Question

a man sold two cycles for 3000 each gaining 20% on one and lodging 20% on the other find his gain or loss on the whole transactionexplain ​

Answer 1

The seller incurs a loss of 4% overall on both cycles.

• Two cycles are sold at Rs. 3000 each.

• On one the seller gains 20% and on one 20% .
• We have to find the overall gain or loss percentage.
• Let us assume the cost price of first be $x_1$ and other be $x_2$.
• We have to calculate the profit and loss on the cycles.
• Profit percentage = $\frac{4752-x_1}{x_1}$ × 100 = 20

$3000-x_1 = 0.20x_1$

3000 = $1.2x_1$

$x_1$ = 3000/1.2 = 2500 Rs.

• Therefore cost price of the cycle where the seller gains 20% is Rs. 2500.
• Loss percentage = $\frac{x_2-3000}{x_2}$ × 100 = 20

$x_2-3000$  = $0.2x_2$

$0.8x_2$  = 3000

$x_2$ = Rs. 3750

• Therefore cost price of the cycle where the seller loses 20% is Rs. 3750.
• Now we have to calculate the net profit or loss percentage, we find the total cost price of two cycles,
• Total cost price = 2500 + 3750 = 6250 Rs.

• Now ,Profit on cycle 1 - Loss on cycle 2 = Net gain

(3000-2500) - (3750-3000) = Net gain

Net gain = 500 - 750 = -250

• Therefore the seller gains a loss of 250 Rs. total on both cycles.

• Now net loss percentage = $\frac{Net \ loss}{total \ cost \ price}$ × 100  

Net loss percentage = $\frac{250}{6250}$ × 100 = 4%