A shopkeeper sold two radio at Rs 700 each. On one he gains 12% and on the other he less 20%. Find the loss or gain percent in the whole transaction.
Answers
Answer:
» To Find :
The Profit or Loss Percentage in the whole transaction.
» Given :
Cost Price of the Two Radios = ₹ 700.
Profit percentage on the first Radio = 12 %
Loss Percentage on the second Radio = 20 %
» We Know :
Selling Price :
\sf{\underline{\boxed{SP = \left(1 \pm \dfrac{Profit/loss}{100}\right)\:of\:CP}}}
SP=(1±
100
Profit/loss
)Of CP
Profit Percentage :
\sf{\underline{\boxed{P\% = \left(\dfrac{P}{CP} \times 100\right)\%}}}
P%=(
CP
P
×100)%
Loss Percentage :
\sf{\underline{\boxed{L\% = \left(\dfrac{L}{CP} \times 100\right)\%}}}
L%=(
CP
L
×100)%
Where ,
P = Profit
L = Loss
SP = Selling Price
CP = Cost Price
P% = Profit Percentage
L% = Loss Percentage
Profit /Loss :
Profit = SP - CP
Loss = CP - SP
» Concept :
According to the question , we have to find the Profit/loss % on the whole transaction.
So ,first we have to find the total Cost Price and then the total selling price of the transaction.
And then , by using the profit /loss Percentage Formula, we can find the Total Gain/Loss Percentage.
» Solution :
Total Cost Price :
Cost of the two radios = 700
So, the If we add the cost price of the two radios ,then we will get the total cost Price i.e,
\sf{\Right Arrow 700 + 700}⇒700+700
\sf{\Right Arrow 1400}⇒1400
Hence, the Total Cost Price of the whole transaction is ₹ 1400.
Total Selling Price :
Selling price of the First Radio :
CP = ₹ 700
P % = 12 %
Using the formula ,and substituting the value in it ,we get :
\sf{\underline{\boxed{SP = \left(1 + \dfrac{Profit}{100}\right)\:of\:CP}}}
SP=(1+
100
Profit
)Of CP
\sf{\Right Arrow SP = \left(1 + \dfrac{12}{100}\right) \times 700}⇒SP=(1+
100
12
)×700
\sf{\Right Arrow SP = \left(\dfrac{100 +12}{100}\right) \times 700}⇒SP=(
100
100+12
)×700
\sf{\Right Arrow SP = \left(\dfrac{112}{100}\right) \times 700}⇒SP=(
100
112
)×700
\sf{\Right Arrow SP = \left(\dfrac{112}{\cancel{100}}\right) \times 7\cancel{00}}⇒SP=(
100
112
)×7
00
\sf{\Right Arrow SP = 112 \times 7}⇒SP=112×7
\sf{\Right Arrow SP = 784}⇒SP=784
Hence ,the selling price for first Radio is ₹ 784.
Selling price of the second Radio :
CP = ₹ 700
L % = 20 %
Using the formula ,and substituting the value in it ,we get :
\sf{\underline{\boxed{SP = \left(1 - \dfrac{Loss}{100}\right)\:of\:CP}}}
SP=(1−
100
Loss
)Of CP
\sf{\Rightarrow SP = \left(1 - \dfrac{20}{100}\right) \times 700}⇒SP=(1−
100
20
)×700
\sf{\Rightarrow SP = \left(\dfrac{100 - 20}{100}\right) \times 700}⇒SP=(
100
100−20
)×700
\sf{\Rightarrow SP = \left(\dfrac{80}{100}\right) \times 700}⇒SP=(
100
80
)×700
\sf{\Rightarrow SP = \left(\dfrac{80}{\cancel{100}}\right) \times 7\cancel{00}}⇒SP=(
100
80
)×7
00
\sf{\Rightarrow SP = 80 \times 7}⇒SP=80×7
\sf{\Rightarrow SP = 560}⇒SP=560
Hence ,the selling price for first Radio is ₹ 560.
Total Selling Price = Selling Price on the First Radio + Selling Price on the second Radio.
\sf{\Rightarrow 784 + 560}⇒784+560
\sf{\Rightarrow 1344}⇒1344
Hence, the Total selling Price of the whole transaction is ₹ 1344.
ATS ,
Since ,the Selling Price is less than the Cost Price , it is loss.
To Find the Loss For the Whole transaction :
Total Selling Price = ₹ 1344
Total Cost Price = ₹ 1400
Using the formula ,and Substituting the values in it ,we get :
\sf{\underline{\boxed{Loss = CP - SP}}}
Loss=CP−SP
\sf{\Rightarrow Loss = 1400 - 1344}⇒Loss=1400−1344
\sf{\Rightarrow Loss = 56}⇒Loss=56
Hence , the loss on the whole transaction is ₹ 56.
Loss Percentage :
Loss = ₹ 56
CP = ₹ 1400
Using the formula and substituting the values in it , we get :
\sf{\underline{\boxed{L\% = \left(\dfrac{L}{CP} \times 100\right)\%}}}
L%=(
CP
L
×100)%
\sf{\Rightarrow L\% = \left(\dfrac{56}{1400} \times 100\right)\%}⇒L%=(
1400
56
×100)%
\sf{\Rightarrow L\% = \left(\dfrac{56}{14\cancel{00}} \times \cancel{100}\right)\%}⇒L%=(
14
00
56
×
100
)%
\sf{\Rightarrow L\% = \left(\dfrac{56}{14}\right)\%}⇒L%=(
14
56
)%
\sf{\Rightarrow L\% = \left(\dfrac{\cancel{56}}{\cancel{14}}\right)\%}⇒L%=(
14
56
)%
\sf{\Rightarrow L\% = 4 \%}⇒L%=4%
Hence ,the loss Percentage on the whole transaction is 4 %.
» Additional information :
Percentage Less =
\left(\dfrac{(Greater - smaller)}{Greater} \times 100\right)\%(
Greater
(Greater−smaller)
×100)%
CP =
\dfrac{100 \times SP}{100 \pm Profit/Loss\%}
100±Profit/Loss%
100×SP