Verified answer

Answer:

[tex]\qquad\boxed{ \sf{ \: \sf \: Selling\:price \: of \: remaining \: rice \:is \: Rs \: 28 \: per \: kg \: }}\\ \\ [/tex]

Step-by-step explanation:

Given that, grocer purchased 200 kg of rice at Rs. 25 per kg.

So,

[tex]\sf \: Cost\:price \: of \: 200 \: kg \: of \: rice \: = \: 25 \times 200 = Rs \: 5000 \\ \\ [/tex]

Case :- 1

[tex]\sf \: Cost\:price \: of \: 80 \: kg \: of \: rice \: = \: 25 \times 80 = Rs \: 2000 \\ \\ [/tex]

[tex]\sf \: Gain\% \: = \: 10\% \\ \\ [/tex]

So,

[tex]\sf \: Selling\:price \: of \: 80 \: kg \: of \: rice \: \\ \\ [/tex]

[tex]\sf \: = \: \dfrac{(100 + Gain\%) \times Cost\:price}{100} \\ \\ [/tex]

[tex]\sf \: = \: \dfrac{(100 + 10) \times 2000}{100} \\ \\ [/tex]

[tex]\sf \: = \: 110 \times 20 \\ \\ [/tex]

[tex]\sf \: = \: Rs \: 2200 \\ \\ [/tex]

Case :- 2

[tex]\sf \: Cost\:price \: of \: 80 \: kg \: of \: rice \: = \: 25 \times 40 = Rs \: 1000 \\ \\ [/tex]

[tex]\sf \:Loss\% \: = \: 4\% \\ \\ [/tex]

So,

[tex]\sf \: Selling\:price \: of \: 40 \: kg \: of \: rice \: \\ \\ [/tex]

[tex]\sf \: = \: \dfrac{(100 - Loss\%) \times Cost\:price}{100} \\ \\ [/tex]

[tex]\sf \: = \: \dfrac{(100 - 4) \times 1000}{100} \\ \\ [/tex]

[tex]\sf \: = \: 96 \times 10 \\ \\ [/tex]

[tex]\sf \: = \: Rs \: 960 \\ \\ [/tex]

Case :- 3

Let assume that the remaining 80 kg of rice be sold for Rs x per kg so as gain 8 % on his investment.

So, we have

[tex]\sf \: Cost\:price \: of \: 200 \: kg \: of \: rice \: = \: Rs \: 5000 \\ \\ [/tex]

[tex]\sf \: Gain\% \: = \: 8\% \\ \\ [/tex]

[tex]\sf \: Selling\:price \: of \: 200 \: kg \: of \: rice \: = \: 2200 + 960 + x = Rs \: 3160 + 80x\\ \\ [/tex]

Now, We know

[tex]\sf \: Selling\:price \: = \: \dfrac{(100 + Gain\%) \times Cost\:price}{100} \\ \\ [/tex]

[tex]\sf \: 3160 + 80x \: = \: \dfrac{(100 + 8) \times 5000}{100} \\ \\ [/tex]

[tex]\sf \: 3160 + 80x \: = \: 108 \times 50 \\ \\ [/tex]

[tex]\sf \: 3160 + 80x \: = \: 5400 \\ \\ [/tex]

[tex]\sf \: 80x \: = \: 5400 - 3160 \\ \\ [/tex]

[tex]\sf \: 80x \: = \: 2240 \\ \\ [/tex]

[tex]\sf\implies \sf \: x = 28 \\ \\ [/tex]

Hence,

[tex]\sf\implies \sf \: Selling\:price \: of \: remaining \: rice \:is \: Rs \: 28 \: per \: kg\\ \\ [/tex]

Answer: Hence the selling price of the remaining rice [tex]=\frac{2240}{80}=Rs.28/kg[/tex]

As per the data given in the above question,

In the above question, it is given that,

A grocer purchased 200 kg of rice at Rs. 25 per kg.

He sold 80 kg of it at a gain of 10% and 40 kg at a loss of 4%.

The cost of purchase is [tex]=200 \times 25=Rs.5000[/tex]

The selling price of 80 kg rice - at 10% gain ⇒ 110% of the price

[tex]=\frac{110}{100}\times Rs.25[/tex]

The selling price of 40 kg rice  at a loss of 4% ⇒  96% of the price

[tex]=\frac{96}{100}\times Rs.25[/tex]

Money earned by selling 40 kg [tex]=40\times \frac{96}{100}\times 25 =Rs.960[/tex]

Remaining quantity[tex]=200-40-80=80kg[/tex]

Total gain required = 8%  ⇒

Overall money to be earned thru sales[tex]=\frac{108}{100}\times cost=\frac{108}{100}5000=Rs.5400[/tex]

Money to be earned through the sale of the remaining 80 kg

[tex]=Rs.5400-Rs.2200-Rs.960=Rs.2240[/tex]

The selling price of the remaining rice [tex]=\frac{2240}{80}=Rs.28/kg[/tex]

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