Line Chart — Part 1 MCQs with Explanations

$$\eqalign{ & \text{Required average expenditure,} \cr & = \frac{200+250+210+100+140}{5} \cr & = \text{Rs. 180 lakhs} \cr} $$

Required difference, = Rs. [(190 + 170) - (210 + 140)] lakh = Rs. [360 - 350] = Rs. 10 lakh = Rs. 1000000

Required Ratio = 210 : 140 = 3 : 2

Total expenditure of 3 companies in 2005, = (80 + 140 + 200) = Rs. 420 lakh Total expenditure of 3 companies in 2006, = (100 + 190 + 250) = Rs. 540 lakh Total expenditure of 3 companies in 2007, = Rs. 580 lakh Total expenditure of 3 companies in 2008, = Rs. 470 lakh Total expenditure of 3 companies in 2009, = Rs. 530 lakh ∴ The required answer is 2006.

$$\eqalign{ & \text{Required percentage} \cr & = \frac{100+190+250}{80+100+130+200+210}\times100 \cr & = 75\% \cr} $$

Change in production = 12338 - 17213 = - 4875 % change = $$\frac{\text{-}4875}{17213}\times100$$ = -2.9% ≈ -3%

Change in productivity = 113 - 83.2 = 29.8 % change = $$\frac{29.8}{83.2}\times100$$ = 35.8%

Both the Workforce and Production have dropped.

The input into B is 1200 units and the output from B is (250 + 550) = 800 units. Hence, Demand = 1200 - 800 = 400 Units.

C has a net output of 1100 units. If the demand is 225 at C, then to fulfill all conditions we need an input of 1325 into C. This will occur only if the value of M is 1075.

The total demand in E = Total input into E. → 550 + 800 + 650 = 2000 $$\eqalign{ & = \frac{2000\times100}{80} \cr & =2500 \cr} $$ Hence, the demand in A will be 2500.

Demand = A + B + C + D + E = 2500 + 400 + 225 + 650 + 2000 = 5775

Jyotishmati gets supply from two direction one from Vaishali max 300 and rest from Vidisha. all supply given to Panchal is received and supplies 100 for Jyotishmati because it receives only 300 (max flow) from Vaishali. Hence, quantity moved from Avanti to Vidisha, = 200 + 100 + 700 = 1000

Capacity of pipelines is 1,000. It supplies 300 to Jyotishmati through Vaishali, gives to Vaishali and balance 300 is kept free in Avanti-vaishali pipeline.

Quantity moved from Avanti to Vidisha pipeline is 100 and capacity is 1000. Hence, no free capacity is available.

Clearly, Export > Import only when $$\frac{\text{Import}}{\text{Export}}$$ < 1. From the graph it is clear that the above ratio is less than 1 in the years 2005, 2006, 2007 and 2010. Thus (Imports : Exports) < 1 in 4 years

From graph, we find that the ratio of value of import to the value of export in 2006 is 0.85 Let the value of export in 2006 be Rs. $$x$$ crores. Then, $$\eqalign{ & \frac{272}{x} = 0.85 \cr & \Rightarrow x = \frac{272}{0.85} \cr & \Rightarrow x = \frac{272\times100}{85} \cr & \Rightarrow x = 320 \cr} $$ Hence, the value of exports in 2006 was Rs. 320 crores

Let the value of export in 2008 be Rs. $$x$$ crores Then, the value of export in 2009 = Rs. (500 - $$x$$) crores $$\eqalign{ & \frac{250}{x} = 1.25 \cr & \Rightarrow x = \frac{250}{1.25} \cr & \Rightarrow x = \frac{250\times100}{125} \cr & \Rightarrow x = 200 \cr} $$ ∴ Export in 2008 = Rs. 200 crores Export in 2009 = Rs. (500 - 200) crores = Rs. 300 crores Let the value of import in 2009 be Rs. $$y$$ crores Then, $$\eqalign{ & \frac{y}{300} = 1.40 \cr & \Rightarrow y = 1.40\times300 \cr & \Rightarrow y = \frac{140}{100}\times300 \cr & \Rightarrow y = 420 \cr} $$ Hence, the value of import in 2009 was Rs. 420 crores

The imports are minimum proportionate to exports means (value of import) : (value of export) should have minimum value. Clearly, this ratio has a minimum value of 0.35 in 2007

The graph gives only the ratio of value of imports and that of exports. In order to find the percentage increase in imports from 2007 to 2008, we require the value of import or that of export during these years. So, we cannot find the percentage increase in imports. Hence, the data is inadequate to answer the question.

