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Hi.... I   have a small doubt in math....A merchant has 100kg sugar, part of which he sells at 7% profit and rest at 17% profit. He gains 10% on the whole amount of sugar. The amount sold at 7% profit is  ???

 

 

CPhill  Aug 24, 2015

Best Answer 

 #1
avatar+78577 
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Let's assume that the cost per kg = c

 

Then, the total profit made was (the whole cost) x ( 1.10)  ......and the whole cost = 100c ....so....the profit was just (100c)(1.10)  = 110c

 

Now....let the amount that the 7% profit was made on = x.......and the cost of this was x*c......so.....the total profit made on the 7% part was just (cost)* (1.07) = (xc)(1.07)

 

And let the amount that the 17% profit was made on = (100 - x)....and the cost of this was (100 - x)c.... ....so....the total profit made on the 17% part was just  (cost)*(1.17)  = [(100 - x)c] (1.17)

 

Then.......the profit made on both parts = total profit.......so

 

(xc)(1.07) + [(100 - x)c](1.17)  = 110c  ..... simplify

 

1.07xc + 117c - 1.17xc  = 110c       divide through by c

 

1.07x + 117  - 1,17x = 110   

 

-.1x  = -7      divide both sides by -.1

 

x= 70     and this is the number of kg on which the 7% profit was made

 

 

CPhill  Aug 24, 2015
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1+0 Answers

 #1
avatar+78577 
+5
Best Answer

Let's assume that the cost per kg = c

 

Then, the total profit made was (the whole cost) x ( 1.10)  ......and the whole cost = 100c ....so....the profit was just (100c)(1.10)  = 110c

 

Now....let the amount that the 7% profit was made on = x.......and the cost of this was x*c......so.....the total profit made on the 7% part was just (cost)* (1.07) = (xc)(1.07)

 

And let the amount that the 17% profit was made on = (100 - x)....and the cost of this was (100 - x)c.... ....so....the total profit made on the 17% part was just  (cost)*(1.17)  = [(100 - x)c] (1.17)

 

Then.......the profit made on both parts = total profit.......so

 

(xc)(1.07) + [(100 - x)c](1.17)  = 110c  ..... simplify

 

1.07xc + 117c - 1.17xc  = 110c       divide through by c

 

1.07x + 117  - 1,17x = 110   

 

-.1x  = -7      divide both sides by -.1

 

x= 70     and this is the number of kg on which the 7% profit was made

 

 

CPhill  Aug 24, 2015

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