Line Graphs: Formulas, Shortcuts and Solved Examples — MCQs with Answers (Set 5)

The graph’s line for B.Ed. totals 3740 across 5 points. Average = total divided by count = 3740 / 5 = 748. So the average students enrolled of B.Ed. is 748.

In 2014, the graph shows B.A. = 293 and BCA = 724. Ratio = 293 : 724. Dividing both terms by their HCF gives the lowest form: 293 : 724. Check: 293 x 724 = 212132 and 724 x 293 = 212132, confirming the ratio is correct.

The table has 5 rows and 5 columns, so 25 cells in all. Adding every cell together gives 14653. Check: adding each row’s total instead — 2723 + 2783 + 3405 + 2264 + 3478 — also gives 14653. So the grand total students enrolled over all years combined is 14653.

In 2014, the graph’s points across all categories total 2783. Average = total divided by count = 2783 / 5 = 556.6. So the average students enrolled of all categories in 2014 is 556.6.

For B.Tech, the graph shows 2016 = 147 and 2017 = 602. Change = 602 – 147 = 455. Percentage change = ((602-147)/147) x 100 = 309.52%. Rounded, that is a 310% increase from 2016 to 2017.

For Kia, the graph shows 2017 = 137 and 2018 = 136. Change = 136 – 137 = -1. Percentage change = ((136-137)/137) x 100 = -0.73%. Rounded, that is a 1% decrease from 2017 to 2018.

In 2018, the graph’s points across all categories total 776. Average = total divided by count = 776 / 5 = 155.2. So the average cars produced of all categories in 2018 is 155.2.

The graph’s line for Renault gives 5 values: 156, 259, 53, 132, 147. Adding them: 156 + 259 + 53 + 132 + 147 = 747. So the total cars produced of Renault is 747.

In 2015, the graph’s points read: Renault = 156, Tata = 190, Kia = 214, Maruti = 98, Hyundai = 59. Comparing all 5 values, Hyundai is the lowest. So Hyundai had the lowest cars produced in 2015.

In 2015, the graph shows Hyundai = 59 and Maruti = 98. Difference = |59 – 98| = 39. So Hyundai and Maruti differ by 39 in 2015.

The graph’s line for Shimla totals 1401 across 5 points. Average = total divided by count = 1401 / 5 = 280.2. So the average tourists visiting of Shimla is 280.2.

In 2022, the graph shows Udaipur = 274 and Manali = 241. Percentage = (274/241) x 100 = 113.69%. Rounded to the nearest whole number, that is 114%. Check: 114% of 241 is about 275, close to 274.

The graph’s line for Udaipur reads: 2019 = 221, 2020 = 320, 2021 = 307, 2022 = 274, 2023 = 115. Comparing all 5 points, the peak is in 2020. So the tourists visiting of Udaipur was highest in that year.

In 2020, the graph’s points read: Kochi = 78, Shimla = 146, Manali = 382, Darjeeling = 37, Udaipur = 320. Comparing all 5 values, Darjeeling is the lowest. So Darjeeling had the lowest tourists visiting in 2020.

In 2022, the graph’s points across all categories are: 313, 430, 241, 368, 274. Adding them: 313 + 430 + 241 + 368 + 274 = 1626. So the total tourists visiting of all categories in 2022 is 1626.

In 2019, the graph’s points across all categories total 1577. Average = total divided by count = 1577 / 5 = 315.4. So the average tourists visiting of all categories in 2019 is 315.4.

The graph’s line for Rahul gives 5 values: 99, 46, 97, 78, 95. Adding them: 99 + 46 + 97 + 78 + 95 = 415. So the total runs scored of Rahul is 415.

In Match 1, the graph shows Aditya = 40 and Karan = 127. Percentage = (40/127) x 100 = 31.50%. Rounded to the nearest whole number, that is 31%. Check: 31% of 127 is about 39, close to 40.

In Match 5, the graph’s points read: Karan = 112, Rahul = 95, Manoj = 63, Vikram = 27, Aditya = 13. Comparing all 5 values, Karan is the highest. So Karan had the highest runs scored in Match 5.

In Match 5, the graph’s points across all categories are: 112, 95, 63, 27, 13. Adding them: 112 + 95 + 63 + 27 + 13 = 310. So the total runs scored of all categories in Match 5 is 310.

