Arvind bought a dining table for Ã¢â€šÂ¹ 23,850. This includes 6 % sales tax. The shopkeeper has made a profit of $12\frac{1}{2}$% on his investment. If the shopkeeper has spent Ã¢â€šÂ¹ 1000 on polishing and transportation, what is the actual cost of the table?

Given :

Arvind bought a dining table for Rs. 23,850.

Sales tax $=$ 6%.

The shopkeeper made a profit of $12\frac{1}{2}$% on his investment.

Cost of polishing and transportation = Rs. 1000.

To do :

We have to find the cost of the table.

Solution :

Let the cost of the table be Rs P.

This implies,

Total cost for shopkeeper $= Rs. (P + 1000)$

Profit $=12\frac{1}{2} = \frac{(12\times 2+1)}{2} = \frac{25}{2}$%.

Sale price without tax $= Rs. \frac{(100+25)}{100} \times (P + 1000) = Rs. \frac{125}{100} \times (P + 1000) = Rs. \frac{5}{4}(P+1000)$

Sales tax $= Rs. \frac{6}{100} \times \frac{5}{4}(P + 1000) = Rs. \frac{30}{400} (P+1000) = Rs. \frac{3}{40} (P+1000)$

Therefore,

Total price paid by Arvind $= Sale price without tax + Sales tax$

$= Rs. \frac{5}{4}(P+1000) + Rs. \frac{3}{40}(P+1000)$

$= Rs. (P + 1000) (\frac{5}{4} + \frac{3}{40})$

$= Rs. (P + 1000) (\frac{50}{40} + \frac{3}{40})$

$= Rs. (P + 1000) (\frac{53}{40})$

$Rs. 23,850 = Rs. (P + 1000) (\frac{53}{40})$

$23850 \times 40 = 53P + 53000$

$954000 = 53P + 53000$

$53P = 954000 - 53000$

$53P = 901000$

$P = \frac{901000}{53}$

$P = 17000$.

Therefore, the actual cost of the table is Rs. 17,000.

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