Percentages — Set #2 | Practice

{"setId":"979ccea4-3635-489f-9416-fb58617bca99","setTitle":"Percentage Aptitude Quiz 2 – UPSC CSAT","topicName":"Percentages","topicSlug":"percentages","setNumber":2,"totalQuestions":10,"questions":[{"id":"d82ab1aa-808d-4689-ba2d-422a6338109e","order":1,"statement":"In the Asia Cup of Cricket, the batsman can score in three ways. He can score sixes or fours or by running between the wickets. Batsman Sanjay Kohli scored 100 runs. Had the batsman scored an equal number of fours and sixes, what can be the percentage of the total score he would have made by running between the wickets?","options":{"A":"50%","B":"36%","C":"85%","D":"45%"},"correctOption":"A","solution":"Since fours and sixes are scored in equal numbers, their combined runs must be a multiple of 10 (since 4+6=10). So runs from running between wickets = 100-10K, which is also a multiple of 10. Checking each option, only 50% (i.e., 50 runs) is a multiple of 10, making it the valid answer."},{"id":"b4f5fcac-ebab-4cee-a755-195c084c740a","order":2,"statement":"In a mathematics test, a student needs to score at least 50% to pass. If a student scores 60 marks and fails by 20 marks, what are the maximum marks possible for the test?","options":{"A":"80","B":"100","C":"140","D":"160"},"correctOption":"D","solution":"Let maximum marks = x. Passing marks = 0.50x. Since the student scored 60 and failed by 20, passing marks = 60+20 = 80. So 0.50x=80, giving x=160."},{"id":"dee26311-d1b7-45ce-8fe0-c2bc6c4d6953","order":3,"statement":"A Typist types 60 lines on a page in 30 minutes, but he leaves 10% margin on the left side of the page. Now he has to type 25 pages with 50 lines on each page for which he leaves 25% more margin than before. How much time is now required to type these 25 pages?","options":{"A":"620 minutes","B":"640 minutes","C":"650 minutes","D":"607.6 minutes"},"correctOption":"D","solution":"Effective typing = 90% initially (100-10). In 30 minutes, effective lines typed = (60×90)/100 = 54 lines. New additional margin = (10×25)/100 = 2.5%, so effective typing becomes 90-2.5 = 87.5%. For 25 pages with 50 lines each, effective lines = (25×50×87.5)/100 = 1093.75 lines. Time required = (1093.75×30)/54 = 607.6 minutes."},{"id":"6e4cdc26-45bb-4a66-9d52-d25d41c730be","order":4,"statement":"In an examination, Pankaj scored 30 marks more than Bijender. If Bijender scored 30% less marks than Pankaj, how many total marks did Pankaj and Bijender score?","options":{"A":"170","B":"190","C":"185","D":"215"},"correctOption":"A","solution":"Let Pankaj's score = P, Bijender's score = B. Given P=B+30 and B=0.7P. Substituting: P=0.7P+30, giving 0.3P=30, so P=100. Then B=0.7×100=70. Total = 100+70 = 170."},{"id":"827601d2-2d2d-4416-972f-4b05807329c1","order":5,"statement":"What number when decreased by 45% and then added to 225 equals the original number?","options":{"A":"280","B":"350","C":"500","D":"550"},"correctOption":"C","solution":"Let the number be x. Given 0.55x+225=x, so 0.45x=225, giving x=225/0.45=500."},{"id":"bb7574c1-a530-437b-bcde-df85d38f52d5","order":6,"statement":"The population of a town decreases at the rate of 8% per annum. Two years ago if its population was 25,000 then what is the present population of the town?","options":{"A":"14600","B":"18500","C":"20160","D":"21160"},"correctOption":"D","solution":"Present population = 25000×(1-8/100)² = 25000×(0.92)² = 25000×0.8464 = 21160."},{"id":"93f62b9d-64cb-464c-8d08-638efd8bd5b6","order":7,"statement":"A student multiplied a number by 2/5 instead of 5/2 then the percentage error in the calculation is","options":{"A":"82.5%","B":"80%","C":"72.5%","D":"84%"},"correctOption":"D","solution":"Let the original number be a. Error = 5a/2 - 2a/5 = (25a-4a)/10 = 21a/10. Percentage error = (21a/10)/(5a/2) × 100 = (21/10)×(2/5)×100 = 0.84×100 = 84%."},{"id":"8a4f16d5-080d-4f07-9edb-c736f19b1fe2","order":8,"statement":"Raman needs 50% marks to pass an exam, he secures 50 marks and failed by 50 marks, Then what were the maximum marks in the examination?","options":{"A":"200","B":"400","C":"300","D":"100"},"correctOption":"A","solution":"Let maximum marks = X. Marks needed to pass = marks scored + marks short = 50+50 = 100. Since 50% of X = 100, X = 200."},{"id":"370f9129-afe8-4641-8f9b-0adbbdeab889","order":9,"statement":"If a number is reduced by 35% and then the resulting value is increased by 35%, what is the overall percentage change?","options":{"A":"25%","B":"17.5%","C":"12.25%","D":"No change"},"correctOption":"C","solution":"Let the original value be 100. A decrease of 35% makes it 65. An increase of 35% on 65 gives 1.35×65=87.75. Change in value = 100-87.75=12.25. Overall percentage change = 12.25% (a net decrease)."},{"id":"8ca8550d-f9b0-4b7f-8761-dca76b470d03","order":10,"statement":"In a school, 85% of the students passed their final examination, and 45 students failed. What was the total number of students who took the examination?","options":{"A":"130","B":"300","C":"260","D":"330"},"correctOption":"B","solution":"If total students = x, then students who failed = 15% of x = 45. So x = (45/15)×100 = 300."}]}