Pie Chart — Part 1 MCQs with Explanations

House rent per month = 18% of Rs. 33650 = Rs. $$\frac{18\times33650}{100}$$ = Rs. 6057

Annual provident fund saving = 12% of (Rs. 33650 × 12) = $$\frac{12\times33650\times12}{100}$$ = Rs. 48456

Remaining income = (100 - 12 - 18)% of Rs. 33650 = Rs. $$\frac{70\times33650}{100}$$ = Rs. 23555

Spent on food and entertainment = 34% of Rs. 33650 = $$\frac{34\times33650}{100}$$ = Rs. 11441

Required % increase = $$\frac{\left(160-130\right)\times100}{130}$$ = 23.07% ≈ 23%

Interest in 1990-91 = 30% of 130 = 39 lakh Interest in 1991-92 = 40% of 160 = 64 lakh Hence, difference = Rs. 25 lakh

Total interest = (30% of 130) + (40% of 160) = 39 + 64 = Rs. 103 lakh Given that, This interest is calculated on 20% of borrowed fund. Hence, borrowed funds = $$\frac{103\times100}{20}$$ = Rs 515 lakh

Retained profit in 1990-91 = 25% of 130 = Rs. 32.5 lakh Retained profit in 1991-92 = 20% of 160 = Rs. 32 lakh ∴ Decrease = $$\frac{32.5-32}{32.5}$$ × 100 = 1.53% ≈ 1.5%

Total dividend earned by share holder in 1991-92, = 8% of 160 = Rs 12.8 lakh

Total sales in 1998 = 7890 Sales of Toshiba = 12% = $$\frac{7890\times12}{100}$$ = 946.8 ≈ 947 Total sales in 1999 = 7890 + (16.5% of 7890) = 9191 Sales of Toshiba = 8% of 9191 = 735 Change in sales = 947 - 735 = 212 % change = $$\frac{212\times100}{986}$$ = 21.5% ≈ 22%

There is no percentage change in the given three company.Thus, All of these is the correct answer.

Sale of Compaq in 1998, = 21% = $$\frac{7890\times21}{100}$$ =1657 Sales of IBM in 1999, = 17% = $$\frac{9191\times17}{100}$$ = 1562 Ratio = $$\frac{1657}{1562}$$ = 1.06 We have calculated total sales in 1999 is 9191 in question no. 1.

The maximum increase in sales is of Compaq which is 4%. Thus, it will got maximum absolute value too.

IBM's sales in 1998 = 17% of 7890 = 1341 Samsung sales in 1999 = 24% of 9191 = 2205 ∴ Required answer = $$\frac{1341}{2205}\times100$$ = 60.8%

Corresponding angle for expenditure on electricity = 72° ∵ 360° ≡ 100% ∴ Total expenditure on electricity $$\eqalign{ & = \frac{72}{360}\times100 \cr & = 20\% \cr} $$

Corresponding angle for raw materials = 90° ∵ 360° ≡ 100% Percentage of raw material $$\eqalign{ & = \frac{90}{360}\times100 \cr & = 25\% \cr} $$

Corresponding angle for conveyance = 90° ∵ 360° ≡ Rs. 60000 ∴ Total expenditure of conveyance $$\eqalign{ & = \frac{90}{360}\times60000 \cr & =\text{Rs. 15000} \cr} $$

Corresponding angle for overhead expenses = 108° ∵ 360° ≡ Rs. 60000 Amount spent on overhead expenses $$\eqalign{ & = \frac{108}{360}\times60000 \cr & = \text{Rs. 18000} \cr} $$

Store Nokia Cellular Phones Samsung Cellular Phones Total Number of Cellular Phones P 896 672 1568 Q 840 280 1120 R 1120 896 2016 S 1568 1344 2912 T 448 1792 2240 U 704 640 1344 Percentage of cellular phones (both Nokia and Samsung) sold by Store S = 26% ∴ Required central angle = $$\frac{26}{100}$$ × 360 = 93.6°

Store Nokia Cellular Phones Samsung Cellular Phones Total Number of Cellular Phones P 896 672 1568 Q 840 280 1120 R 1120 896 2016 S 1568 1344 2912 T 448 1792 2240 U 704 640 1344 Total Nokia Phone sold by stores P, R, S and T = 896 + 1120 + 1568 + 448 = 4032 ∴ Required average = $$\frac{4032}{4}$$ = 1008

