A retailer buys an article at a discount of 15% on the printed price from a wholesaler. He marks up the price by 10% on the printed price but due to competition in the market, he allows a discount of 5% on the marked price to a buyer. If the rate of GST is 12% and the buyer pays Rs. 468.16 for the article inclusive of tax (under GST), find (i) the printed price of the article (ii) the profit percentage of the retailer

(i) Let us assume the printed price of the article be Rs. x

The retailer marks up the price by 10% on the printed price

So, the marked price by the retailer

$=\text{ }Rs.\text{ }x\text{ }+\text{ }10%\text{ }of\text{ }Rs.\text{ }x$

$=\text{ }Rs.\text{ }x\text{ }+\text{ }Rs.\text{ }0.1x$

or,

$=\text{ }Rs.\text{ }1.1x$

Due to competition the retailer allows discount of 5% on the marked price, then

The selling price of the article

$~=\text{ }Rs.\text{ }1.1x\text{ }\text{ }discount$

Discount

$=\text{ }5%\text{ }of\text{ }Rs.\text{ }1.1x$

or,

$=\text{ }Rs.~\left( 5/100 \right)\text{ }x\text{ }1.1x$

$=\text{ }Rs.\text{ }0.055x$

The rate of GST

$=\text{ }12%$

The tax (under GST) for the purchase

= 12% of the selling price set by the retailer

$=\text{ }12%\text{ }of\text{ }Rs.~\left( 1.1x\text{ }\text{ }0.055x \right)$

$=\text{ }Rs.~\left( 12/100 \right)\text{ }x\text{ }\left( 1.045x \right)$

Thus, the price of the article inclusive of GST

$=\text{ }Rs.\text{ }1.045x\text{ }+\text{ }Rs.~\left( 12/100 \right)\text{ }x\text{ }\left( 1.045x \right)$

Given, buyer pays Rs. 468.16 for the article inclusive of tax (under GST)

So,

$1.045x\text{ }+\text{ }\left( 12/100 \right)\text{ }x\text{ }\left( 1.045x \right)\text{ }=\text{ }468.16$

or,

$1.045x\text{ }+\text{ }0.1254x\text{ }=\text{ }468.16$

$1.1704x\text{ }=\text{ }468.16$

or,

$x\text{ }=\text{ }468.16/1.1704$

or,

$x\text{ }=\text{ }Rs.\text{ }400$

Therefore, the printed price of the article is Rs. 400

(ii) The retailer buys at 15% discount of the printed price,

and

sells at 5% discount for the marked price of 10% on the printed price

So,

Bought at

$=\text{ }400\text{ }\text{ }15%\text{ }of\text{ }Rs.\text{ }400$

$=\text{ }Rs.\text{ }400\text{ }\text{ }Rs.\text{ }60\text{ }=\text{ }Rs.\text{ }340$

Sold at

$\begin{array}{*{35}{l}} =\text{ }\left( Rs.\text{ }400\text{ }+\text{ }10%\text{ }of\text{ }Rs.\text{ }400 \right)\text{ }\text{ }5% \\ of\text{ }\left( Rs.\text{ }400\text{ }+\text{ }10%\text{ }of\text{ }Rs.\text{ }400 \right) \\ \end{array}$

$=\text{ }Rs.\text{ }\left( 400\text{ }+\text{ }40 \right)\text{ }\text{ }\left[ \left( 5/100 \right)\text{ }x\text{ }Rs.\text{ }400\text{ }+\text{ }40 \right)]$

$=\text{ }Rs.\text{ }440\text{ }\text{ }Rs.~\left( 0.05\text{ }x\text{ }440 \right)$

or,

$=\text{ }Rs.\text{ }440\text{ }\text{ }Rs.\text{ }22$

$=\text{ }Rs.\text{ }418$

So, profit = Selling price – cost price

$=\text{ }Rs.\text{ }418\text{ }\text{ }Rs.\text{ }340\text{ }=\text{ }Rs.\text{ }78$

Hence, the profit percentage

$=\text{ }\left( 78/340 \right)\text{ }x\text{ }100\text{ }=\text{ }22.94%$

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