# Incomeâˆ’Expense ratio

When the ratio of incomes and expenses of two persons are given and their savings is being asked.

Example

The ratio of the incomes of Mr Vinay Singh and Mr Arun Sharma is 3:5 and the ratio of their expenses is 1:3. Who is saving more?

Solution

Let us assume the values of income and expenses of A and B,

So, Vinay saves more than Arun.

In the other case,

So, savings of both of them is equal.

So, in this case Mr Singh is saving less than Mr Sharma.
Thus, it is difficult to determine who is saving more.
The concept tells us: If the value of the ratio of income is more than the value of the ratio of expenses, then we cannot determine who is saving more. If the value of the ratio of expenses is more than the value of the ratio of income, then we can determine who is saving more. (Ratio should be taken in such a way that the value of ratio is less than 1, i.e., the numerator should be less than the denominator.)
In the above case, the value of the ratio of income = 3/5 = 0.6 and value of ratio of expenses = 1/3 = 0.33
Since the value of ratio of expenses < value of the ratio of income, we cannot determine who is saving more.
However, in the above question, if we take the ratio of income of Vinay and Arun as 3:5 and the ratio of their expenses as 3:1, then Arun is saving more.

# Partnership

If two or more than two persons are investing their money in a joint venture, then the profit or loss incurred is distributed among everybody in the ratio of the time period for which the money has been invested by each of them.

It can be observed here that the partnership is a typical case of direct variation.

It can be observed here that the partnership is a typical case of direct variation.

Example

A, B, C,â€¦, K, L invested money in the ratio of 12:11:10:â€¦: 2:1. The duration for which they invested the money is in the ratio of 1:2:3 :â€¦: 11:12. Who will obtain the maximum profit at the end of year?

Solution

Profit will be distributed in the ratio of product of the time and money of every individual.
So, the ratio of profit = 12 Ã— 1:11 Ã— 2:10 Ã— 3:9 Ã— 4:8 Ã— 5:7 Ã— 6:6 Ã— 7:5 Ã— 8:4 Ã— 9:3 Ã— 10:2 Ã— 11:1 Ã— 12.
So, the maximum profit will be obtained by F and G both.