Learn Time and Work for Maths Section of AILET

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Learn Time and Work for Maths Section of AILET‘Time and work’ is used to calculate how much time will be taken to finish a work and how much work can be finished in a given time ​​ The concept of time and work is although widely used in our daily lives, it could often be considered as a part that is a little difficult and confusing to solve. But remember, there are certain tricks and formulas that can make it easy to solve questions from this concept quite quickly and correctly. The following points given​​ if kept in mind all the time, you will never ever lose a mark from this part.​​ If a man completes a work in T days or unit​​ time,​​ the work done in 1 day or in one unit time is 1/T.​​ If the work done in 1 day is given, then the total no. of days taken to finish the entire work is 1/work done in one day.If a person does 1/w work in one unit of time, then the unit of time required to​​ complete the entire work is w days.If A completes a work in x days, then the work done in one day is (1/x) of the total work. If B finishes 1/y of the total work in 1 day, then the work will be completed in y days. Therefore, if working together, both can finish 1/z (1/x + 1/y = 1/z) work in one day and complete the task in ‘z’ days.If a person A does a work in ‘a’ days​​ and​​ person B can finish the work in’b’ days, they can finish the work together in ab/ (a+b) days.I f a person A does a work in ‘a’ days , B can finish the work in’b’ days and Person C can finish it in ‘c’ days ​​ they can finish the work together in abc/ (a+b+c) days.The work done is proportional to time if the number of persons doing it, is constant.The time is inversely proportional to the number of men if the amount of work if fixed.Sometimes there are specific questions involving cistern and water tank. Always remember that there are two​​ pipes connected​​ to a water tank. One pipe which fills up the water is called inlet and one which throws the​​ water out is called the outlet.If a pipe fills the water​​ tank​​ in X​​ hours,​​ then in one hours it will fill​​ 1/X of the tank. Therefore the work done in pipe in one hour is 1/x.If an outlet empties a tank in Y hours, then it will empty 1/Y tank in one hour and therefore the work done by the outlet in one hour is (-1/Y) i.e. negative work.(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));