(Trees planted by C in Tamil Nadu) - (Trees planted by A in Haryana) = 160 - 80 = 80

$$\eqalign{ & \text{Required %} \cr & = \left(\frac{100+60}{80+88}\times100\right)\% \cr & = \left(\frac{160}{168}\times100\right)\% \cr & = \frac{2000}{21}\% \cr & \approx 95\% \cr} $$

Total number of trees planted by A and B in: Bihar → 100 + 60 = 160 Punjab → 120 + 80 = 200 Haryana → 140 + 80 = 220 Assam → 150 + 160 = 310 Tamil Nadu → 140 + 180 = 320 It is second lowest in Punjab

Average number of trees planted in Haryana by 3 NGOs $$\eqalign{ & = \frac{1}{3}\left(80+140+167\right) \cr & = \frac{387}{3} \cr & = 129 \cr} $$

Required ratio = 180 : 120 : 150 = 6 : 4 : 5

$$\eqalign{ & \text{Required %} \cr & = \left(\frac{400}{550}\times100\right)\% \cr & = \frac{800}{11}\% \cr & = 72.7\% \cr & \approx 73\% \cr} $$

Production of Company B in 2006 = $$\left(\frac{4}{5}\text{ of } 750\right) \text{tonnes}$$ = 600 tonnes Production of Company B in 2008 = $$\left(\frac{4}{3}\text{ of } 600\right) \text{tonnes}$$ = 800 tonnes ∴ Required ratio = 600 : 800 = 3 : 4

Average production of company B from 2006 to 2011 $$=\frac{1}{6}\times \left[ \left(\frac{4}{5}\times750\right) + \left(\frac{7}{8}\times800\right) + \left(\frac{4}{3}\times600\right) + \left(\frac{12}{11}\times550\right) + \left(\frac{13}{14}\times700\right) + \left(\frac{14}{13}\times650\right) \right] \text{tonnes}$$ = $$\frac{1}{6}$$ (600 + 700 + 800 + 600 + 650 + 700) tonnes = $$\frac{4050}{6}$$ tonnes = 675 tonnes

Percentage increase in production of A from 2009 to 2010 $$\eqalign{ & = \left(\frac{700-550}{550}\times100\right)\% \cr & = \left(\frac{150}{550}\times100\right)\% \cr & = \frac{300}{11}\% \cr & = 27.2\% \cr & \approx 27\% \cr} $$

Total production of Company A = (750 + 800 + 600 + 550 + 700 + 650) tonnes = 4050 tonnes Total sales of Company A = (300 + 550 + 450 + 400 + 500 + 550) tonnes = 2750 tonnes ∴ Required ratio = 4050 : 2750 = 81 : 55

$$\eqalign{ & \text{Required %} \cr & = \left(\frac{35\times1000}{167.5\times1000}\times100\right)\% \cr & = \frac{350\times100}{1675}\% \cr & = \frac{1400}{67}\% \cr & = 20.89\% \cr & \approx 21\% \cr} $$

Ratio of number of students from Town B to that from Town A $$\eqalign{ & = \frac{32.5\times1000}{40\times1000} \cr & = \frac{325}{400} \cr & = \frac{13}{16} \cr & = 13:16 \cr} $$

(Students from Towns C and D) : (Students from Towns A, D and E) $$\eqalign{ & = \frac{\left(17.5+42.5\right)\times1000}{\left(40+42.5+35\right)\times1000} \cr & = \frac{60}{117.5} \cr & = \frac{600}{1175} \cr & = \frac{24}{47} \cr & = 24 : 47 \cr} $$

Average number of students appearing in Aptitude Test from all towns $$ = \frac{\left(40+32.5+17.5+42.5+35\right)\times1000}{5}$$ $$\eqalign{ & = \frac{167.5\times1000}{5} \cr & = 33.5\times1000 \cr & = 33500 \cr} $$

$$\eqalign{ & \text{Required percentage} \cr & = \left(\frac{42.5\times1000}{17.5\times1000}\times100\right)\% \cr & = \left(\frac{425}{175}\times100\right)\% \cr & = \frac{425\times4}{7}\% \cr & = \frac{1700}{7}\% \cr & = 242.85\% \cr & \approx 243\% \cr} $$

