A seller makes an offer of selling certain articles that can be described by the equation x = 25 -2y where ‘x’ is the price per unit and ‘y’ denotes the number of unit. The cost price of the article is Rs. 10 per unit. The maximum quantity that can be offered in a single deal to avoid loss is. (a) 6 (b)7 (c)8 (d)9?

Question

Answer

Given information:
- x = 25 - 2y (price per unit)
- Cost price = Rs. 10 per unit

To avoid loss, the selling price should be greater than or equal to the cost price.
So, we can write the inequality:
x ≥ 10
Substituting the value of x from the given equation, we get:
25 - 2y ≥ 10
Solving for y, we get:
y ≤ 7.5
Since y represents the number of units, it cannot be a fractional value. So, we take the maximum integer value of y that satisfies the inequality:
y ≤ 7
Substituting this value of y in the given equation, we get:
x = 25 - 2(7) = 11
So, the maximum price per unit that can be offered without loss is Rs. 11.
To find the maximum quantity that can be offered in a single deal, we need to check the total revenue and total cost for different values of y.

For y = 1, x = 23
Total revenue = xy = 23(1) = 23
Total cost = 10(1) = 10
Profit = 23 - 10 = 13

For y = 2, x = 21
Total revenue = xy = 21(2) = 42
Total cost = 10(2) = 20
Profit = 42 - 20 = 22

For y = 3, x = 19
Total revenue = xy = 19(3) = 57
Total cost = 10(3) = 30
Profit = 57 - 30 = 27

For y = 4, x = 17
Total revenue = xy = 17(4) = 68
Total cost = 10(4) = 40
Profit = 68 - 40 = 28

For y = 5, x = 15
Total revenue = xy = 15(5) = 75
Total cost = 10(5) = 50
Profit = 75 - 50 = 25

For y = 6, x = 13
Total revenue = xy = 13(6) = 78
Total cost = 10(6) = 60
Profit = 78 - 60 = 18

For y = 7, x = 11
Total revenue = xy = 11(7) = 77
Total cost = 10(7) = 70
Profit = 77 - 70 = 7

For y = 8, x = 9
Total revenue = xy = 9(8) = 72
Total cost = 10(8) = 80
Profit = 72 - 80 = -8

We can see that the profit becomes negative for y = 8. So, the maximum quantity that can be offered in a single deal to avoid loss is 7 units (option b).

Answer

7

Answer

8

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