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A grocer has 60 kg of rice, a part of which he sells at 6% profit and 20 May 2022, 08:15
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15% (low)

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85% (01:38) correct 15% (02:16) wrong based on 74 sessions

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A grocer has 60 kg of rice, a part of which he sells at 6% profit and the rest at 16%. He gains 12% on the whole. Find the quantity sold at 16% profit.

(A) 15 kg
(B) 20 kg
(C) 30 kg
(D) 32 kg
(E) 36 kg
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E
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A grocer has 60 kg of rice, a part of which he sells at 6% profit and 20 May 2022, 08:51
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Assume buying price=100/kg
X kg is sold at 6% profit
Hence, selling price=106/kg
Rest (60-X) kg is sold at 16%profit
Selling price=116/kg

Now,

106x+(60-x)116=112*60
-10x=-4*60
x=4*60/10
x=24

Qty sold at 16% profit= 60-24=36 kg

Option E

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A grocer has 60 kg of rice, a part of which he sells at 6% profit and 20 May 2022, 12:01
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Number Line Method:

6%_______12%_________16%
Distance Ratio: 6:4= 3:2
Weight Ratio: 2:3
Therefore, 3/5×60=36
Ans E

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A grocer has 60 kg of rice, a part of which he sells at 6% profit and 22 May 2022, 00:36
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On the whole, the grocer received 12% profit; this is a mixture of 2 profits, one of 6% and another of 16%.

The rule of mixtures can be applied to find out the ratio in which the 2 components are mixed to obtain an overall profit of 12%.

Let N1 and N2 be the weightages of the parts that were sold at 16% and 6% respectively.
Then, as per rule of mixtures, \(\frac{N1 }{ N2}\) = \(\frac{(A – A2) }{ (A1 – A)}\)

\(\frac{N1 }{ N2}\) = \(\frac{12 - 5 }{ 16 – 12}\)

Simplifying, we have, \(\frac{N1 }{ N2}\) = \(\frac{3 }{ 2}\).

Therefore, 60kg has to be divided in the ratio of 3:2
Proportion of the part that was sold at 16% profit = \(\frac{3 }{ (3 + 2)}\) * 60 = \(\frac{3}{ 5}\) * 60 = 36 kg.

The correct answer is E.
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A grocer has 60 kg of rice, a part of which he sells at 6% profit and 23 May 2022, 09:00
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6 --- 12 --- 16
%6 : %16=(16-12):(12-6)=2/3
%6 + %16=60kg
----> %16=36kg

E
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Bunuel
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