Question

Prince sold 2 tables at 40,000. One at 20% loss and other at 25% profit, find the CP of both and overall profit/loss %.

Answer 1

Answer:

Cost price of 1st table is ₹ 50000.

Cost price of 2nd table is ₹ 32000.

There was overall 2.44 % loss in the transaction.

Step-by-step-explanation:

We have given that,

Selling price of 2 tables ( SP ) = ₹ 40000

Loss on 1st table = 20 %

Profit on 2nd table = 25 %

We have to find the cost price, CP of both tables and overall profit or loss percentage.

We know that,

Loss % = ( Loss / CP ) * 100

⇒ 20 = ( Loss / CP ) * 100

⇒ Loss / CP = 20 / 100

⇒ Loss / CP = 1 / 5

We know that,

Loss = Cost price - Selling price

⇒ ( CP - SP ) / CP = 1 / 5

⇒ ( CP - 40000 ) / CP = 1 / 5

⇒ 5 ( CP - 40000 ) = CP

⇒ 5CP - 200000 = CP

⇒ 5CP - CP = 200000

⇒ 4CP = 200000

⇒ CP = 200000 / 4

⇒ CP = 50000

∴ Cost price of 1st table = ₹ 50000

Now, we know that,

Profit % = ( Profit / CP ) * 100

⇒ 25 = ( Profit / CP ) * 100

⇒ Profit / CP = 25 / 100

⇒ Profit / CP = 1 / 4

We know that,

Profit = Selling price - Cost price

⇒ ( SP - CP ) / CP = 1 / 4

⇒ ( 40000 - CP ) / CP = 1 / 4

⇒ 4 ( 40000 - CP ) = CP

⇒ 160000 - 4CP = CP

⇒ CP + 4CP = 160000

⇒ 5CP = 160000

⇒ CP = 160000 / 5

⇒ CP = 32000

∴ Cost price of 2nd table = ₹ 32000

Now,

Total selling price of 2 tables = 2 * 40000

⇒ Total selling price = ₹ 80000

Now,

Total cost price = Cost price of 1st table + Cost price of 2nd table

⇒ Total cost price = ₹ 50000 + ₹ 32000

⇒ Total cost price = ₹ 82000

Here,

Cost price ( 82000 ) > Selling price ( 80000 )

∴ There was loss in the overall transaction.

Now,

Loss % = ( Loss / CP ) * 100

⇒ Loss % = [ ( CP - SP ) / CP ] * 100

⇒ Loss % = [ ( 82000 - 80000 ) / 82000 ] * 100

⇒ Loss % = ( 2000 / 82000 ) * 100

⇒ Loss % = ( 2 / 82 ) * 100

⇒ Loss % = ( 1 / 41 ) * 100

⇒ Loss % = 100 / 41

⇒ Loss % = 2.439

⇒ Loss % ≈ 2.44

∴ There was overall 2.44 % loss in the transaction.

Answer 2

Given:-

• Cost of each tables is 40,000.
• Loss% on 1st table is 20%
• Profit on 2nd table is 25%.

To find:-

• Total profit/loss %.

Solution:-

Firstly calculate the cost of table 1.

$\large\underline{\bf{ \longmapsto \frac{20}{100} \times 40000 }}$

$\large\underline{\bf{ \longmapsto 8000}}$

$\large\underline{\bf{ \longmapsto40000 - 8000}}$

$\large\underline{\bf{ \implies32000}}$

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Calculating the SP of 2nd table.

$\large\underline{\bf{ \longmapsto \frac{25}{100} \times 40000}}$

$\large\underline{\bf{ \longmapsto25 \times 400}}$

$\large\underline{\bf{ \longmapsto10000}}$

$\large\underline{\bf{ \longmapsto40000 + 10000}}$

$\large\underline{\bf{ \implies50000}}$

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Calculating profit/loss%.

$\large{\bf{ \longmapsto \frac{50000 + 32000 }{40000 + 40000} \times 100}}$

$\large\longmapsto{\bf{ \frac{82000 \times 100}{80000} }}$

$\large\underline{\bf{ \longmapsto102.5}}$

Subtracting to 100 .

• 102.5-100
• 2.5%

Hence the profit percentage was of 2.5%.