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]
[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]
[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]
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Answers & Comments
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]