Question

. David sells two calculators for ₹1500 each. He earns a profit of 25% on one and sugjers
a loss of 25% on the other. Find his total profit or loss on the whole deal. Also calculate it as a percentage.​

Answer 1

Solution :

1st Case :

• Selling Price of Calculator = Rs 1500

• Profit = 25 %

$\bigstar \: \boxed{ \sf \: Cost \: Price \: _ {1}= \dfrac{Selling \: Price \times 100}{100 + Profit} \: }$

$\longrightarrow \sf \: Cost \: Price \: _{1} = \dfrac{1500 \times 100}{100 + 25}$

$\longrightarrow \sf \: Cost \: Price \: _{1} = \cancel\dfrac{150000}{125}$

$\longrightarrow \sf \: Cost \: Price \: _{1} = Rs \: 1200$

2nd Case :

• Selling Price of Calculator = Rs 1500

• Loss = 25%

$\bigstar \: \boxed{ \sf \: Cost \: Price \: _ {2}= \dfrac{Selling \: Price \times 100}{100 - Loss} }$

$\longrightarrow \sf \: Cost \: Price \: _{2} = \dfrac{1500 \times 100}{100 - 25}$

$\longrightarrow \sf \: Cost \: Price \: _{2} = \cancel \dfrac{150000}{75}$

$\longrightarrow \sf \: Cost \: Price \: _{2} = Rs \: 2000$

Now,

→ Total Selling Price = Rs 1500 + Rs 1500

→ Total Selling Price = Rs 3000

→ Total Cost Price = Rs 1200 + Rs 2000

→ Total Cost Price = Rs 3200

Cost Price > Selling Price. Hence,David creates Loss

$\bigstar \: \boxed{ \sf \: Loss = Cost \: Price - Selling \: Price }$

$\longrightarrow \sf \: Loss = Rs \: (3200 - 3000)$

$\longrightarrow \sf \: Loss = Rs \:200$

Now, Let's Find Loss %

$\bigstar \: \boxed{ \sf \: Loss \: \% = \dfrac{Loss}{Cost \: Price } \times 100 }$

$\longrightarrow \sf \: Loss \%= \dfrac{200}{3200} \times 100$

$\longrightarrow \sf \: Loss \%= \dfrac{25}{4}$

$\longrightarrow \sf \: Loss \%= 6.25\%$

$\therefore$ Loss% of David in the whole Deal is 6.25%

Answer 2

✬ Loss % = 6.25 % ✬

Step-by-step explanation:

Given:

• Selling price of two calculators = Rs 1500 each.
• On first calculator he earns a profit of 25% and on second he suffers a loss of 25%.

To Find:

• What is his total loss or profit percentage on whole transaction?

Solution: First we need to find the Cost Price of both the calculators.

→ To find Cost Price when Selling Price and Profit % are given we use the formula:

★ C.P = 100/(100 + Profit %) x S.P ★

• Putting all the values on above formula•

$\small\implies{\sf }$ C.P = 100/(100 + 25) x 1500

$\small\implies{\sf }$ C.P = 100/125 x 1500

$\small\implies{\sf }$ C.P = 150000/125

$\small\implies{\sf }$ C.P = Rs 1200

• Hence, Cost price of first calculator is Rs 1200.

→ To find Cost Price when Selling Price and Loss % are given we use the formula :

★ C.P = 100/(100 – Loss %) x S.P ★

• Putting values on formula •

$\small\implies{\sf }$ C.P = 100/(100 – 25) x 1500

$\small\implies{\sf }$ C.P = 100/75 x 1500

$\small\implies{\sf }$ C.P = 150000/75

$\small\implies{\sf }$ C.P = Rs 2000

• Hence, Cost Price of second calculator is Rs 2000

∴ Total Cost Price of both calculators = (1200 + 2000) = Rs 3200.

and Total Selling Price of both calculators = (1500 + 1500) = Rs 3000.

• Comparing S.P and C.P •

→ 3000 < 3200

Here, Cost Price is greater than Selling price so there is Loss

★ Loss = Cost Price – Selling Price ★

$\small\implies{\sf }$ Loss = (3200 – 3000)

$\small\implies{\sf }$ Loss = Rs 200

∴ Loss % =( Loss / Cost Price) x 100

$\small\implies{\sf }$ Loss % = ( 200/3200) x 100

$\small\implies{\sf }$ Loss % = 1/16 x 100

$\small\implies{\sf }$ 100 / 16

$\small\implies{\sf }$ 6.25%

Hence, David suffers a loss of 6.25% on whole deal.