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)%
Answers
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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