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Question

A fruit seller has 24 kg of apples. He sells a part of these at a gain of 20% and the balance at a loss of 5%. If on the whole, he earns a profit of 10%, the quantity of apples sold at loss is ....?

A
4.6 kg
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B
6 kg
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C
9.6 kg
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D
11.4 kg
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Solution

The correct option is A 9.6 kg
Given: Total weight of apples =24 kg

Let the cost price of each kg of apple be Rs.y

The total cost price of 24 kgs of apples is Rs.24y

Let us consider the weight of apples sold at 5% loss as x kg

Then the cost price of x kg of apples will be Rs.xy and selling price be SP1

We know Loss %=CPSPCP×100

5=xySP1xy×100

xy20=xySP1

SP1=xyxy20

SP1=1920xy ...(1)

Given: Rest of the apples apples i.e., (24x) kgs are sold at a gain of 20%

Then, the CP of (24x) kg of apples will be (24x)y and its SP be SP2

We know Profit %=SPCPCP×100

20=SP2(24x)y(24x)y×100

(24x)y5=SP2(24x)y

SP2=(24x)y5+(24x)y

SP2=65(24x)y ...(2)


Hence, Total SP =SP1+SP2

=Rs. [1920xy+65(24x)y]

=Rs.[1920xy+1445y65xy]

=Rs.[1445y14xy]

Given, the seller earns a profit of 10% on the whole
10=[1445y14xy]24y24y×100

12y5=[1445y14xy]24y

14xy=1445y125y24y

14xy=1325y24y

14xy=1321205y

14xy=125y

x=485

x=9.6 kg

The amount of apples sold at a loss of 5% is 9.6 kg

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