Question

A shopkeeper bought 20 liters of sunflower oil for Rs. 64 per liter and decided to sell it for Rs. 80 per liter. By mixing X liters of other oil to it, he can increase his profit by 12%, while by mixing 4x liters of other oil, he can increase his profit by (100/3)%. In what ratio should he mix the two types of oils to earn a profit of (300/7)%?
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Answer 1

The two types of oils should be mixed in the ratio 1 : 4

Step-by-step explanation:

Cost of 1 litre of sunflower oil = 64 Rs.

Cost of 20 litres of sunflower oil = 64 × 20 = 1280 Rs.

If it is sold for Rs. 80 per then profit = (80 - 64) × 20 = 320 Rs.

12% of 320 = $320\times\frac{12}{100}=38.4$ Rs.

100/3% of 320 = $320\times\frac{100}{3\times 100}=106.67$ Rs.

300/7% of 320 = $320\times\frac{300}{7\times 100}=137.14$ Rs.

If the shopkeeper mixes X litres of oil

Then

Quantity of sunflower = 20 - X

Cost of this quantity of sunflower

$=(20-X)\times 64$ Rs.

$=64(20-X)$ Rs.

Now if he sells it then the profit is increased by 38.4 Rs.

Thus,

$80\times 20-64(20-X)=320+38.4$

$\implies 1600-1280+64X=320+38.4$

$\implies 64X=38.4$

$\implies X=\frac{38.4}{64}=0.6$ Litres

Similarly, if he mixes 4x quantity of another oil then

$80\times 20-64(20-4x)=320+106.67$

$\implies 1600-1280+256X=320+106.67$

$\implies 256X=106.67$

$\implies X=\frac{106.67}{256}=0.416$ Litres

Let the quantities mixed be $n_1$ and $n_2$

Then

$80\times 20-64(20-0.6n_1-0.416n_2)=320+137.14$

$\implies 38.4n_1+26.6675n_2=137.14$

If we take $n_1=1$

$38.4+26.6675n_2=137.14$

$\implies 26.6675n_2=98.74$

$\implies n_2=\frac{98.74}{26.6675}$

$\implies n_2=3.7\approx 4$

Therefore, the shopkeeper should mixed the two oils in ratio 1:4

Hope this answer is helpful.

Know More:

Q: Amit bought 20 liters of oil at the rate of 75 rs/liter and the same amount of oil at the rate of 115 rs/liter and mixed them. If he sold the mixture at 100 rs/liter. Find his total profit?

Click Here: https://brainly.in/question/11191873

Answer 2

Given :  A shopkeeper bought 20 liters of sunflower oil for Rs. 64 per liter and decided to sell it for Rs. 80 per liter. By mixing X liters of other oil to it, he can increase his profit by 12%, while by mixing 4x liters of other oil, he can increase his profit by (100/3)%

To find : In what ratio should he mix the two types of oils to earn a profit of (300/7)%

Solution:

20 liters of sunflower oil  Rs. 64 per liter  

Cost price = 20 * 64 = Rs 1280

Selling price = 20 * 80 = Rs 1600

Profit  = 1600 - 1280  = Rs 320

Profit % = (320/1280) * 100 = 25 %

x litre oil of rs y per litre added  

cost price = 1280 + yx

Selling price = 1600 + 80x

Profit = 320 + x(80 - y)

Profit % =  100 (320 + x(80 - y))/ ( 1280 + yx)

profit increased by 12 %  

=> Profit % = 25 + 12 = 37 %

=>  37 =   100 (320 + x(80 - y))/ ( 1280 + yx)

=> 37( 1280 + yx)  = 100 * 320 + 100x(80 - y)   Eq1

4x litre oil of rs y per litre added  

cost price = 1280 + 4yx

Selling price = 1600 + 4x*80

Profit = 320 + 4x(80 - y)

Profit % =  100 (320 + 4x(80 - y))/ ( 1280 + 4yx)

profit increased by 100/3 %  

=> Profit % = 25 + 100/3 = 175/3 %

=> 175/3 =   100 (320 + 4x(80 - y))/ ( 1280 + 4yx)

=> 175( 1280 + 4yx)  =300 * 320 + 1200x(80 - y)   Eq2

12 * Eq1 - Eq2

=> 1280(269) -256yx   =900 * 320

=> 256yx = 56320

=> xy = 220

x = 455/80 = 91/16

x = 91/16

y = 3520/91  ( price of other oil)

Let say Ratio mixed two types of oil is k:1

Cost price =  64k + 3520/91

Selling price= 80k + 80

Profit =  16k  +3760/91

Profit %   = (300/7)  = 100 *  (16k  +3760/91)/ (64k +  3520/91)  

= 192k + 10560/91  = 112k + 26320/91

=> 80k = 15760/91

=> k = 197/91

197:91 is the ratio in which two oil mixed

if profit increased by 300/7 %

then

Cost price =  64k + 3520/91

Selling price= 80k + 80

Profit =  16k  +3760/91

Profit %   = (25 + 300/7)  = 100 *  (16k  +3760/91)/ (64k +  3520/91)  

=> k = 50/91

50:91 is the ratio in which two oil mixed

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