Store Nokia Cellular Phones Samsung Cellular Phones Total Number of Cellular Phones P 896 672 1568 Q 840 280 1120 R 1120 896 2016 S 1568 1344 2912 T 448 1792 2240 U 704 640 1344 Number of Nokia phones sold by store S = 1568 Number of Samsung Phones sold by store T and U together = 1792 + 640 = 2432 $$\eqalign{ & \therefore \text{ Required ratio} \cr & = \frac{1568}{2432} \cr & = \frac{49}{76} \cr & = 49:76 \cr} $$

Store Nokia Cellular Phones Samsung Cellular Phones Total Number of Cellular Phones P 896 672 1568 Q 840 280 1120 R 1120 896 2016 S 1568 1344 2912 T 448 1792 2240 U 704 640 1344 Number of Nokia phones sold by store R = 1120 Number of Samsung phones sold by store P and Q together = 672 + 280 = 952 $$\eqalign{ & \therefore \text{Required percentage} \cr & = \frac{1120-952}{952}\times100 \cr & = \frac{16800}{952}\% \cr & = \frac{300}{17}\% \cr & = 17\frac{11}{17}\% \text{ more} \cr} $$

Store Nokia Cellular Phones Samsung Cellular Phones Total Number of Cellular Phones P 896 672 1568 Q 840 280 1120 R 1120 896 2016 S 1568 1344 2912 T 448 1792 2240 U 704 640 1344 Number of cellular phones (both Nokia and Samsung) sold by store Q in October = 11200 × $$\frac{10}{100}$$ = 1120 ∵ Number of cellular phones (both Nokia and Samsung) sold by store Q in November = 1120 × $$\frac{115}{100}$$ = 1288 Number of cellular phones (both Nokia and Samsung) sold by store T in October = 11200 × $$\frac{20}{100}$$ = 2240 ∵ Number of cellular phones (both Nokia and Samsung) sold by store T in November = 2240 × $$\frac{105}{100}$$ = 2352 ∵ Total number of cellular phones (both Nokia and Samsung) sold by Q and T together in November = 1288 + 2352 = 3640

Percent of Dell Laptops sold by store Q = 25% Total number of Dell Laptops bold by store Q $$\eqalign{ & = 2400\times\frac{25}{100} \cr & = 600 \cr} $$ Percent of Laptops Dell and Lenovo sold by store R = 35% Number of Laptops Dell and Lenovo sold by store R $$\eqalign{ & = 4500\times\frac{35}{100} \cr & = 1575 \cr & \therefore \text{Required Percentage} \cr & = \frac{600}{1575}\times100 \cr & = 38.095 \cr & \approx 38\% \cr} $$

Number of Dell laptops sold by store T $$\eqalign{ & = 2400\times\frac{21}{100} \cr & = 504 \cr} $$ Number of Laptops sold by store P $$\eqalign{ & = 2400\times \frac{15}{100} \cr & = 360 \cr} $$ Required Percentage $$\eqalign{ & = \frac{504-360}{360}\times100 \cr & = 40\% \cr} $$

Percent of Dell Laptops sold by P, R and S together = 15% + 30% + 9% = 54% Total Dell Laptops sold by P, R and S together $$\eqalign{ & = 2400\times\frac{54}{100} \cr & = 1296 \cr & \therefore \text{ Average} \cr & = \frac{1296}{3} \cr & = 432 \cr} $$

Percent of Laptops Dell and Lenovo sold by store Q = 23% Number of Laptops Dell and Lenovo sold by store Q $$\eqalign{ & = 4500\times\frac{23}{100} \cr & = 45\times23 \cr & = 1035 \cr} $$ Percent of Laptops Dell and Lenovo sold by R and S together = 35% + 11% = 46% Now, total number of Laptops Lenovo and Dell sold by R and S together $$\eqalign{ & = 4500\times\frac{46}{100} \cr & = 2070 \cr} $$ Percent of Dell Laptops sold by R and S together = 30% + 9% = 39% Number of Dell Laptops sold by R and S together $$\eqalign{ & = 2400\times\frac{39}{100} \cr & = 936 \cr} $$ Number of Lenovo Laptops = 2070 - 936 = 1134 Required difference = 1134 - 1035 = 99

Dell laptops sold by store S = 9% Central angle corresponding to number of Dell Laptops sold by store S $$\eqalign{ & = \frac{9}{100}\times360 \cr & = 32.4° \cr} $$

