A man purchased a table and a chair for Rs $2000$ . He sold the table at a profit of $20 %$ and the chair at a profit of $30 %$ . His total profit was $23 %$ . Find the cost price of the table.

1400

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600

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1100

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1200

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Solution

The correct option is A Rs $1400$
Let cost price of a table $= x$ Rs and cost price of chair $= y$ Rs.

Total cost $= 2000$ Rs (Given)

$∴ x + y = 2000 . . . (1)$

Table is sold at a profit of $20 %$ .

$∴ S e l l i n g P r i c e o f t a b l e = C P + \frac{C P \times P r o f i t P e r c e n t a g e}{100} = x + \frac{x \times 20}{100} = \frac{6 x}{5}$

Chair is sold at a profit of $30 %$

$∴ S e l l i n g P r i c e o f c h a i r = C P + \frac{C P \times P r o f i t P e r c e n t a g e}{100} = y + \frac{y \times 30}{100} = \frac{13 y}{10}$

$∴ T o t a l s e l l i n g p r i c e = \frac{6 x}{5} + \frac{13 y}{10}$

Given that, total profit $= 23 %$

$∴ S e l l i n g P r i c e = C P + \frac{C P \times P r o f i t}{100} = 2000 + \frac{2000 \times 23}{100} = 2460 R s$

$\Rightarrow \frac{6 x}{5} + \frac{13 y}{10} = 2460$

$\Rightarrow 12 x + 13 y = 24600 . . . (2)$

From equation (1), we get $y = 2000 - x$

Putting the value of y in equation (2),

We get $12 x + 13 (2000 - x) = 24600$

$\Rightarrow 26000 - x = 24600$

$∴ x = 1400$

So, the cost price of the table is $x = 1400$ Rs.

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A man purchased a table and a chair for Rs 2000. He sold the table at a profit of 20% and the chair at a profit of 30%. His total profit was 23%. Find the cost price of the table.

A man purchased a table and a chair for Rs $2000$ . He sold the table at a profit of $20 %$ and the chair at a profit of $30 %$ . His total profit was $23 %$ . Find the cost price of the table.