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)%? 1. 1: 2 2. 1: 4 3. 1: 6 4. 1: 8​

Answer 1

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

None of the option matches answer. Seems mistake in data

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