Number of lecturers in various subjects are: $$\eqalign{ & \text{Chemistry → } \frac{13}{100}\times1600 = 208 \cr & \text{Education → } \frac{18}{100}\times1600 = 288 \cr & \text{Hindi → } \frac{12}{100}\times1600 = 192 \cr & \text{Mathematics → } \frac{21}{100}\times1600 = 336 \cr & \text{Physics → } \frac{14}{100}\times1600 = 224 \cr & \text{Zoology → } \frac{22}{100}\times1600 = 352 \cr} $$ Subject Number of Males Number of Females Chemistry 208 × $$\frac{1}{8}$$ = 26 208 - 26 = 182 Education 288 × $$\frac{5}{8}$$ = 180 288 - 180 = 108 Hindi 192 × $$\frac{1}{4}$$ = 48 192 - 48 = 144 Mathematics 336 × $$\frac{3}{7}$$ = 144 336 - 144 = 192 Physics 224 × $$\frac{9}{14}$$ = 144 224 - 144 = 80 Zoology 352 × $$\frac{7}{16}$$ = 154 352 - 154 = 198 Required difference = 352 - (26 + 180) = 352 - 206 = 146

Number of lecturers in various subjects are: $$\eqalign{ & \text{Chemistry → } \frac{13}{100}\times1600 = 208 \cr & \text{Education → } \frac{18}{100}\times1600 = 288 \cr & \text{Hindi → } \frac{12}{100}\times1600 = 192 \cr & \text{Mathematics → } \frac{21}{100}\times1600 = 336 \cr & \text{Physics → } \frac{14}{100}\times1600 = 224 \cr & \text{Zoology → } \frac{22}{100}\times1600 = 352 \cr} $$ Subject Number of Males Number of Females Chemistry 208 × $$\frac{1}{8}$$ = 26 208 - 26 = 182 Education 288 × $$\frac{5}{8}$$ = 180 288 - 180 = 108 Hindi 192 × $$\frac{1}{4}$$ = 48 192 - 48 = 144 Mathematics 336 × $$\frac{3}{7}$$ = 144 336 - 144 = 192 Physics 224 × $$\frac{9}{14}$$ = 144 224 - 144 = 80 Zoology 352 × $$\frac{7}{16}$$ = 154 352 - 154 = 198 Total number of male lecturers in the university = 26 + 180 + 48 + 144 + 144 + 154 = 696

Number of lecturers in various subjects are: $$\eqalign{ & \text{Chemistry → } \frac{13}{100}\times1600 = 208 \cr & \text{Education → } \frac{18}{100}\times1600 = 288 \cr & \text{Hindi → } \frac{12}{100}\times1600 = 192 \cr & \text{Mathematics → } \frac{21}{100}\times1600 = 336 \cr & \text{Physics → } \frac{14}{100}\times1600 = 224 \cr & \text{Zoology → } \frac{22}{100}\times1600 = 352 \cr} $$ Subject Number of Males Number of Females Chemistry 208 × $$\frac{1}{8}$$ = 26 208 - 26 = 182 Education 288 × $$\frac{5}{8}$$ = 180 288 - 180 = 108 Hindi 192 × $$\frac{1}{4}$$ = 48 192 - 48 = 144 Mathematics 336 × $$\frac{3}{7}$$ = 144 336 - 144 = 192 Physics 224 × $$\frac{9}{14}$$ = 144 224 - 144 = 80 Zoology 352 × $$\frac{7}{16}$$ = 154 352 - 154 = 198 $$\eqalign{ & \text{Required %} \cr & = \left(\frac{192}{192+182}\times100\right)\% \cr & = \left(\frac{192}{374}\times100\right)\% \cr & = \frac{9600}{187}\% \cr & = 51.3\% \cr & \approx 51\% \cr} $$

Number of lecturers in various subjects are: $$\eqalign{ & \text{Chemistry → } \frac{13}{100}\times1600 = 208 \cr & \text{Education → } \frac{18}{100}\times1600 = 288 \cr & \text{Hindi → } \frac{12}{100}\times1600 = 192 \cr & \text{Mathematics → } \frac{21}{100}\times1600 = 336 \cr & \text{Physics → } \frac{14}{100}\times1600 = 224 \cr & \text{Zoology → } \frac{22}{100}\times1600 = 352 \cr} $$ Subject Number of Males Number of Females Chemistry 208 × $$\frac{1}{8}$$ = 26 208 - 26 = 182 Education 288 × $$\frac{5}{8}$$ = 180 288 - 180 = 108 Hindi 192 × $$\frac{1}{4}$$ = 48 192 - 48 = 144 Mathematics 336 × $$\frac{3}{7}$$ = 144 336 - 144 = 192 Physics 224 × $$\frac{9}{14}$$ = 144 224 - 144 = 80 Zoology 352 × $$\frac{7}{16}$$ = 154 352 - 154 = 198 Required difference = 198 - 48 = 150