In Match 3, the graph shows Manoj = 20 and Rahul = 97. Ratio = 20 : 97. Dividing both terms by their HCF gives the lowest form: 20 : 97. Check: 20 x 97 = 1940 and 97 x 20 = 1940, confirming the ratio is correct.

In 2020, the graph shows IT = 144 and Finance = 263. Difference = |144 – 263| = 119. So IT and Finance differ by 119 in 2020.

The graph’s line for Sales gives 5 values: 375, 267, 83, 67, 474. Adding them: 375 + 267 + 83 + 67 + 474 = 1266. So the total employees working of Sales is 1266.

The graph’s line for Finance totals 1170 across 5 points. Average = total divided by count = 1170 / 5 = 234. So the average employees working of Finance is 234.

In 2017, the graph’s points read: IT = 213, R&D = 70, Finance = 240, Sales = 267, Logistics = 149. Comparing all 5 values, Sales is the highest. So Sales had the highest employees working in 2017.

In 2018, the graph shows IT = 333 and Finance = 258. Percentage = (333/258) x 100 = 129.07%. Rounded to the nearest whole number, that is 129%. Check: 129% of 258 is about 333, close to 333.

In 2017, the graph’s points read: Darjeeling = 256, Jaipur = 168, Goa = 106, Ooty = 155, Shimla = 376. Comparing all 5 values, Goa is the lowest. So Goa had the lowest tourists visiting in 2017.

For Ooty, the graph shows 2019 = 426 and 2020 = 235. Change = 235 – 426 = -191. Percentage change = ((235-426)/426) x 100 = -44.84%. Rounded, that is a 45% decrease from 2019 to 2020.

In 2019, the graph shows Jaipur = 254 and Shimla = 289. Difference = |254 – 289| = 35. So Jaipur and Shimla differ by 35 in 2019.

The table has 5 rows and 5 columns, so 25 cells in all. Adding every cell together gives 6434. Check: adding each row’s total instead — 1061 + 1127 + 1900 + 1125 + 1221 — also gives 6434. So the grand total tourists visiting over all years combined is 6434.

In 2017, the graph’s points read: Darjeeling = 256, Jaipur = 168, Goa = 106, Ooty = 155, Shimla = 376. Comparing all 5 values, Shimla is the highest. So Shimla had the highest tourists visiting in 2017.

The graph’s line for Jaipur reads: 2017 = 168, 2018 = 342, 2019 = 254, 2020 = 362, 2021 = 249. Comparing all 5 points, the peak is in 2020. So the tourists visiting of Jaipur was highest in that year.

The graph’s line for Arjun totals 333 across 5 points. Average = total divided by count = 333 / 5 = 66.6. So the average runs scored of Arjun is 66.6.

In Match 4, the graph shows Karan = 105 and Rahul = 21. Ratio = 105 : 21. Dividing both terms by their HCF gives the lowest form: 5 : 1. Check: 5 x 21 = 105 and 1 x 105 = 105, confirming the ratio is correct.

The table has 5 rows and 5 columns, so 25 cells in all. Adding every cell together gives 1848. Check: adding each row’s total instead — 460 + 426 + 236 + 384 + 342 — also gives 1848. So the grand total runs scored over all matches combined is 1848.

For Arjun, the graph shows Match 2 = 91 and Match 3 = 89. Change = 89 – 91 = -2. Percentage change = ((89-91)/91) x 100 = -2.20%. Rounded, that is a 2% decrease from Match 2 to Match 3.

For Aditya, the graph shows Match 1 = 104 and Match 2 = 48. Change = 48 – 104 = -56. Percentage change = ((48-104)/104) x 100 = -53.85%. Rounded, that is a 54% decrease from Match 1 to Match 2.

In Match 2, the graph’s points across all categories total 254. Average = total divided by count = 254 / 5 = 50.8. So the average runs scored of all categories in Match 2 is 50.8.

The graph’s line for Manoj gives 5 values: 94, 63, 87, 84, 112. Adding them: 94 + 63 + 87 + 84 + 112 = 440. So the total runs scored of Manoj is 440.

In Match 2, the graph’s points read: Aditya = 48, Manoj = 63, Vikram = 16, Suresh = 47, Karan = 80. Comparing all 5 values, Vikram is the lowest. So Vikram had the lowest runs scored in Match 2.

In Match 5, the graph shows Vikram = 68 and Aditya = 126. Difference = |68 – 126| = 58. So Vikram and Aditya differ by 58 in Match 5.