A shopkeeper earns a profit of 15% if he mixes 85 kg of A-type cement with 35 kg of B-type cement and sells the mixture at Rs. 46 per kg. He can increase his profit to 25% if he mixes 65 kg of A-type cement with 35 kg of B-type cement and sells the mixture at Rs. 46.5 per kg. At what price should he sell a mixture of 30 kg A-type cement and 50 kg B-type cement to earn a profit of 75%?

A shopkeeper earns a profit of 15% if he mixes 85 kg of A-type cement with 35 kg of B-type cement and sells the mixture at Rs. 46 per kg. He can increase his profit to 25% if he mixes 65 kg of A-type cement with 35 kg of B-type cement and sells the mixture at Rs. 46.5 per kg. At what price should he sell a mixture of 30 kg A-type cement and 50 kg B-type cement to earn a profit of 75%? Correct Answer Rs. 42

Formula Used:

Cost price = (Selling price × 100)/(100 + profit%)

Calculation:

Let the cost price of A-type cement be Rs. ‘x’ per kg and that of B-type cement be Rs. ‘y’ per kg

Considering mixture of 85 kg A-type cement with 35 kg B-type cement,

Total quantity of mixture = 85 + 35 = 120 kg

⇒ Cost price per kg = (85x + 35y)/120

⇒ Cost price per kg = 4600/115 = Rs. 40

⇒ 85x + 35y = 4800  ----(1)

Similarly,

Considering mixture of 65 kg A-type cement with 35 kg B-type cement,

Total quantity of mixture = 65 + 35 = 100 kg

⇒ Cost price per kg = (65x + 35y)/100 = 4650/125 = Rs. 37.2

⇒ 65x + 35y = 3720  ----(2)

Subtracting (2) from (1), we get,

⇒ 85x + 35y - 65x - 35y = 4800 - 3720

⇒ 20x = 1080

⇒ x = 1080/20 = Rs. 54

Substituting in (1),

⇒ y = (4800 - 4590)/35 = Rs. 6

Now,

If he makes a mixture of 30 kg A-type cement with 50 kg B-type cement,

Total quantity of mixture = 30 + 50 = 80 kg

⇒ Cost price per kg = /80 = 1920/80 = Rs. 24