Questions to Practice Averages for CLAT 2021

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  Questions to Practice Averages for CLAT 2020Q 1: Average of five numbers is 15 while average of three of those numbers​​ is 11. Find the average of remaining two numbers.Q 2: Average weight of 32 students is 42 kg. If the weight of faculty is included, the average weight increases by 1kg. What is the weight of teacher?​​ Q 3: Sonam calculates average of 10 positive 2 digit integers. By mistake she interchanges the digits of one number while calculating the average. Because of which, the average becomes 2.7 less than the correct answer. What is the difference between the two digits of the number which was reversed while calculating the average?Q 4: Two groups of travelers with average ages for the group as 20 yrs and 30 yrs. If the two groups are combined to form the third group, the average age becomes 24 yrs. What is the ratio of number of travelers in the first group to the number of travelers in the second group? ​​ Q 5: The average age of a board of 10 consultants of a firm is same as it was 2 yrs back on account of the replacement of one of the older consultants by a younger man.​​ Find the difference between the age of the old consultant and the young man.Q 6: A farmer wants to mix 100 kg of Rs. 40/kg rice and some quantity of Rs. 60/kg rice. What quantity of 60kg rice should be mixed to get Rs. 50 /kg rice mix?​​ Q 7: A milk vendor mixes 25 litres of water with 75 litres of milk and sells 1/5th​​ of the mixture. He then refills his can with the same amount of water as was sold. What is the current proportion of water to milk?Q 8: The average monthly salary of 12 labors and 3 supervisors was Rs. 1200. When one of the Supervisors whose salary was Rs. 1500 was replaced with new Supervisor, the average salary went up to Rs. 1300. What is the salary of new​​ Supervisor?Q 9: John inherits Rs. 200000, and invests a part of money in bonds with an interest rate of 11% per annum, and saves the remainder at 9% per annum. He receives Rs. 20400 as interest for 1 year. What amount he invested at 11% and 9 % respectively?Q 10: ​​ In the previous question, What is the overall interest rate earned by John. Answer and SolutionsAns:​​ 21Sol:​​ Average of 5 numbers = 15  ​​ ​​​​ Sum of these 5 numbers = 15*5 = 75  ​​ ​​​​ Average of 3 of those numbers = 11  ​​ ​​​​ Sum of these 3 numbers = 11*3 = 33  ​​ ​​​​ Sum of remaining two numbers = 75-33 = 42  ​​ ​​​​ Average of remaining two numbers = 42/2 = 21Ans:​​ 75 kgSol:​​ Average weight of 32 students = 42,​​ Hence, the Sum of weights of all students = 42*32 = 1344Average weight when faculty is included = 43,​​ Sum of weights of students including faculty = 43*33 =1419Weight of Faculty = Sum of weights of Students - Sum of weights of Students including faculty  ​​​​ = 1419-1344 = 75kgAns:​​ 3Sol:​​ Let the original number be (10b+a)  ​​ ​​​​ Because of interchange, the mistaken number is (10a+b)  ​​ ​​​​ Given that, 10b+a = 10a+b +(2.7*10) => 9b-9a = 27 => b-a = 3Ans:​​ 7:3​​ Sol:​​ ​​ Let the number of travelers in group one and two be a and b.​​ Total age of group a = a*20Total age of group b = b*30Total age after merging the two group = 23(a+b) = a*20 + b*3023a + 23b = 20a+30b3a = 7ba:b = 7:3Ans:​​ 20Sol: ​​ Let the average age of board of consultants before replacement by a old consultant be a years. The sum of the ages of the consultants on the board = 10*aThe average age of the board of consultants 2 years age = a-2The sum of the ages of the consultants on the board 2 years ago = 10(a-2)​​ After the older consultant was replaced with a younger man, the average remains the same as it was 2 yrs ago i.e., 10a hence, the younger man was 20 years younger to the old consultant.