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

Question:

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%. At what rate per kg should he sell the remainder to gain 8% on his total investment?

Solution:

CP of $1 \mathrm{~kg}$ of rice $=$ Rs 25

C.P of $200 \mathrm{~kg}$ rice $=\mathrm{Rs}(200 \times 25)=\mathrm{Rs} 5000$

CP of $80 \mathrm{~kg}$ of rice=Rs $(25 \times 80)=$ Rs 2000

CP of $40 \mathrm{~kg}$ of rice $=$ Rs $(25 \times 40)=$ Rs 1000

$\mathrm{SP}$ of $80 \mathrm{~kg}$ of rice $=\frac{100+\text { gain } \%}{100} \times \mathrm{CP}$

$=$ Rs $\frac{110}{100} \times 2000$

$=$ Rs 2200

SP of $40 \mathrm{~kg}$ rice $=\frac{100-\text { loss } \%}{100} \times \mathrm{CP}$

$=$ Rs $\frac{96}{100} \times 1000$

$=$ Rs 960

$\mathrm{SP}$ of $200 \mathrm{~kg}$ rice $=\frac{100+\text { gain } \%}{100} \times \mathrm{CP}$

$=\mathrm{Rs} \frac{108}{100} \times 5000$

$=\mathrm{Rs} 5400$

Remaining quantity of rice = (200 − 80 + 40) kg = 80 kg

​SP of the remaining rice (80 kg) = Rs (5400 − 2200 − 960)

= Rs 2240

$\therefore$ Rate per $\mathrm{kg}=\mathrm{Rs} \frac{2240}{80}=\mathrm{Rs} 28$

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