Percentages — Set #1 | Practice

{"setId":"06ae7693-f840-4f92-b8fe-b95fda6fd2a4","setTitle":"Percentage Aptitude Quiz – UPSC CSAT","topicName":"Percentages","topicSlug":"percentages","setNumber":1,"totalQuestions":10,"questions":[{"id":"ac53b97e-e056-4e5d-8c34-49ddc44318b6","order":1,"statement":"If 40% of (x-y) = 30% of (x+y), then what percent of 'x' is 'y'?","options":{"A":"14 2/7%","B":"7 1/7%","C":"14 1/2%","D":"700%"},"correctOption":"A","solution":"From 40%(x-y)=30%(x+y): 4x-4y=3x+3y, giving x=7y. Let a% of x = y, so (a/100)×x = y, meaning (a/100)×7y = y, giving a = 100/7 = 14 2/7%."},{"id":"a999f5b6-5c26-4144-b756-a25ee65ce4ba","order":2,"statement":"Ramesh plans to purchase a laptop that costs ₹40,000. However, he realizes that he only has 60% of the required amount. To cover the remaining cost, he borrows ₹10,000 from his brother. What percentage of the laptop's price does Ramesh have after borrowing the money?","options":{"A":"85%","B":"80%","C":"75%","D":"70%"},"correctOption":"A","solution":"Amount Ramesh initially has = 60% of ₹40,000 = ₹24,000. After borrowing ₹10,000, total amount = ₹24,000+₹10,000 = ₹34,000. Percentage of laptop's price = (34,000/40,000)×100 = 85%."},{"id":"50b46212-50bc-4825-971d-07ec9f57fdbc","order":3,"statement":"If population of a town increased by 10% and 20% in two successive years. What is the overall increase in population after two years?","options":{"A":"30%","B":"38%","C":"32%","D":"40%"},"correctOption":"C","solution":"For successive percentage increases of x% and y%, the overall increase = [x+y+(xy/100)]%. Here x=10, y=20: overall increase = 10+20+(10×20/100) = 30+2 = 32%."},{"id":"d632b171-f9b2-400f-94cf-91d4e1cc973f","order":4,"statement":"Wheat sold earlier for Rs. 10 per kg is now sold for Rs. 12 per kg. What is the percentage increase in the selling price of wheat?","options":{"A":"20%","B":"25%","C":"18%","D":"15%"},"correctOption":"A","solution":"Percentage change = [(Final value - Initial value)/Initial value]×100. Change in price = 12-10 = Rs.2. Percentage change = (2/10)×100 = 20%."},{"id":"a93b7815-db2e-4c2c-a36f-22e3c51b4741","order":5,"statement":"Raman needs 50% marks to pass an exam, he secures 50 marks and failed by 50 marks, then what were the maximum marks for 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":"59843590-9307-4c23-8a84-90121df5a272","order":6,"statement":"Two numbers 'A' and 'B' are respectively 25% and 28% less than the third number 'C'. By what percentage is the number 'B' less than 'A'?","options":{"A":"4%","B":"8%","C":"5%","D":"3%"},"correctOption":"A","solution":"Let C=100x. Then A=0.75×100x=75x and B=0.72×100x=72x. Required percentage = [(75x-72x)/75x]×100 = (3x/75x)×100 = 4%."},{"id":"d43b4997-db14-4847-80b5-fb22f47e189a","order":7,"statement":"A number exceeds 60% of itself by 64 then the number is?","options":{"A":"640","B":"400","C":"124","D":"160"},"correctOption":"D","solution":"Let the number be N. Then N = 60% of N + 64, so N-(60/100)N = 64, giving (40/100)N = 64, so N = (64×100)/40 = 160."},{"id":"e9ab2622-9cc7-422a-9503-6f2bd5492909","order":8,"statement":"If 50% of 'P' = 25% of 'Q', then P = x% of 'Q'. Find 'x'.","options":{"A":"125","B":"25","C":"150","D":"50"},"correctOption":"D","solution":"Given 0.50P = 0.25Q, so P = (0.25/0.50)×Q = Q/2 = 50% of Q. Therefore, x = 50."},{"id":"973004b4-6ff4-4b57-af8e-e823b8df3aa2","order":9,"statement":"B's salary is 40% more than A's, and C's salary is 25% less than B's. By what percentage is C's salary more than A's?","options":{"A":"5%","B":"7.5%","C":"15%","D":"10%"},"correctOption":"A","solution":"Let A's salary = 100x. B's salary = 100x+40% of 100x = 140x. C's salary = 140x-25% of 140x = 140x-35x = 105x. Required percentage = [(105x-100x)/100x]×100 = 5%."},{"id":"a3862477-c6c7-4d00-87dd-0706572455f1","order":10,"statement":"40% of a number when increased by 50, the resultant becomes 20% less than the original number. Find the original number.","options":{"A":"125","B":"140","C":"175","D":"180"},"correctOption":"A","solution":"Let the number be x. 40% of x = 0.40x. 20% less than x = 0.80x. Given 0.40x+50 = 0.80x, so 0.40x = 50, giving x = 50/0.4 = 125."}]}