A shopkeeper bought 15 kg of rice at the rate of Rs. 29 per kg and 25 kg of rice at the rate of Rs. 20 per kg. He sold the mixture of both types of rice at the rate of Rs. 27 per kg. His profit in this transaction is -
(A) Rs. 125
(B) Rs. 150
(C) Rs. 140
(D) Rs. 145
Solution:
According to the question, Cost price of the mixture = 15 × 29 + 25 × 20 = Rs. 935 Selling price of the mixture = 27 × 40 = Rs. 1080 Profit = Selling price - Cost price Profit = 1080 - 935 = Rs. 145
92.
An alloy is made by mixing metal A costing Rs. 2000 per kg and metal B costing Rs. 400 per kg in the ratio A : B = 3 : 1. What is the cost (in Rs.) of 8 kg of this alloy?
(A) 1600
(B) 9800
(C) 6400
(D) 12800
Solution:
Metal A = 2000 per kg Metal B = 400 per kg ∴ Cost of 8 kg of alloy = By mixing 6 kg metal A and 2 kg metal B Cost = 6 × 2000 + 2 × 400 = Rs. 12,800
93.
3 L water is taken out from vessel full of water and substituted by pure milk. This process is repeated two more times. Finally, the ratio of milk and water in the solution becomes 1728 : 27. Find the volume of the original solution.
(A) 3 L
(B) 5 L
(C) 4 L
(D) 9 L
Solution:
We use formula for it where n = number of time process of out going repeated. y = Out going milk in process. x = Volume of original solution. F = Final milk left in mixture. $$F = x{\left( {1 - \frac{y}{x}} \right)^n}$$ Final quantity of water, $$F = x{\left( {1 - \frac{3}{x}} \right)^3}$$ $$\frac{F}{x} = {\left( {\frac{{x - 3}}{x}} \right)^3}$$ $$\frac{{27}}{{1728}} = {\left( {\frac{{x - 3}}{x}} \right)^3}$$ $${\left( {\frac{3}{{12}}} \right)^3} = {\left( {\frac{{x - 3}}{x}} \right)^3}$$ $$\frac{3}{{12}} = \frac{{x - 3}}{x}$$ $$x = 4 \,\text{L}$$
94.
The ratio of the quantities of sugar, in which sugar costing Rs. 20 per kg and Rs. 15 per kg, should be mixed so that here will be neither loss nor gain on selling the mixed sugar at the rate of Rs. 16 per kg, is -
(A) 2 : 1
(B) 1 : 2
(C) 4 : 1
(D) 1 : 4
Solution:
According to the question, When there is no profit no loss, Here, Cost price = Selling price ∴ Cost price of mixed sugar = Rs. 16/kg Apply alligation $$ \Rightarrow {\text{Ratio }} \to 1:4$$