Ratio & Proportion — Set #2 | Practice

{"setId":"f2c7f9d4-dace-4446-a34f-5db9d2187997","setTitle":"Ratio and Proportion 2 – UPSC CSAT","topicName":"Ratio & Proportion","topicSlug":"ratio-proportion","setNumber":2,"totalQuestions":10,"questions":[{"id":"f27cf1c0-4cf3-428a-8fcd-3101135307f3","order":1,"statement":"If salaries of Rohit and Mohit are in the ratio 3:5, respectively. If the salary of each is increased by Rs. 3,000, the new ratio becomes 63:65. What is Mohit's new salary (in Rs.)?","options":{"A":"3250","B":"3150","C":"6200","D":"3900"},"correctOption":"A","solution":"Let original salaries be 3x and 5x. Given (3x+3000)/(5x+3000)=63/65. Cross multiplying: 65(3x+3000)=63(5x+3000), giving 195x+195000=315x+189000, so 6000=120x, x=50. Mohit's new salary = 5x+3000 = 5(50)+3000 = Rs. 3,250."},{"id":"d1d001a1-78db-44bc-bb26-596bd3ce83d2","order":2,"statement":"The ratio of monthly income of Manjeet and Sanjeet is 4:3 while the ratio of their expenditure is 3:2, respectively. If each of them saves Rs. 2,500, then their respective incomes are?","options":{"A":"₹10,000 and ₹7,500","B":"₹7,000 and ₹7,500","C":"₹1,000 and ₹750","D":"₹6,000 and ₹8,000"},"correctOption":"A","solution":"Let incomes be 4x and 3x, expenditures be 3y and 2y. Given 4x-3y=2500 and 3x-2y=2500. Setting them equal: 4x-3y=3x-2y, giving x=y. Substituting into first equation: 4x-3x=2500, so x=2500. Incomes = 4(2500)=10000 and 3(2500)=7500."},{"id":"b601488e-2c19-4430-b037-54376d7463cb","order":3,"statement":"A certain sum of money is distributed among Rohit, Rahul and Mohit in the ratio 8:6:7, respectively in such a way that the share of Rohit was ₹1,000 less than the sum of the share of Rahul and Mohit. Find the difference between the shares of Rohit and Mohit.","options":{"A":"Rs. 250","B":"Rs. 50","C":"Rs. 200","D":"Rs. 300"},"correctOption":"C","solution":"Let shares be 8x,6x,7x. Given (6x+7x)-8x=1000, so 13x-8x=5x=1000, giving x=200. Rohit's share=8(200)=1600, Mohit's share=7(200)=1400. Difference = 1600-1400 = Rs. 200."},{"id":"4848c58a-99d6-43e7-9ddb-cf33f4ea40b6","order":4,"statement":"The monthly ratio of expenditure to savings of Jack is 23:6. If his monthly income is Rs. 7,192, then what is his monthly savings?","options":{"A":"Rs. 7,200","B":"Rs. 1,450","C":"Rs. 1,445","D":"Rs. 1,488"},"correctOption":"D","solution":"Let expenditure=23x, savings=6x. Total income = 23x+6x=29x=7192, giving x=248. Savings = 6x = 6(248) = Rs. 1,488."},{"id":"8d4188b6-1742-4e7b-b708-7caaaf08ab02","order":5,"statement":"30 meter of a uniform wire weighs 40 kg. What will be the weight of the same wire of 132 meter length?","options":{"A":"148 kg","B":"160 kg","C":"120 kg","D":"176 kg"},"correctOption":"D","solution":"Using proportion: 30/40 = 132/x, so x = (132×40)/30 = 176 kg."},{"id":"4e353d3d-c30b-4ff1-ae44-846a62d7612a","order":6,"statement":"In a classroom, the number of girls is 40% more than that of boys. The strength of the class is 60. If 5 more girls are admitted to the class, the ratio of the number of boys to that of the girls will be?","options":{"A":"2:5","B":"5:8","C":"3:7","D":"7:3"},"correctOption":"B","solution":"Since girls=140% of boys, ratio of boys:girls=5:7. Number of boys=(5/12)×60=25, girls=60-25=35. After 5 more girls join, girls=40. New ratio of boys:girls = 25:40 = 5:8."},{"id":"afd6f99f-5282-49cf-bbfb-dc770cb29b48","order":7,"statement":"The salaries of 'A', 'B', 'C' are in the ratio 2:3:5, respectively. If the increments of 20%, 25% and 30% are allowed respectively in their salaries, then what will be the new ratio of their salaries?","options":{"A":"24:15:36","B":"130:70:60","C":"38:50:65","D":"48:75:130"},"correctOption":"D","solution":"Let initial salaries be 2k,3k,5k. New salaries: A=1.2×2k=12k/5, B=1.25×3k=15k/4, C=1.3×5k=13k/2. Multiplying by LCM(5,4,2)=20 to clear denominators: A=48k, B=75k, C=130k. New ratio = 48:75:130."},{"id":"ac121783-1c10-4a1f-8c4e-d4d8a60ce45c","order":8,"statement":"In a college, ratio of number of boys to that of girls is 4:3 while the ratio of number of girls to that of Lecturer is 9:1. Then the ratio of total students in the college to lecturers is?","options":{"A":"56:3","B":"21:1","C":"49:3","D":"36:1"},"correctOption":"B","solution":"Let boys=4x, girls=3x. Since girls:lecturers=9:1, lecturers=(1/9)×3x=x/3. Total students=4x+3x=7x. Required ratio=7x:(x/3)=21:1."},{"id":"2d7b6771-add3-4a9c-8bdc-05b092f1e998","order":9,"statement":"Find the mean proportion between 3 and 12.","options":{"A":"9","B":"6","C":"10","D":"36"},"correctOption":"B","solution":"Mean proportion between a and b = √(ab). Mean proportion of 3 and 12 = √(3×12)=√36=6."},{"id":"62739a90-f5dc-4e39-a076-275546c72b01","order":10,"statement":"If 4, 8 and 'X' are in continued proportion, then what is the value of 'X'?","options":{"A":"16","B":"12","C":"10","D":"14"},"correctOption":"A","solution":"For 4,8,X in continued proportion: 4:8::8:X. So 4/8=8/X, giving X=(8×8)/4=16."}]}