Question

Amisha sells a cycle to Amir at a profit of 10%. Amir sells the same cycle to Abhishekh at a profit of 20%. If Abhishekh has sold it for Rs 3300 there by earning a profit of 25%,find the cost price of it for Amisha
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Answer 1

Given :

Profit percent of Amisha : 10%

Profit percent of Amir : 20%

Selling price of Abhishek : ₹3300

Profit percent of Abhishek : 25%

To find :

The cost price of Amisha.

Solution :

First, we should find the cost price of Abhishek.

We also know that the cost price of Abhishek is same as selling price of Amir.

Cost price of Abhishek :

$\sf \dashrightarrow \dfrac{100}{(100 + Profit\%)} \times SP$

$\sf \dashrightarrow \dfrac{100}{(100 + 25)} \times 3300$

$\sf \dashrightarrow \dfrac{100}{125} \times 3300$

$\sf \dashrightarrow \dfrac{4}{5} \times 3300$

$\sf \dashrightarrow \dfrac{4 \times 3300}{5} = \dfrac{13200}{5}$

$\sf \dashrightarrow \cancel \dfrac{13200}{5} = 2640$

Now, we should find the cost price of Amir. We also know that the cost price of Amir is same as the selling price of Amisha.

Cost price of Amir :

$\sf \dashrightarrow \dfrac{100}{(100 + Profit\%)} \times SP$

$\sf \dashrightarrow \dfrac{100}{(100 + 20)} \times 2640$

$\sf \dashrightarrow \dfrac{100}{120} \times 2640$

$\sf \dashrightarrow \dfrac{5}{6} \times 2640$

$\sf \dashrightarrow \dfrac{5 \times 2640}{6} = \dfrac{13200}{6}$

$\sf \dashrightarrow \cancel \dfrac{13200}{6} = 2200$

Now, we can find the cost price of Amisha.

Cost price of Amisha :

$\sf \dashrightarrow \dfrac{100}{(100 + Profit\%)} \times SP$

$\sf \dashrightarrow \dfrac{100}{(100 + 10)} \times 2200$

$\sf \dashrightarrow \dfrac{100}{110} \times 2200$

$\sf \dashrightarrow \dfrac{10}{11} \times 2200$

$\sf \dashrightarrow \dfrac{10 \times 2200}{11} = \dfrac{22000}{11}$

$\sf \dashrightarrow \cancel \dfrac{22000}{11} = 2000$

Hence, the cost price of Amisha is ₹2000.