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A shopkeeper has 100 kg of good grade rice and x kg of bad grade rice. He brought good and bad grade rice for Rs. 20 and Rs. 10 respectively. He can sell the good and bad grade rice at Rs. 30 and Rs. 13.5 respectively. Out of x kg, if he mixes y kg of bad grade rice with good grade, he will get a profit of 69 2/7% from total sale. If he mixes y/2 kg of bad grade rice with good grade, he will get a profit of 57.5%. What is the profit he would have got if he sold honestly? (in rupees)

A shopkeeper has 100 kg of good grade rice and x kg of bad grade rice. He brought good and bad grade rice for Rs. 20 and Rs. 10 respectively. He can sell the good and bad grade rice at Rs. 30 and Rs. 13.5 respectively. Out of x kg, if he mixes y kg of bad grade rice with good grade, he will get a profit of 69 2/7% from total sale. If he mixes y/2 kg of bad grade rice with good grade, he will get a profit of 57.5%. What is the profit he would have got if he sold honestly? (in rupees) Correct Answer 1280

Total cost to shopkeeper = 100 × 20 + x × 10 = 2000 + 10x

Profit/kg on selling good grade rice = 30 – 20

⇒ Rs. 10

Profit/kg on selling bad grade rice honestly = 13.5 – 10

⇒ Rs. 3.5

Profit/kg on selling bad grade rice as good grade rice = 30 – 10

⇒ Rs. 20

Total profit by selling y kg mixing = 100 × 10 + 3.5 × (x – y) + 20 × y

⇒ 1000 + 3.5x + 16.5y

Profit % = 55

According to question,

(1000 + 3.5x + 16.5y) / (2000 + 10x) × 100 = 69 2/7

⇒ (1000 + 3.5x + 16.5y) / (2000 + 10x) = 485/7

⇒ (1000 + 3.5x + 16.5y) / (2000 + 10x) = 97/140

⇒ 140000 + 490x + 2310y = 194000 + 970x

⇒ 2310y = 54000 + 480x ÷ 30

⇒ 77y = 1800 + 16x      ---- 1

Total profit by selling y/2 kg mixing = 100 × 10 + 3.5 × (x – y/2) + 20 × y/2

Profit% = 57.5

⇒ (1000 + 3.5x + 8.25y) / (2000 + 10x) = 57.5/100

⇒ (1000 + 3.5x + 8.25y) / (2000 + 10x) = 23/40

⇒ 40000 + 140x + 330y = 46000 + 230x

⇒ 330y = 6000 + 90x ÷ 30

⇒ 11y = 200 + 3x      ---- 2

Now, Equation 1 – 7 × Equation 2

0 = 400 – 5x

⇒ x = 80

∴ Original profit honestly = 100 × 10 + x × 3.5

⇒ 1280

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