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 ?

Question

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 ?

A.140000
B.90000
C.40000
D.240000

Answer 1

To find the minimum value of sales above which the salesman would prefer the second scheme, we need to compare the earnings under both schemes.

Let's consider the two schemes:

Scheme 1:
- Fixed salary: Rs 3700
- Commission: 2% on sales above Rs 50000

Scheme 2:
- No salary
- Commission starting from 3% of sales for the first Rs 50000 or part thereof, increasing at the rate of 1 percentage point for every increase of Rs 50000 or part thereof sales, up to a maximum of 20% of sales.

Now, we need to find the sales value where the earnings under the second scheme are greater than the earnings under the first scheme.

Let's assume the sales value as 'X' (in Rs).

Under Scheme 1, the earnings would be:
- Fixed Salary: Rs 3700
- Commission: 2% on (X - Rs 50000)

Under Scheme 2, the earnings would be:
- Commission: 3% of Rs 50000 + (1% * [(X - Rs 50000) / Rs 50000 increased sales segments above Rs 50000])

Now we can set up the equation to find the minimum value of sales where earnings from Scheme 2 become greater:

3700 + 0.02 * (X - 50000) < 0.03 * 50000 + 0.01 * [(X - 50000) / 50000 increased sales segments above 50000]

Simplifying the equation:
3700 + 0.02X - 1000 < 1500 + 0.01 * [(X - 50000) / 50000 increased sales segments above 50000]

Combine like terms and simplify further:
0.01 * [(X - 50000) / 50000 increased sales segments above 50000] > 2200 + 0.02X

To find the minimum value of sales (X), we need to solve this inequality.

X > 220000 - 20000 * (1 increased sales segment)
X > 220000 - 20000
X > 200000

Therefore, the minimum value of sales above which the salesman would prefer the second scheme is Rs 200,000.

So, the correct option is:
D. 240000