Question

-The ratio of amount of pure milk and water in the mixture of 50 liters of milk is 7:3.
(a) Find the amount of pure milk and water in the mixture.
(b) If the cost of 1 liter mixture of milk is Rs. 100, how much liters of milk can be bought in Rs. 900?
(c) A shopkeeper bought the total of 50 liters milk in Rs. 5000. He mixed 5 liters of water and sold the milk allowing 5 % discount on the price that he purchased. How much profit or loss will the shopkeeper have finally?
(d) How much price should the shopkeeper sell the total amount of milk without mixing water to make a profit of 10%?​

Answer 1

Answer:

a)

Pure milk = 35 liters

Water = 15 liters

b)9 liters

c) Profit: Rs. 225.

d)Rs. 5500

Step-by-step explanation:

To solve this problem, we'll use the concept of ratios and proportions.

Given:

The ratio of pure milk to water in the mixture is 7:3.

Total amount of mixture is 50 liters.

(a) To find the amount of pure milk and water in the mixture:

Let's denote the amount of pure milk as 7x and the amount of water as 3x, where x is a constant multiplier.

Given that the total amount of mixture is 50 liters, we can set up the equation:

7x + 3x = 50

Combining like terms:

10x = 50

Now, solve for x:

$x = \dfrac{50}{10}$

x = 5

Now we can find the amounts of pure milk and water:

Pure milk = 7x = 7 × 5 = 35 liters

Water = 3x = 3 × 5 = 15 liters

So, there are 35 liters of pure milk and 15 liters of water in the mixture.

(b) To find how much liters of milk can be bought in Rs. 900:

Given that the cost of 1 liter of mixture is Rs. 100, we can find out how many liters can be bought for Rs. 900 by dividing the total amount by the cost per liter:

$\textsf{Number of liters } = \dfrac{900}{100} \\\\= 9 \, \textsf{liters}$

So, 9 liters of milk can be bought for Rs. 900.

(c) To find the profit or loss the shopkeeper will have finally:

The shopkeeper buys 50 liters of milk for Rs. 5000, which means the cost price per liter is:

$\textsf{Cost price per liter }= \dfrac{5000}{50} \\\\ \sf = Rs. \, 100$

He mixes 5 liters of water, so now he has 55 liters of mixture.

He sells the milk with a 5% discount on the purchased price.

Selling price per liter after discount = Cost price - discount amount

= Rs. 100 - 5% × 100

= Rs. 100 - Rs. 5

= Rs. 95

Total selling price for 55 liters = 55 × 95 = Rs. 5225

Profit or loss = Selling price - Cost price

Profit or loss = 5225 - 5000 = Rs. 225

Since the selling price is higher than the cost price, the shopkeeper makes a profit of Rs. 225.

(d) To find the selling price of the total amount of milk without mixing water to make a profit of 10%:

Cost price for 50 liters = Rs. 5000

To make a 10% profit, the selling price should be:

Selling price = Cost price + Profit % of Cost price

Selling price = 5000 + 10% of 5000

Selling price= 5000 + 0.1 × 5000

Selling price = 5000 + 500

Selling price = Rs. 5500

So, the shopkeeper should sell the total amount of milk without mixing water for Rs. 5500 to make a profit of 10%.