Question

A merchant buys a kind of tea at Rs 80 per kg and mixes it with another kind of tea at Rs 140 per kg and makes a profit of 25% on selling the mixture at Rs 125 per kg. Find the ratio in which two varieties were mixed​

Answer 1

Answer:

2:1

Step-by-step explanation:

answer is in the attachment

Answer 2

Let the two type of tea be Tea 1 and Tea 2.

Cost of Tea 1 = Rs 80 per KG

Cost of Tea 2 = Rs 140 per kg

Define x and y:

Amount of Tea 1 in the mixture = x

Amount of Tea 2 in the mixture = y

Since both tea made up 1 kg of the mixture

⇒ x + y = 1 kg

⇒ x = 1 - y

Cost of the 1 kg of the mixture:

Tea 1 = 80x

Tea 2 = 140y

Total Cost = 80x + 140y

Find the profit:

Profit = 25 % of (80x + 140y)

Profit = 0.25(80x + 140y)

Profit = 20x + 35y

Find the Selling Price

Selling Price = Cost Price + Profit

Selling Price = 80x + 140y + 20x + 35y

Selling Price = 100x + 175y

Given that the Selling Price = Rs 125

⇒ 100x + 175 = 125

⇒ 4x + 7y = 5

Solve x and y:

x = 1 - y       ------------- [ 1 ]

4x + 7y = 5 ------------- [2]

Sub [ 1 ] into [ 2 ]:

4(1 - y) + 7y = 5

4 - 4y + 7y = 5

4 + 3y = 5

3y = 1

y = 1/3

Sub y = 1/3 into [ 1 ]:

x = 1 - 1/3

y = 2/3

Ratio of x to y:

x : y = 2/3 : 1/3

x : y = 2 : 1

Answer: The ratio of the two tea is 2 : 1