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A shopkeeper mixed two varieties of sugar costing Rs. 36 per kg and Rs. 25 per kg. He sold the mixture at a price of Rs. 40 per kg and earned a profit of 25%. In what ratio did he mixed the two varieties?

A shopkeeper mixed two varieties of sugar costing Rs. 36 per kg and Rs. 25 per kg. He sold the mixture at a price of Rs. 40 per kg and earned a profit of 25%. In what ratio did he mixed the two varieties? Correct Answer 7 ∶ 4

Short Trick:

Cost price of the mixture = 40 × 100/125 = Rs. 32

Required ratio = (32 - 25) : (36 - 32) = 7 : 4

Detailed Solution:

Let the shopkeeper mix ‘x’ kg of sugar costing Rs. 36 per kg with ‘y’ kg of sugar costing Rs. 25 per kg

Total weight of mixture = (x + y) kg

Total cost price of (x + y) kg mixture = 36x + 25y

Now, selling price of 1 kg mixture = Rs. 40

Profit = 25%

⇒ Cost price of 1 kg mixture = 40/1.25 = Rs. 32

⇒ Cost price of (x + y) kg mixture = 32x + 32y

Hence, we get,

⇒ 36x + 25y = 32x + 32y

⇒ 36x - 32x = 32y - 25y

⇒ 4x = 7y

⇒ x/y = 7/4

∴ He mixed the two varieties in the ratio 7 ∶ 4

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