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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

#1**+5 **

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

#1**+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