Hello everyone, today we are going to start with the session called Partnership and
Mixtures. Both of these topics are Applications of Ratio and Proportion.
So, let’s first begin with Partnership and considering A, B and C, starts a business with an
investment of 16 lakhs, 12 lakhs and 20 lakhs respectively and the time period of the
investment is 12 months, 8 months and 6 months respectively. Now at the end of the year
the profits or loss ratio is all dependent on the types of partnership. If it is a case of simple
partnership then we consider only investment ratio as a ratio of profit or loss, that is ratio of
16 is to 12 is to 20 that is 4 is to 3 is to 5. Whereas on the other hand, if it is a case of
compound partnership, we do give importance to time period and hence the ratio of profit
or loss is the ratio of investment into time period, that is 16 into 12 is to 12 into 8 is to 20
into 6, which can be further simplified as 192 is to 96 is to 120, which can be further
simplified as 8 is to 4 is to 5. Now, what is our recommendation? Instead of taking product
and then simplifying, can you first cancel the factors and then multiply. Let’s see how, what I
can do is, I can find common factor from each of these three terms. The first common factor
4 into 4, 4 x 4 = 16, 4 x 3 = 12, 4 x 5= 20 and next is 2 x 6 = 12, 2 x 4 = 8 and 2 x 3 = 6 and
finally I can say, 3 x 2, 3 x 1, 3 x 1, so finally we are left out with the term 4 into 2 = 8 is to 1
into 4 = 4 is to 5 into 1 = 5. So, that’s the ratio of profit or loss that is 8 is to 4 is to 5.
Now, while dealing with the questions of partnerships, you need to remember two points.
The first point is, if nothing is mentioned about the type of partnership then you need to
assume it to be compound partnership. And sometimes, salary is a part of distribution, so
what you need to do is, you need to remove the salary first than distribute the profit. That is,
it says, in case an employee or one of the partners need to be given a salary then first
deduct that from the profit and then divide the profit in the given ratio.
Next is, mixtures. To understand this topic mixtures, what I will do is, I will consider one
example. It says that, a vessel contains milk and water in the ratio 3 is to 5. When 6 litres of
water is added to this solution, the ratio of milk and water becomes 5 is to 9. The question
is, how many litres of the solution was present in the vessel originally? The situation is, let’s
understand.