​​ Ans:​​ 200kgSol:​​ Let the rice quantity of Rs. 60 /kg rice be x.Price for Rs. 40 /kg = 200*40Price for Rs. 60/kg = x*60After mixing the two types of rice the price = 50*(200+x)The price will remain same after and before mixing, hence the equation becomes:200*40 + x*60 = 50(200+x)x(60-50) = 200*(50-40)10x = 200*10X = 200 kg​​ Ans:​​ 2:3​​ Sol:​​ Earlier water​​ and milk quantity was 25 and 75 liters respectively. Hence, total quantity becomes 100​​ liters. He sold 1/5th​​ of total i.e. 20 liters, hence 20 liter water was added in the solution. But what was the quantity of water and milk left after selling?It will be (1-1/5) of original; hence water content after selling= 25*4/5 = 20 liter,Milk content after selling = 75*4/5 = 60 literWater added was 20 liter hence, new water content= 20+20 = 40 literWater to milk ratio = 40/60 = 2:3​​ Ans:​​ 3000Sol:​​ The initial total salary amount = 1200*(12+3) = 1200*15= 18000 Salary of Supervisor who left = 1500New total salary =​​ 15*1300 = 19500Salary of new Supervisor = (19500 – 15000+1500) =​​ 3000 ​​ ​​​​ Ans:​​ 120000 & 80000Sol:​​ Let x be the amount invested in bonds then 200000-x will be saved by John.As per the questions, the interest earned is 20400 which includes both bonds and savings. Hence x*11/100 + 9*(200000-x) /100 = 204002x = 2040000-1800000 =​​ 240000X= 120000 (Invested in bonds)Savings = 200000-120000 = 80000 ​​​​ Ans:​​ 10.2%Sol:​​ Interest earned= 20400Interest rate = (20400/200000)% = 10.2% (function( $ ) { //footnotes $('.defaultNote').children(":first").css('cursor', 'pointer'); $('.defaultNote').children(":first").click(function(){ var gotoID = '#' + $(this).parent().attr('id'); $('html, body').animate( { scrollTop: $('a[href="' + gotoID + '"]').offset().top - 60, }, 250, 'linear' ) }); }(jQuery)); var numFormat = ",."; (function( $ ) { "use strict"; //do some cleaning on load var sortCells = $('td[data-sorting], th[data-sorting]'); sortCells.each(function(){ var first = $(this).text().trim().charAt(0); if (first == '@'){ var oldHTML = $(this).html(); var newHTML = oldHTML.replace('@', ''); $(this).html(newHTML); } }); function sortingTable(node, pos, ordBy){ var rows = node.children('tbody').children('tr').get(); rows.sort(function(a, b) { var X = $(a).children('td').eq(pos).text().toUpperCase(); var Y = $(b).children('td').eq(pos).text().toUpperCase(); if (numFormat != '.,'){ //we are dealing with a different locale and we need to do some //transformation in numbers X = convert2number(X); Y = convert2number(Y); } else { X = X.replace(/,/g, '').replace(/ /g, ''); Y = Y.replace(/,/g, '').replace(/ /g, ''); } var currencies = ['$', '¥', '£', '€']; var arrayLength = currencies.length; var XX = X; var YY = Y; for (var i = 0; i < arrayLength; i++) { XX = XX.replace(currencies[i], ''); YY = YY.replace(currencies[i], ''); } if (!isNaN(XX) && !isNaN(YY)){ var floatXX = parseFloat(XX); var floatYY = parseFloat(YY); return -(floatYY-floatXX) * ordBy; } else if (!isNaN(XX) && isNaN(YY)){ return -1 * ordBy; } else if (isNaN(XX) && !isNaN(YY)){ return ordBy; } else { if(X < Y) { return -1 * ordBy; } if(X > Y) { return 1 * ordBy; } return 0; } }); $.each(rows, function(index, row) { node.children('tbody').append(row); }); } function removeTableCellDecoration() { $("td[data-sorting], th[data-sorting]").removeClass('sortDecorator'); } //unbind the click event just in case we are loading more than one document $("td[data-sorting], th[data-sorting]").off('click'); $("td[data-sorting], th[data-sorting]").click(function(){ removeTableCellDecoration(); $(this).addClass('sortDecorator'); //get desired ordering var ordering = $(this).attr('data-sortOrdering'); if (ordering == 'ASC'){ var ordBy = -1; $(this).attr('data-sortOrdering', 'DESC'); } else { var ordBy = 1; $(this).attr('data-sortOrdering', 'ASC'); } var cellPosition = $(this).prevAll().length; var table = $(this).parents('table:first'); sortingTable(table, cellPosition, ordBy); }); function convert2number(str) { str = str.trim(); if (str.match(/^\d+/)) { //we have to take special care when the thousand separators are '.' var result_0 = str.replace(/\./g, '_@_'); var result_1 = result_0.replace(window.numFormat[0], '.'); var result = result_1.replace(/_@_/g, ''); result .replace(/ /g, ''); return result; } else { return str; } } }(jQuery));