Let the investment of A in 2008 be Rs. $$x$$. Then, $$\eqalign{ & \left(\frac{160}{100}\times x\right) = 24\text{ lakh} \cr & \Rightarrow x = \left(24\times\frac{5}{8}\right) \text{lakh} \cr & \Rightarrow x = 15 \text{ lakh} \cr} $$ ∴ Investment of A in 2008 = 15 lakh Profit of A in 2008 = Rs. (24 - 15) lakh = Rs. 9 lakh Investment of A in 2007 = Investment of A in 2008 = Rs. 15 lakh Profit of A in 2007 $$\eqalign{ & =\text{Rs.} \left(\frac{45}{100}\times15\text{ lakh}\right) \cr & =\text{Rs.} \frac{27}{4}\text{ lakh} \cr & =\text{Rs. 6.75 lakh} \cr} $$ Difference between the profits of A in 2007 and 2008 = Rs. (9 - 6.75) lakh = Rs. 2.25 lakh

Let the investment of A in 2009 be Rs. $$x$$ Then, Investment of B $$\eqalign{ & = \text{50% of Rs. }x\cr & =\text{Rs.} \left(x\times\frac{50}{100}\right) \cr & =\text{Rs. } \frac{x}{2} \cr & \therefore \left(x+\frac{x}{2}\right) = 27 \text{ lakh} \cr & \Rightarrow \frac{3x}{2} = 27 \text{ lakh} \cr & \Rightarrow x = \left(27\times\frac{2}{3}\right) \text{lakh} \cr & \Rightarrow x = \text{18 lakh} \cr} $$ ∴ Investment of A in 2009 = Rs. 18 lakh and investment of B = Rs. 9 lakh. $$\eqalign{ & \text{Profit of A} \cr & =\text{Rs.} \left(18\text{ lakh}\times \frac{75}{100}\right) \cr & = \text{Rs. 13.50 lakh} \cr & \text{Profit of B} \cr & =\text{Rs.} \left(9\text{ lakh}\times \frac{80}{100}\right) \cr & = \text{Rs. 7.20 lakh} \cr & \therefore \text{Total profit of A and B} \cr & = \text{Rs.}\left(13.50+7.20\right)\text{lakh} \cr & = \text{Rs. 20.70 lakh} \cr} $$

Let the investment of A in 2006 be Rs. $$x$$ Then, $$\eqalign{ & \text{Profit = 55% of Rs. }x \cr & =\text{Rs.}\left(x\times\frac{55}{100}\right) \cr & =\text{Rs.}\left(\frac{11x}{20}\right) \cr & \therefore \frac{11x}{20} = 10.12\text{ lakh} \cr & \Rightarrow \frac{11x}{20} = 10.12\times100000 \cr & \Rightarrow \frac{11x}{20} = 1012000 \cr & \Rightarrow x = 1012000\times\frac{20}{11} \cr & \Rightarrow x = 1840000 \cr & \Rightarrow x = \text{18.4 lakh} \cr} $$ $$\Rightarrow$$ Investment of A in 2006 = 18.4 lakh

Let the investment of each in 2005 be Rs. $$x$$ Then, (Income of A) : (Income of B) = Rs. ($$x$$ + 70% of $$x$$) : Rs. ($$x$$ + 55% of $$x$$) [∵ Income = (Investment) + (Profit)] $$\eqalign{ & = \left(x+\frac{70x}{100}\right) : \left(x+\frac{55x}{100}\right)\cr & = \left(x+\frac{7x}{10}\right) : \left(x+\frac{11x}{20}\right) \cr & = \frac{17x}{10} : \frac{31x}{20} \cr & = 34 : 31 \cr} $$

$$\eqalign{ & \text{Investment of A in 2007} \cr & = \text{Rs. 12 lakh and profit%} \cr & = 45\% \cr & \text{Income of A in 2007} \cr & = \text{Rs.}\left(\frac{145}{100}\times12\text{ lakh}\right) \cr & = \text{Rs. 17.4 lakh} \cr & \text{Amount invested by A in 2008} \cr & = \text{Rs.}\left(\frac{100}{160}\times17.4\text{ lakh}\right) \cr & = \text{Rs.}\left(10.875\times100000\right) \cr & = \text{Rs. 1087500} \cr} $$