Number of lecturers in various subjects are: $$\eqalign{ & \text{Chemistry → } \frac{13}{100}\times1600 = 208 \cr & \text{Education → } \frac{18}{100}\times1600 = 288 \cr & \text{Hindi → } \frac{12}{100}\times1600 = 192 \cr & \text{Mathematics → } \frac{21}{100}\times1600 = 336 \cr & \text{Physics → } \frac{14}{100}\times1600 = 224 \cr & \text{Zoology → } \frac{22}{100}\times1600 = 352 \cr} $$ Subject Number of Males Number of Females Chemistry 208 × $$\frac{1}{8}$$ = 26 208 - 26 = 182 Education 288 × $$\frac{5}{8}$$ = 180 288 - 180 = 108 Hindi 192 × $$\frac{1}{4}$$ = 48 192 - 48 = 144 Mathematics 336 × $$\frac{3}{7}$$ = 144 336 - 144 = 192 Physics 224 × $$\frac{9}{14}$$ = 144 224 - 144 = 80 Zoology 352 × $$\frac{7}{16}$$ = 154 352 - 154 = 198 Required ratio = 80 : 144 = 5 : 9

Cost estimated on painting and flooring together $$\eqalign{ & = \text{Rs. } \frac{15+14}{100}\times120000 \cr & = \text{Rs. } \frac{29}{100}\times120000 \cr & = \text{Rs. 34800} \cr} $$

$$\eqalign{ & \text{Required Difference} \cr & = \text{Rs. } \frac{19-11}{100}\times120000 \cr & = \text{Rs. } \frac{8}{100}\times120000 \cr & = \text{Rs. 9600} \cr} $$

$$\eqalign{ & \text{Amount spent on furniture} \cr & = \text{Rs. } \frac{88}{100}\times\frac{13}{100}\times120000 \cr & = \text{Rs. 13728} \cr} $$

Estimated cost of furniture and miscellaneous expenditure $$\eqalign{ & = \text{Rs. } \frac{13+8}{100}\times120000 \cr & = \text{Rs. } \frac{21}{100}\times120000 \cr & = \text{Rs. 25200} \cr & \text{Actual cost of furniture} \cr & = \text{Rs. } \frac{88}{100}\times\frac{13}{100}\times120000 \cr & = \text{Rs. 13728} \cr} $$ Actual cost of furniture and miscellaneous expenditure = Rs. (13728 + 10200) = Rs. 23928 Total amount spent in renovating the house = Rs. (120000 - 25200 + 23928) = Rs. 118728

Number of mobile phones sold by B during October $$\eqalign{ & = 45000\times\frac{8}{100}\times\frac{5}{12} \cr & = 1500 \cr & \therefore \text{Required profit} \cr & = \text{Rs. }\left(1500\times433\right) \cr & = \text{Rs. 649500} \cr} $$

Number of mobile phones sold by B during July $$\eqalign{ & = 45000\times\frac{17}{100}\times\frac{7}{15} \cr & = 3570 \cr} $$ Number of mobile phones sold by B during December $$\eqalign{ & = 45000\times\frac{16}{100}\times\frac{9}{16} \cr & = 4050 \cr & \therefore \text{Required ratio} \cr & = \frac{3570}{4050} \cr & = \frac{119}{135} \cr & = 119:135 \cr} $$

Number of mobile phones sold by A during July $$\eqalign{ & = 45000\times\frac{17}{100}\times\frac{8}{15} \cr & = 4080 \cr} $$ Number of mobile phones sold by A during December $$\eqalign{ & = 45000\times\frac{16}{100}\times\frac{7}{16} \cr & = 3150 \cr & \text{Let 4080 = }x\%\text{ of 3150} \cr & \text{Then,} \cr & \frac{x}{100}\times3150 = 4080 \cr & \Rightarrow x = \frac{4080\times2}{63} \cr & \Rightarrow x = 129.5 \cr & \Rightarrow x \approx 130 \cr & \text{Required percentage = 130%}\cr} $$