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
A
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 A
Change in B
Change 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?
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 Method
CP 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 Method
Since 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 =
V
25%
T
20%
So, 20% T = 30 mins
T = 150 mins = 2 hours
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 = 40
Product 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 P
Hence, (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
Length
Breadth
Area
Initially ---- 10
10
100
Finally ------- 12.5
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 A
Change in B
Change in P
0%
0%
So,
0%
1
1
corresponds to
. It means that if we increase A by 2%, then B is needed to be decreased by 1.96%(approx.)
51
50
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 A
Change in B
Change in P
15% =
20
23
0%
35% =
7
7
20
27
0%
