Question

A man sold two articles for Rs 2200 each. While he gained 10% on the
first article, he lost 12 % on the 2nd article. Find his gain or loss percent in the whole transaction.

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Answer 1

Given :

Selling price of each article : ₹2200

Gain percent of first article : 10%

Loss percent of second article : 12%

To find :

The gain or loss percent on the whole transaction.

Solution :

First, we should find the cost price of both the articles.

Cost price of first article :

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

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

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

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

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

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

Cost price of second article :

$\sf \dashrightarrow \dfrac{100}{(100 - Loss\%)} \times SP$

$\sf \dashrightarrow \dfrac{100}{(100 - 12)} \times 2200$

$\sf \dashrightarrow \dfrac{100}{88} \times 2200$

$\sf \dashrightarrow \dfrac{100}{8} \times 200$

$\sf \dashrightarrow \dfrac{100 \times 200}{8} = \dfrac{20000}{8}$

$\sf \dashrightarrow \cancel \dfrac{20000}{8} = 2500$

Now, we should find the total cost price and total selling price.

Total cost price :

$\sf \dashrightarrow 2000 + 2500$

$\sf \dashrightarrow Rs.4500$

Total selling price :

$\sf \dashrightarrow 2200 + 2200$

$\sf \dashrightarrow Rs 4400$

As we can see that the cost price is greater than the selling price. So,

Loss rupees :

$\sf \dashrightarrow 4500 - 4400$

$\sf \dashrightarrow Rs.100$

Now, we can find the loss percentage.

Loss percentage :

$\sf \dashrightarrow \dfrac{Loss}{Cost \: price} \times 100$

$\sf \dashrightarrow \dfrac{100}{4500} \times 100$

$\sf \dashrightarrow \dfrac{1}{45} \times 100$

$\sf \dashrightarrow \dfrac{1 \times 100}{45} = \dfrac{100}{45}$

$\sf \dashrightarrow \dfrac{100}{45} = 2.22\%$

Hence, the loss percentage on the whole transaction is 2.22%.