Question

(e)
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.​

Answer 1

$\textrm{ ⚝GIVEN:-}$

$\tt f1st \: radio - \\ \tt s.p = rs.700 \\ \tt gain = 12\%$

$\tt 2nd \: radio - \\ \tt s.p = rs.700 \\ \tt gain = 20\%$

$⍣ \tt FIND:-$

Total gain or loss in whole transaction.

$\tt ❂SOLUTION:-$

$\tt selling \: price = \frac{100+p}{(100)} \times c.p. \\ \tt = \frac{100+12}{100} \times 700 \\ \tt = \frac{ 112}{ 1\cancel{00}}\times7\cancel{00}= rs.784$

$\tt selling\: price = \frac({100-L}{100 } ) \times c.p. \\ \tt = \frac{100-20}{100} \times 700 = \frac{80}{100} \times 700 \\ \tt = \frac{80}{1\cancel{00}} \times 1\cancel{00}= rs.560$

$\tt \therefore total \: selling\: price \: is = rs.784+ 560 \\ \tt = rs.1,344$

$\tt total \: cost \: price \: is = rs.700 \times 2 \\ \tt = rs.1400$

$\tt Thus, \: cost \: price \: is \: greater \: than \: \\ \tt selling \: price$

$\tt hence, \: there \: is \: a \: loss \: of:-$

$C.P.-S.P.=1,400-1,344=rs.56$

$\tt L\% = \frac{ L}{cost\:price}\times100$

$\tt = \frac{56}{14\cancel{00}}\times1\cancel{00}$

$\tt=4\%$

${\boxed \therefore Total loss \% is 4\%}$

Answer 2

» 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 :

$\sf{\underline{\boxed{SP = \left(1 \pm \dfrac{Profit/loss}{100}\right)\:of\:CP}}}$

Profit Percentage :

$\sf{\underline{\boxed{P\% = \left(\dfrac{P}{CP} \times 100\right)\%}}}$

Loss Percentage :

$\sf{\underline{\boxed{L\% = \left(\dfrac{L}{CP} \times 100\right)\%}}}$

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,

$\sf{\Rightarrow 700 + 700}$

$\sf{\Rightarrow 1400}$

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 :

$\sf{\underline{\boxed{SP = \left(1 + \dfrac{Profit}{100}\right)\:of\:CP}}}$

$\sf{\Rightarrow SP = \left(1 + \dfrac{12}{100}\right) \times 700}$

$\sf{\Rightarrow SP = \left(\dfrac{100 +12}{100}\right) \times 700}$

$\sf{\Rightarrow SP = \left(\dfrac{112}{100}\right) \times 700}$

$\sf{\Rightarrow SP = \left(\dfrac{112}{\cancel{100}}\right) \times 7\cancel{00}}$

$\sf{\Rightarrow SP = 112 \times 7}$

$\sf{\Rightarrow SP = 784}$

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 :

$\sf{\underline{\boxed{SP = \left(1 - \dfrac{Loss}{100}\right)\:of\:CP}}}$

$\sf{\Rightarrow SP = \left(1 - \dfrac{20}{100}\right) \times 700}$

$\sf{\Rightarrow SP = \left(\dfrac{100 - 20}{100}\right) \times 700}$

$\sf{\Rightarrow SP = \left(\dfrac{80}{100}\right) \times 700}$

$\sf{\Rightarrow SP = \left(\dfrac{80}{\cancel{100}}\right) \times 7\cancel{00}}$

$\sf{\Rightarrow SP = 80 \times 7}$

$\sf{\Rightarrow SP = 560}$

Hence ,the selling price for first Radio is ₹ 560.

Total Selling Price = Selling Price on the First Radio + Selling Price on the second Radio.

$\sf{\Rightarrow 784 + 560}$

$\sf{\Rightarrow 1344}$

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 :

$\sf{\underline{\boxed{Loss = CP - SP}}}$

$\sf{\Rightarrow Loss = 1400 - 1344}$

$\sf{\Rightarrow Loss = 56}$

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 :

$\sf{\underline{\boxed{L\% = \left(\dfrac{L}{CP} \times 100\right)\%}}}$

$\sf{\Rightarrow L\% = \left(\dfrac{56}{1400} \times 100\right)\%}$

$\sf{\Rightarrow L\% = \left(\dfrac{56}{14\cancel{00}} \times \cancel{100}\right)\%}$

$\sf{\Rightarrow L\% = \left(\dfrac{56}{14}\right)\%}$

$\sf{\Rightarrow L\% = \left(\dfrac{\cancel{56}}{\cancel{14}}\right)\%}$

$\sf{\Rightarrow L\% = 4 \%}$

Hence ,the loss Percentage on the whole transaction is 4 %.

» Additional information :

• Percentage Less =

$\left(\dfrac{(Greater - smaller)}{Greater} \times 100\right)\%$

• CP =

$\dfrac{100 \times SP}{100 \pm Profit/Loss\%}$