Question

DOUBLE POINTS QUESTION
A dealer sells two mobile phones at Rs.5000 each. On the first mobile phone, he earns a profit of 10% and a loss of 10% on the other mobile phone. Which of the following is true about the net gain or loss on selling the two phones?

Answer 1

Correct Question

A dealer sells two mobile phones at Rs.5000 each. On the first mobile phone, he earns a profit of 10% and a loss of 10% on the other mobile phone. Find the total gain or loss percentage of both mobiles.

Answer

Given :

Selling price of each mobile : ₹5000

Profit percent of first mobile : 10%

Loss percent of second mobile : 10%

To find :

The total gain or loss percentage on whole transaction.

Solution :

First, we should find the cost prices of both mobiles.

Cost price of first mobile :

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

$\sf \dashrightarrow \dfrac{100}{(100 + 10)} \times 5000$

$\sf \dashrightarrow \dfrac{100}{110} \times 5000$

$\sf \dashrightarrow \dfrac{10}{11} \tines 5000$

$\sf \dashrightarrow \dfrac{10 \times 5000}{11} = \dfrac{50000}{11}$

$\sf \dashrightarrow \cancel \dfrac{50000}{11} = 4545.45$

Cost price of second mobile :

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

$\sf \dashrightarrow \dfrac{100}{(100 - 10)} \tines 5000$

$\sf \dashrightarrow \dfrac{100}{90} \times 5000$

$\sf \dashrightarrow \dfrac{10}{9} \times 5000$

$\sf \dashrightarrow \dfrac{10 \times 5000}{9} = \dfrac{50000}{9}$

$\sf \dashrightarrow \cancel \dfrac{50000}{9} = 5555.55$

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

Total cost price :

$\sf \dashrightarrow 4545.45 + 5555.55$

$\dashrightarrow$₹$\sf 10101$

Total selling price :

$\sf \dashrightarrow 5000 + 5000$

$\dashrightarrow$₹$\sf 10000$

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

Loss rupees :

$\sf \dashrightarrow 10101 - 10000$

$\dashrightarrow$₹$\sf 101$

Now, we can find teh loss percentage.

Loss percentage :

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

$\sf \dashrightarrow \dfrac{101}{10101} \times 100$

$\sf \dashrightarrow \dfrac{101 \times 100}{10101} = \dfrac{10100}{10101}$

$\sf \dashrightarrow \cancel \dfrac{10100}{10101} = 0.99$

Hence, the the loss percentage on the whole transaction is 0.99%.