Arun is a cashew merchant in Telangana. He has cashews in sealed wooden boxes of 10 kg each. The price of the cashew increases by Rs. 20 per kg every year, but at the same time 10 percent of the cashews are eaten by rodents every year. If the price of 1 kg of fresh cashew is Rs. 120, what is the change of profits if he sells a sealed box after one year of storage rather than selling it fresh?

Question

Arun is a cashew merchant in Telangana. He has cashews in sealed wooden boxes of 10 kg each. The price of the cashew increases by Rs. 20 per kg every year, but at the same time 10 percent of the cashews are eaten by rodents every year. If the price of 1 kg of fresh cashew is Rs. 120, what is the change of profits if he sells a sealed box after one year of storage rather than selling it fresh?

Vedantu Content Team · Accepted Answer

Hint: At first find out the price of 10 kg fresh cashew in the present time. Then find the quantity he will be selling after one year. Find out the selling price after one year. Then find out the profit.

Complete step-by-step solution -
According to the given question, Arun is a cashew merchant. He has 10 kg cashews in a wooden box.
It is given in the question that the price of 1kg cashew is Rs. 120.
Therefore, the price of 10 kg cashew is: 120 multiplied by 10 = Rs. 1200.
Per year the price of the cashew increases by Rs. 20. That means after one year the price of 1 kg cashew will be: Rs. (120 + 20) = Rs. 140.
But 10 percent of the cashews are eaten by rodents every year.
10 percent of 10 kg will be:
$10\times \dfrac{10}{100}=\dfrac{100}{100}=1$
Therefore, 1 kg cashews are eaten by rodents in one year.
So, now Arun has (10 – 1) = 9 kg cashews.
If he sells his cashews after one year he will get Rs. 140 per kg.
Therefore, the price of 9 kg cashews will be:
$140\times 9=Rs.\text{ }1260$
So, he bought 10 kg cashews for Rs. 1200 and sold them for Rs. 1260.
Hence, the profit is, Rs. (1260 – 1200) = Rs. 60
Therefore, if he sells the cashews after one year his profit will be Rs. 60.

Note: Alternatively we can assume that, if he sells the cashews after one year his profit will be Rs. x. As rodents eat 10% of cashew, so 10% of 10kg is 1 kg, so he will just have 9 kg to sell in the next year. Then we can form an equation according to the given conditions.
Profit = Selling price of next year for – Cost price of present year
$x=9\times \left( 120+20 \right)-\left( 120\times 10 \right)$
We can find out his profit by solving the above equation.