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A vendor bought two varieties of tea, brand A and brand B, costing Rs. 15 per 100 g and Rs. 18 per 100 g, respectively, and mixed them in a certain ratio. Then, he sold the mixture at Rs. 20 per 100 g, making a profit of 20%. What was the ratio of brand A to brand B tea in the mixture?

A vendor bought two varieties of tea, brand A and brand B, costing Rs. 15 per 100 g and Rs. 18 per 100 g, respectively, and mixed them in a certain ratio. Then, he sold the mixture at Rs. 20 per 100 g, making a profit of 20%. What was the ratio of brand A to brand B tea in the mixture? Correct Answer 4 : 5

Given:

Brand A costing Rs. 15 per 100 g

Brand B costing Rs. 18 per 100 g

Sold the mixture at Rs. 20 per 100 g, making a profit of 20%

Formula used:

Profit% or Loss% = (Profit or Loss/Cost price) × 100

Calculation:

Let x gram of brand A and y gram of brand B is mixed.

For 100g brand A costs Rs. 15

For x g brand A will cost 15x/100

For 100g brand B costs Rs. 18

For y g brand B will cost 18x/100

So, the total cost price for (x + y) grams is

⇒ x + y = 15x/100 + 18y/100      ----(i)

Sold at Rs. 20 with 120% profit, Cost price will be

⇒ 100% = (20/120) × 100 = Rs. 100/6

Cost price for 100g is Rs. 100/6,

Now find cost price for (x + y) grams

⇒ x + y = (100/6) × {(x + y)/100}

⇒ x + y = (x + y)/6

Put value of equation(i)

⇒ 15x/100 + 18y/100 = (x + y)/6

⇒ 90x + 108y = 100x + 100y

⇒ 8y  = 10x

⇒ x/y = 8/10 = 4/5

∴ The ratio of the mixture of Brand A and B is 4 : 5

∴ The ratio of the mixture of Brand A and B is 4 : 5

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