand of C}} \times 100 \cr & = \frac{1450}{2600} \times 100\% \cr & = 55\%\, \left( \text{App.}\right) \cr} $$

$$\eqalign{ & \text{Required ratio} \cr & = \frac{\left(\text{A + D}\right)}{\left(\text{B, C, E and F}\right)} \cr & = \frac{2}{4} \cr & = \frac{1}{2} \cr & = 1:2 \cr} $$

$$\eqalign{ & \text{Required%} \cr & = \frac{\text{Demand fo B}}{\text{Profit of F}} \times 100\% \cr & = \frac{3150}{4500} \times 100 \cr & = 70\% \cr} $$

$$\eqalign{ & = \frac{100 + 200}{150 + 225} \times 100 \cr & = \frac{300}{375} \times 100 \cr & = 80\% \cr} $$

$$\eqalign{ & \frac{150 - 125}{150} \times 100 \cr & = \frac{25}{150} \times 100 \cr & = 16.6\% \approx 16.3\% \cr} $$

$$\eqalign{ & = \frac{\text{Type Q } \left(2010 \right)}{\text{Type P } \left(2014 \right)} \times 100 \cr & = \frac{150}{275} \times 100 \cr & = 54.5 \cr} $$

P → 100 + 125 + 200 + 225 + 275 + 275 = 1200 Q → 175 + 150 + 125 + 175 + 175 + 225 = 1025 P : Q 1200 : 1025 48 : 41

Average production (Type P) = 200 No. of years production of Type P is higher than average = 3

$$\frac{33.65+32.85+34.04+32.76+38.51+40.01+43.47}{7}$$ $$\eqalign{ & = \frac{255.29}{7} \cr & = 36.47 \cr}$$