Product Stability Ratio We encounter the relationship where product of two quantities equals third quantity = Constant. Example- Speed Time = Distance Price Consumption = Expenditure No. of persons days = Work done Length Breadth = Area of rectangle Apart from these cases, we encounter a no. of times where one quantity is increased to get another quantity, e.g if we increase Cost Price to obtain a certain profit, we obtain Selling price Or if we increase Principal, we obtain amount.If we generalize Product Stability Ratio, it can be written like Now, if A is increased by some certain percentage, then B is required to be decreased by some certain percentage so that Product (P) remains stable. For example, if we increase A by 25% and P has to be constant, then B is needed to be decreased by 20%. This whole procedure can be summed up in following way:- Change in AChange in BChange in P 100%50%0% 50%33.33%0% 33.33%25%0% 25%20%0% 20%16.66%0% 16.66%14.28%0% 14.28%12.5%0% 12.5%11.11%0% 11.11%10%0% 10%9.09%0% 9.09% 8.33%0% 8.33%7.69%0% And so on

So, if A is increased by 25%, then we need to decrease B by 20% to maintain the product stable.This one mathematical information can be used in so many forms: 1.Percentage If A is 25% more than B, then by how much percentage B is less than A? A B = P 2.Profit and Loss An article is sold for Rs. 125 at a profit of 25%. What is the Cost Price of the article? 3. TSD- When speed of a car is increased by 25%, time taken reduces by 20 minutes in covering a certain distance. What is the actual time taken to cover the same distance by actual speed? 4.TSD- Mayank goes to hjs office from his home at a speed of 20 kmph and gets late by 10 minutes. However when he increases his speed to 25 kmph, he is 20 minutes early. What is the distance from his office to his home? 5.Time and Work-Efficiency of Amit is 25% more than Vinit. Vinit takes 20 days to complete a work. How many days will Amit take to do the same work? 6.Time and Work- 20 men can do some job in 50 days. In how many days will 25 men do the same job? 7.SI-Rate of interest is 12.5% per annum SI. What is the principal if amount obtained after two years is Rs. 1250? 8.Percentage- Due to a price hike of 25%, 5 kgs less sugar is available for Rs.100. What is the original price per kg? 9.Mensuration- Length of a rectangle is increased by 25%. By what percentage should the breadth be decreased so that area remains constant? In all the above written situations, just one mathematical information has been used i.e. if A is increased by 25%, then B decreases by 20%. Let us see the solution of all the questions given above: Solution 1- Normal Method Let us assume B = 100, then A= 125 Now, B is 25 less than A.Percentage B is less than A = 25/125 100 = 20% Product Stability Ratio Method Using product stability rule, since A is 25% more than B, so B is 20% less than A. Solution 2 Normal MethodCP 1.25 = SP So, CP = SP/1.25=125/1.25= Rs. 100 Product Stability Ratio Method If we increase CP by 25%, we will get SP. So, if we decrease SP by 20%, we will get CP. Hence CP = Rs. 100 Solution 3 - Normal MethodSince we know S = V T (Distance = Speed Time) New speed = 1.25 V, so new time = T/ 1.25 So, reduction in time = T T/1.25 = 0.25 T/ 1.25 = T / 5 T / 5 = 20 mins. T = 100 mins Product Stability Ratio Method Since speed has been increased by 25%, so time will reduce by 20%. Now, 20% T(Time) = 20 mins So, Total time = 100 mins. Solution 4- Normal Method Let us assume that distance = D So, D/20 D/25 = 30/60 hr. = So, D = 50 km Product Stability Ratio Method S=VT 25% 20% So, 20% T = 30 mins T = 150 mins = 2hours So, total distance = 20 2 = 50 kms Solution 5 - Normal Method Vinit is taking 20 days to complete the work i.e. Vinit is doing 100% work in 20 days. So, Vinit is doing 5% work in a day. Since efficiency of Amit is 25% more than Vinit, so, Amit is doing 6.25% work per day.So, no. of days taken by Amit = 100/6.25 days = 16 days Product Stability Ratio Method Efficiency of Amit is 25% more than Vinit. So, Amit will take 20% less days than Vinit. So, no. of days taken by Amit = 16 days Solution 6 Normal Method Using Work = No. of persons No. of days Work = 20 50 = 1000 Now, 1000 = 25 D So, D = 40Product Stability Ratio Method No. of persons increases by 25%, so no. of days will decrease by 20%.So, no. of days = 40 days Solution 7 - Normal Method Using the formula for SI= PRT/100 P = (SI 100)/RT Putting the values gives us P = Rs.1000 Product Stability Ratio Method Interest for two years = 25% So, if we decrease amount by 20%, then we will be getting Principal. Hence Principal = Rs. 1000 Solution 8 Normal Method Let us assume that Original price per kg = Rs. P per kg So, final price per kg = Rs. 1.25 PHence, (120 /P) (120/1.25P) = 5 Solving this equation gives P = Rs. 4 per kg.Product Stability Ratio Method Since price hike is 25%, 20% less quantity of sugar will be available for Rs. 100. 20% = 5 kgs 100% = 25 kgs So. 25 kgs were available for Rs. 100 initially. So, Price = Rs. 4/kg Solution 9 - Normal Method LengthBreadthArea Initially ----1010=100 Finally -------12.5B=100 So, B = 8 Percentage decrease = 20% Product Stability Ratio Method Till now, it must have become very obvious that Breadth will decrease by 20% to keep the area constant. Extension of Product Stability Ratio This table is a two-way table, i.e. if we decrease A by 50%, then B is needed to be decreased by 100%. If we express the percentage figures given in above product-stability-table in ratios, then it comes like the following: Change in AChange in BChange in P 11 21 0% 21 31 0% 31 41 0% So, 501 corresponds to 511. It means that if we increase A by 2%, then B is needed to be decreased by 1.96%(approx.) so that P remains constant. And similarly it can be done with all the reciprocals. But the problem which lies with this table is that it has the values which are reciprocals only. So, what we are required to do if we increase A by 15%? Take this as: Change in AChange in BChange in P 15% =203 2330% 35% = 207 2770%