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A cashew nut cultivator cultivates a bumper production of cashew of about 1000kg. The market price for plain cashew nuts is Rs. 200/kg and of roasted cashew nuts is Rs. 1200/kg. What percentage of the crop should be sold as plain cashew nuts to earn 180% profit by year-end, if the production cost of plain cashew nuts is Rs. 100/kg and that of roasted cashew nuts is Rs. 400/kg. Also, find his amount of profit.

A cashew nut cultivator cultivates a bumper production of cashew of about 1000kg. The market price for plain cashew nuts is Rs. 200/kg and of roasted cashew nuts is Rs. 1200/kg. What percentage of the crop should be sold as plain cashew nuts to earn 180% profit by year-end, if the production cost of plain cashew nuts is Rs. 100/kg and that of roasted cashew nuts is Rs. 400/kg. Also, find his amount of profit. Correct Answer 20%, Rs. 6,12,000

Solution :

Given data :

Total cultivation of cashew nuts = 1000 kg

The market price of plain cashew nuts = Rs. 200/kg

The market price of roasted cashew nuts = Rs. 1200/kg

Percentage profit in the whole transaction = 180%

The production cost of plain cashew nuts = Rs. 100/kg

The production cost of roasted cashew nuts = Rs. 400/kg

Formulae :

Profit (%) = × 100

Profit = C.P. ×( P%/100)

Calculation :

Percentage profit in plain cashew nuts = × 100

⇒ (100/100) × 100

⇒ 100%

Percentage profit in roasted cashew nuts = × 100

⇒ (800/400) × 100

⇒ 200%

Now applying allegation for-profit percentages of plain cashew nuts and roasted cashew nuts to get overall profit percentage; the resultant ratio got is of quantities of both the varieties of cashew nuts.

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Total cashew is 1000 kg

⇒ 1 + 4 = 5 = 1000 kg

⇒ 5 = 1000 kg

Plain cashew,

⇒ 1 = 1000/5 = 200 kg

Rosted cashew,

⇒ 4 = 200 × 4 = 800 kg

⇒ 1/5 of total cashew nuts is to be sold as plain cashew

⇒ Percentage to be sold as plain cashew nuts = (1/5) × 100

⇒ 20%

The production cost of plain cashew nuts = 200 × 100

⇒ Rs. 20,000

The production cost of roasted cashew nuts = 800 × 400

⇒ Rs. 3,20,000

Total production cost = 20,000 + 3,20,000

⇒ Rs. 3,40,000

Total profit = 3,40,000 × (180/100)

⇒ Rs. 6,12,000

∴ The cultivator sells 20% of stocks as plain cashew nuts and earns Rs. 6,12,000 as profit in the whole transaction.

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