My Scooty gives an average of 40 kmpl of petrol. But after recent filling at the new petrol pump, its average dropped to 38 kmpl. I investigated and found out that it was due to adulterated petrol. Petrol pumps add kerosene, which is \(\frac{2}{3}\) cheaper than petrol, to increase their profits. Kerosene generates excessive smoke and knocking and gives an average of 18 km per 900 ml. If I paid Rs. 30 for a litre of petrol, what was the additional amount the pump-owner was making ?
In the question it is given that the Capacity of Kerosene=(18 ÷900) ×1000=20km/ltr
Cost of Petrol is given=Rs.30/ltr
Cost of Kerosene= \(\frac{2}{3}\)(Cheaper than Petrol)=\(\frac{1}{3}\) (Petrol)
Cost of Kerosene = \(\frac{1}{3}\)(30) = Rs.10/ltr
Let take the Quantity of Kerosene is x ltr in 1 ltr of mixture
The capacity of Kerosene=20km/ltr
The capacity of Petrol=40km/ltr
If there is x Ltr Petrol in 1 Ltr
Then,
20(x)+40(1-x)=38
20x + 40 - 40x = 38
Solving the equation, we get
x = -\(\frac{-2}{-20}\)
x = 0.1 ltr
The Cost of mixture will be = 10(.1) +30(.9)=Rs.28
The Cost of Petrol which I gave was Rs.30 but the Original Amount is Rs.28
Than, the Additional Amount that the Pump Owner was Charging
=Rs.30-Rs.28
= Rs.2
The correct option is (D)
A furniture trader deals in tables and chairs. He has Rs. 75,000 to invest and a space to store at most 60 items. A table costs him Rs. 1,500 and a chair costs him Rs. 1,000. The trader earns a profit of Rs. 400 and Rs. 250 on a table and chair, respectively. Assuming that he can sell all the items that he can buy, which of the following is/are true for the above problem:
(A) Let the trader buy \( x \) tables and \( y \) chairs. Let \( Z \) denote the total profit. Thus, the mathematical formulation of the given problem is:
\[ Z = 400x + 250y, \]
subject to constraints:
\[ x + y \leq 60, \quad 3x + 2y \leq 150, \quad x \geq 0, \quad y \geq 0. \]
(B) The corner points of the feasible region are (0, 0), (50, 0), (30, 30), and (0, 60).
(C) Maximum profit is Rs. 19,500 when trader purchases 60 chairs only.
(D) Maximum profit is Rs. 20,000 when trader purchases 50 tables only.
Choose the correct answer from the options given below: