[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-347401-105":59,"doc-detail-347401-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","cat-formula-sheet-2024-pdf-number-systems-profit-loss-and-discount-math-formula-reference","CAT Formula Sheet 2024 PDF - Number Systems - Profit, Loss, and Discount - Math Formula Reference","","CAT Formula Sheet 2024 PDF compiles core quantitative-math formulas used for timed exams. It covers number systems with sums of natural numbers, squares, cubes, and divisibility via dividend–divisor–quotient with remainders. It details profit, loss, and discount relationships including selling price, marked price, and percentage conversions. It also includes HCF/LCM rules for integers and fractions, simple and compound interest, depreciation, time and work, speed–time–distance, averages, surds & indices, logarithms, and set theory identities.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/cat-formula-sheet-2024-pdf-number-systems-profit-loss-and-discount-math-formula-reference/347401/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/cat-formula-sheet-2024-pdf-number-systems-profit-loss-and-discount-math-formula-reference/347401.png","ImageObject",300,407,{"name":92,"@type":93},"Aurelia","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-09","2026-09-22",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",17,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"Which formula set explains profit, loss, and discount in the sheet?","Question",{"text":113,"@type":114},"Profit Percentage, Loss Percentage, Selling Price relations, and Discount Percentage/Marked Price formulas are listed under “Profit, Loss, and Discount.” It also includes conversions among cost price, profit, and loss.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How are HCF and LCM computed according to the sheet?",{"text":118,"@type":114},"For HCF, the sheet instructs breaking numbers into prime factors and taking the product of common prime factors. For LCM, it similarly uses prime factors and takes the product of the highest powers of all factors present.",{"name":120,"@type":111,"acceptedAnswer":121},"What topics related to interest and growth are included?",{"text":122,"@type":114},"The sheet provides Simple Interest and Amount formulas (SI = Prt/100, A = P(1+rt/100)) and Compound Interest/Amount relations, including half-yearly and quarterly rate cases and differences between CI and SI over multiple years.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},347401,1790247098,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":44,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},1099514068365,"https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?_k=1776742907772140068","CAT Formula Sheet 2024 PDF  \nNumber Systems  \n● Sum of first n natural numbers = n(n+1)/2  \n● Sum of squares of first n natural numbers = n(n+1)(2n+1)/6  \n● Sum of cubes of first n natural numbers = [n(n+1)/2]^2  \n● Sum of first n odd numbers = n^2  \n● Dividend = ( Divisor x Quotient) + Remainder  \nProfit, Loss, and Discount  \n● Profit Percentage = ( Profit/Cost Price) x 100  \n● Loss Percentage = ( Loss/Cost Price) x 100  \n● Selling Price = Cost Price + Profit  \n● Selling Price = Cost Price – Loss  \n● Cost Price = Selling Price – Profit  \n● Cost Price = Selling Price + Loss  \n● Profit = Selling Price – Cost Price  \n● Loss = Cost Price – Selling Price  \n● Discount = Marked Price – Selling Price  \n● Discount Percentage = ( Discount/Marked Price) x 100  \n● Marked Price = Selling Price/( 1 – Discount Percentage/ 100)  \n● Marked Price = Cost Price/( 1 – Profit Percentage/ 100)  \n● Profit Percent = Profit x 100  \nC. P.  \n● Loss Percent = Loss x 100  \nC. P.  \n● Selling Price = Cost Price ( 100 + Profit%) 100  \nOr  \nCost Price ( 100-Loss%)  \n100  \n● Loss% = (x/ 10)2  \n● Value of Loss =  2x2S 1002-x2  \nHCF and LCM  \nTo find the HCF of the given numbers  \n1. Break the given numbers into their prime factors  \n2. The HCF will be the product of all the prime factors common to all the numbers  \nTo find the LCM of given numbers:  \n1. Break the given numbers into their prime factors  \n2. The LCM will be the product of the highest power of all the factors that occur in the given numbers  \n● HCF of A, B and C is the highest divisor which can exactly divide A, B, and C  \n● LCM of A, B and C is the lowest dividend which is exactly divisible by A, B, and C  \n● Other number = LCM x HCF 1st number  \n● HCF of fractions = HCF of the numerators LCM of the Denominators  \n● LCM of fractions = LCM of the numerators HCF of the Denominators  \nSimple Interest  \nIf we are given the Principal ( P) , the Rate of Interest (r) , and the Time Period (t) , we will have  \nSimple Interest (SI) = Prt/100  \nAmount (A) = P + Prt/ 100= P( 1+rt/100) Compound Interest (CI)  \n1. CI = A – P  \nA is the amount including interest and principal (P ) both  \n2. Amount, A = P( 1+r/100)t  \n3. When the rate of interest is half-yearly  \nA = P( 1+r/2/ 100)2t  \n4. When the rate of interest is quarterly  \n5. Difference between CI and SI for two years = p(r/100)2  \n6. Difference between CI and SI for three years = p(r/100)2 (r/100+3)  \n7. Difference between CI and SI for n th year  \n8. For compound interest, if r denotes the rate of interest, the change in amount over the previous year can be calculated or following.  \nSimilarly,  \nDepreciation  \nIt is common knowledge that the prices of certain items depreciate in value over time. When the value of an item decreases in terms of currency, we say that its value is depreciating.  \nWhere,  \nVi = Initial value of the article  \nVf = Final (depreciated) value of article  \nr = rate of interest by which the price of article decreases over the time period ‘t’.  \nTime and Work  \n● Work Done = Time Taken × Rate of Work  \n● Rate of Work = 1 / Time Taken  \n● Time Taken = 1 / Rate of Work  \n● If a piece of work is done by A in n days, then A’s 1 day’s work = 1/n  \n● If A’s 1 day’s work = 1/n, then A can finish the work in n days  \n● If A can do a piece of work in x days and B can do the same work in y days, then the work done by both A and B in one day = 1/x + 1/y  \n● If A can do a piece of work in x days and B can do the same work in y days, then the time taken by both A and B to complete the work together = (xy) / (x + y)  \nSpeed, Time and Distance  \n● Speed = Distance/Time – how quickly or slowly an object is moving or the amount of time it took to travel a certain distance divided by the distance travelled.  \n● Average Speed = (Total distance travelled) / (Total time taken)  \n● Speed is inversely correlated with time and directly correlated with distance. Hence,(a) Distance = Speed X Time, and  \n(b) Time = Distance / Speed, The time required will r","cbCaiiqZXbd2wFBz","https://ap.wps.com/l/cbCaiiqZXbd2wFBz","pdf",197694,"English","# Number Systems\n## Profit, Loss, and Discount\n## HCF and LCM\n## Simple Interest\n## Compound Interest\n## Depreciation\n## Time and Work\n## Speed, Time and Distance\n## Averages\n## Surds and Indices\n## Logarithm\n## Set Theory & Function","[{\"question\":\"Which formula set explains profit, loss, and discount in the sheet?\",\"answer\":\"Profit Percentage, Loss Percentage, Selling Price relations, and Discount Percentage/Marked Price formulas are listed under “Profit, Loss, and Discount.” It also includes conversions among cost price, profit, and loss.\"},{\"question\":\"How are HCF and LCM computed according to the sheet?\",\"answer\":\"For HCF, the sheet instructs breaking numbers into prime factors and taking the product of common prime factors. For LCM, it similarly uses prime factors and takes the product of the highest powers of all factors present.\"},{\"question\":\"What topics related to interest and growth are included?\",\"answer\":\"The sheet provides Simple Interest and Amount formulas (SI = Prt/100, A = P(1+rt/100)) and Compound Interest/Amount relations, including half-yearly and quarterly rate cases and differences between CI and SI over multiple years.\"}]","CAT Formula Sheet 2024 PDF - Number Systems - Profit, Loss, and Discount - Math Formula Reference | PDF",1790066792,23]