Question

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. 4 : 5
• B. 1 : 2
• C. 3 : 4
• D. 2 : 3

Answer 1

Answer:

A. 4 : 5

Solution:

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 $\frac{15x}{100}$

For 100g brand B costs Rs. 18

For y g brand B will cost $\frac{18x}{100}$

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

⇒ $x + y = \frac{15x}{100} + \frac{18y}{100}$      ----(i)

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

⇒ 100% = $(\frac{20}{120})\times{100} = Rs. \frac{100}{6}$

Cost price for 100g is $Rs. \frac{100}{6}$,

Now find cost price for (x + y) grams

⇒$x + y = (\frac{100}{6})\times{\frac{(x + y)}{100}}$

⇒ $x + y = \frac{(x + y)}{6}$

Put value of equation(i)

⇒ $\frac{15x}{100} + \frac{18y}{100} = \frac{(x + y)}{6}$

⇒ 90x + 108y = 100x + 100y

⇒ 8y  = 10x

⇒$\frac{ x}{y}= \frac{8}{10} = \frac{4}{5}$

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

Alternate Method:

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