A salesman has to choose between two schemes of remuneration.The first scheme has a fixed salary of rs 3700 and a commission of 2% on sales above rs 50000. The second scheme has no salary but offer commission only. The commission starting from 3% of sales for the first rs 50000 or part there of increase at the rate of 1 percentage point for every increase of rs 50000 or part there of sales upto a maximum of 20% of sales. what is the minimum value of sales above which he can prefer the second scheme ?
Plz explain easy way
To determine the minimum value of sales above which the salesman can prefer the second scheme, we need to compare the total earnings from both schemes.
Let's start by calculating the total earning under the first scheme:
1. First, calculate the commission earned on sales above Rs 50,000:
Commission = 2% of (Sales - Rs 50,000)
2. Then, calculate the total earning under the first scheme:
Total Earning in Scheme 1 = Fixed Salary + Commission
Next, we'll calculate the total earning under the second scheme:
- In the second scheme, the commission starts at 3% of sales up to Rs 50,000, and it increases gradually with sales.
To find the maximum commission rate, we need to identify the sales value that reaches 20% commission. Since for every increase of Rs 50,000 in sales, the commission increases by 1%, we can set up an equation:
3% + 1% * n = 20%
Where 'n' represents the number of times the sales value increased by Rs 50,000 (or part thereof).
Simplifying the equation:
1% * n = 20% - 3%
1% * n = 0.17
Dividing by 1% on both sides:
n = 0.17 / 0.01
n = 17
So, for every 17 times the sales value increases by Rs 50,000, the commission will reach 20%.
Now, let's calculate the commission under the second scheme for a given sales amount:
For a sales value of Rs X, we can calculate the commission using the following steps:
1. Determine the number of times the sales value increases by Rs 50,000 (or part thereof):
n = ceil((X - Rs 50,000) / Rs 50,000)
Where ceil is the function that rounds up to the nearest whole number.
2. Calculate the commission rate based on the determined 'n' value:
Commission Rate = 3% + (n * 1%)
3. Calculate the commission earned:
Commission = Commission Rate * X
Finally, let's compare the total earnings from both schemes.
If Total Earning in Scheme 2 is greater than Total Earning in Scheme 1, then the salesman should prefer the second scheme.
I hope this explanation helps you understand how to calculate and compare the earnings under both schemes to determine the minimum value of sales above which the second scheme is preferred.