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A man bought two tables for Rs. $5400$ . He sold one at a loss of $5 %$ and the other at a gain of $7 %$ . In the whole transaction, he neither gained nor lost. Find the costs of the tables respectively.

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Rs.

3790

and Rs.

2720

Rs.

3150

and Rs.

2250

Rs.

2670

and Rs.

1850

None of these

answer is B.

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Detailed Solution

Given the cost price of two tables = Rs.5400 and one is sold at a loss of 5% and the other at the gain of 7%.
Let the C.P. of one table

=

Rs.

x

Then, C.P. of the other table

=

Rs.

(5400 - x)

S.P. of the first table at a loss of

5 %

,
S.P. =

\frac{100 - Loss %}{100} \times C . P

\Rightarrow

S.P.

=

Rs.

\frac{95}{100} \times x

S.P. of the other table at a gain of

7 %

,
S.P. =

\frac{100 + Gain %}{100} \times C . P

\Rightarrow

=

Rs.

\frac{107}{100} \times (5400 - x)

Since there is no gain, no loss,
Total S.P.

=

Total C.P

\Rightarrow \frac{95 x}{100} + \frac{107 \times (5400 - x)}{100} = 5400

\Rightarrow \frac{95 x}{100} - \frac{107 x}{100} + \frac{107 \times 5400}{100} = 5400

\Rightarrow \frac{- 12 x}{100} = \frac{5400 \times 100 - 5400 \times 107}{100}

\Rightarrow \frac{- 12 x}{100} = \frac{540000 - 577800}{100}

\Rightarrow - 12 x = - 37800

\Rightarrow x = \frac{37800}{12}

\Rightarrow x =

Rs.

3150

The cost of the first table is Rs.3150 and the second table will be,

Cost =

5400-3150

\Rightarrow Cost =

Rs.2250
Thus, the cost of the two tables are Rs.

3150

and Rs.

2250

.
Therefore, the correct option is 2.

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A man bought two tables for Rs. 5400. He sold one at a loss of 5% and the other at a gain of 7%. In the whole transaction, he neither gained nor lost. Find the costs of the tables respectively.

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A man bought two tables for Rs. $5400$ . He sold one at a loss of $5 %$ and the other at a gain of $7 %$ . In the whole transaction, he neither gained nor lost. Find the costs of the tables respectively.