In our locality, we can find varieties professions. Every people involved in business wants to profit from their business. But is not sure that every business has profit some may go on the loss. Generally, business is the matter of profit and loss. In business, every people's motive is earning a profit. Here, cost price (C.P.) is the invested amount in business. Then Selling Price (S.P.) must be more than cost price to make a profit.
When the selling price is greater than the cost price i.e. S.P. > C.P. then, there is profit.
\(\therefore\) Profit = S.P. - C.P.
and Profit Percentage= \(\frac{Profit\; amount}{cost\;price\;(C.P.)}\) × 100%
When the selling price is less than the cost price i.e. S.P. < C.P. then, there is a loss.
\(\therefore\) Loss = C.P. - S.P.
and Loss Percentage = \(\frac{Loss\;amount}{cost\;price\;(C.P.)}\) × 100%
Some of the conclusion:
i) When S.P. > C.P., then
ii) When S.P. < C.P., then
iii) Profit Percentage = \(\frac{Profit\;amount}{cost\;price\;(C.P.)}\) × 100% = \(\frac{S.P. - C.P.}{C.P.}\) × 100%
iv) Loss Percentage = \(\frac{Loss\;amount}{cost\;price\;(C.P.)}\) × 100% = \(\frac{C.P. - S.P.}{C.P.}\) × 100%
Calculation of SP and CP when profit or loss percentage are given:
i) When CP and Profit percent is given, then SP = \(\frac{100 + P%}{100}\) × CP
ii) When CP and Loss percent is given, then SP = \(\frac{100 - L%}{100}\) × CP
iii) When SP and Profit percent is given, then CP = \(\frac{SP × 100}{100 + P%}\)
iv) When SP and Loss percent is given, then CP = \(\frac{SP × 100}{100 - L%}\)
We can solve the profit and loss related sums using percentage as well as unitary method.
Solution:
Cost Price (CP) = Rs. 1,000
Selling Price (SP) = Rs. 1,200
Here SP > CP
∴ Profit = SP - CP
= Rs. 1,200 - Rs. 1,000
= Rs. 200
Now,
Profit percentage = (\(\frac{Profit}{C.P.}\) * 100)%
= (\(\frac{200}{1000}\) * 100)%
= 20%
∴ Profit percentage = 20%
Solution:
Cost Price (CP) = Rs. 2,000
Selling Price (SP) = Rs. 1,500
Here CP > SP
∴ Loss = CP - SP
= Rs. 2,000 - Rs. 1,500
= Rs. 500
Now,
Loss percentage = (\(\frac{Loss{C.P.}\) * 100)%
= (\(\frac{500}{2000}\) * 100)%
= 20%
∴ Loss percentage = 25%
Solution:
Cost Price (CP) = Rs. 1,000
Selling Price (SP) = Rs. 1,500
Here SP > CP
∴ Profit = SP - CP
= Rs. 1,500 - Rs. 1,000
= Rs. 500
Now,
Profit percentage = (\(\frac{Profit}{C.P.}\) * 100)%
= (\(\frac{500}{1000}\) * 100)%
= 50%
∴ Profit percentage = 50%
Solution:
Cost Price (CP) = Rs. 1,000
Selling Price (SP) = Rs. 800
Here CP > SP
∴ Loss = SP - CP
= Rs. 1,000 - Rs. 800
= Rs. 200
Now,
Loss percentage = (\(\frac{Loss}{C.P.}\) * 100)%
= (\(\frac{200}{1000}\) * 100)%
= 20%
∴ Profit percentage = 20%
Solution:
Cost Price (CP) = Rs 400
Selling Price (SP) = Rs 500
∴ SP > CP so, Ram made a profit
∴ Profit = SP - CP
= Rs 500 - Rs 400
= Rs 100
Again, Profit percentage = (\(\frac{Profit}{C.P.}\) * 100)%
= (\(\frac{100}{400}\) * 100)%
= 25%
Hence, Ram made a profit percentage of 25%.
Solution:
Cost price of radio (CP) = Rs 5000
Profit percentage (P%) = 10
Selling price of radio (SP) = ?
Now,
SP = \(\frac{100 + P%}{100}\) * CP
= \(\frac{100 + 10}{100}\) * 5000
= \(\frac{110}{100}\) *5000
= Rs 5500
Hence, The selling price of radio is Rs 5500.
Solution:
Cost price of TV (CP) = Rs 25000
Profit percentage (P%) =8
Selling price of TV (SP) = ?
Now,
SP = \(\frac{100 + P%}{100}\) * CP
= \(\frac{100 + 8}{100}\) * 25000
= \(\frac{108}{100}\) * 25000
= Rs 27000
Hence, The selling price of TV to Santoshi is Cost price to Shiya. Therefore cost price for Shiya is Rs 27000.
Solution:
Cost Price of Washing Machine (CP) = Rs 50000
Selling Price ofWashing Machine (SP) = Rs 35000
Since, CP > SP there is loss
Loss = CP - SP
= 50000 - 35000
= 15000
Again,
Loss Percentage =(\(\frac{Loss }{C.P.}\) * 100)%
=(\(\frac{15000}{50000}\) * 100)%
= 30%
Hence, She sold it to Maya at 30% loss.
Solution:
Selling price (SP) = Rs 5,000
Loss = Rs 1,000
Cost price (CP) = ?
Now,
CP = SP +Loss
= Rs 5,000 +Rs 1000
= Rs 6,000
Solution:
1 dozen copies = 12 piece of copies
20 dozen copies = 12 * 20 = 240 piece of copies
Then,
1 dozen = 12 copies = Rs 240
1 copy = \(\frac {240}{12}\) = Rs 20
240 copy = Rs 20 * 240 = Rs 4800
Total Cost price (CP) = Rs 4800
Now,
Selling price of 1 copy = Rs 30
Selling price of 240 cpoies = Rs 30 * 240 = Rs 7200
Total Selling price (SP) = Rs 7200
∴ SP > CP
Here,
Profit = SP - CP
= Rs 7200 - Rs 4800
= Rs 2400
Hence, She made profit of Rs 2400 on the transaction.
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after selling a television on its marked price a shopkeeper makes a profit of 25% but on allowing 10%discount he makes a profit Rs. 230. Find the cost price of the television?
Mar 25, 2017
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