A manufacturer undertakes to supply $2000$ pieces of particular component at Rs. $25$ per piece. According to his estimates, even if $5 %$ fail to pass the quality tests, then he will make a profit of $25 %$ . However, as it turned out, $50 %$ of the components were rejected . what is the loss to the manufacturer ?

Rs.

12, 000

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Rs.

13, 000

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Rs.

14, 000

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Rs.

15, 000

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Solution

The correct option is B Rs. $13, 000$
Total number of component $= 2000$
If $15 %$ component found to be defective, then,
No. of non-defective component $= 2000 - 5 %$ of $2000 = 1900$
So, selling price of $190$ component $= 1900 \times 25 = 47500$
This content $25 %$ profit of the manufacturer.
Let total manufacturing price of the component $= x$
SP $= 47500$
$x + 25 %$ of $x = 47500$
$\frac{(100 x + 25 x)}{100} = 47500$
$125 x = 4750000$
$x =$ Rs. $38000$
If $50$ component i.e. $1000$ components are defective. then
Total collection $= 25 \times 1000 = 25000$
Loss $= 38000 - 25000 =$ Rs. $13000$

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