Answer
Verified
423.3k+ views
Hint: We will have to find the selling price and cost price of a hen. Loss is calculated by, Loss=CP-SP and profit is calculated by Profit=SP-CP because when there is loss, cost price is greater than selling price and vice versa for profit. And Loss per cent is calculated by Loss percent=$ \dfrac{CP-SP}{CP}\times 100$ .
Complete step-by-step answer:
First let us assume that the cost price of a hen is CP and selling price is SP.
Loss of one item is calculated by, Loss=CP-SP
Selling price of 144 hens=144SP.
Cost price of 144 hens=144CP.
Selling price of 6 hens=6SP.
Cost price of 6 hens=6CP.
Loss by selling 144 hens=144CP-144SP=144(CP-SP).
From the question we have,
Loss by selling 144 hens= selling price of 6 hens
144(CP-SP)=6SP
Adding 144SP both sides we have,
144CP=6SP+144SP
144CP=150SP
Therefore, $SP=\dfrac{144}{150}CP$ …….(i)
Now we have,
Loss per cent= $\dfrac{Loss}{CP}\times 100$
Since, Loss=CP-SP, we have
Loss per cent= $\dfrac{CP-SP}{CP}\times 100$
Substituting the value of SP from equation (i) we have,
Loss per cent= $\dfrac{CP-\dfrac{144}{150}CP}{CP}\times 100$
Cancelling CP from both numerator and denominator we have,
Loss per cent= $\dfrac{1-\dfrac{144}{150}}{1}\times 100$
$=\left( 1-\dfrac{144}{150} \right)\times 100$
Taking 150 as LCM we have,
$=\left( \dfrac{150-144}{150} \right)\times 100$
$=\dfrac{6}{150}\times 100$
On simplifying we get,
Loss per cent= 4
Hence, the answer is 4%.
Note: We must always remember that Loss per cent of any number of items is equal but Loss varies with the number of items. Therefore, from the starting we were clear that SP and CP were selling price and cost price of one hen otherwise our calculations may contain an error as we proceeded. And when calculating loss per cent the denominator must be CP because whenever we calculate percentage the denominator is always the original value of the item and here the CP was our original value.
Complete step-by-step answer:
First let us assume that the cost price of a hen is CP and selling price is SP.
Loss of one item is calculated by, Loss=CP-SP
Selling price of 144 hens=144SP.
Cost price of 144 hens=144CP.
Selling price of 6 hens=6SP.
Cost price of 6 hens=6CP.
Loss by selling 144 hens=144CP-144SP=144(CP-SP).
From the question we have,
Loss by selling 144 hens= selling price of 6 hens
144(CP-SP)=6SP
Adding 144SP both sides we have,
144CP=6SP+144SP
144CP=150SP
Therefore, $SP=\dfrac{144}{150}CP$ …….(i)
Now we have,
Loss per cent= $\dfrac{Loss}{CP}\times 100$
Since, Loss=CP-SP, we have
Loss per cent= $\dfrac{CP-SP}{CP}\times 100$
Substituting the value of SP from equation (i) we have,
Loss per cent= $\dfrac{CP-\dfrac{144}{150}CP}{CP}\times 100$
Cancelling CP from both numerator and denominator we have,
Loss per cent= $\dfrac{1-\dfrac{144}{150}}{1}\times 100$
$=\left( 1-\dfrac{144}{150} \right)\times 100$
Taking 150 as LCM we have,
$=\left( \dfrac{150-144}{150} \right)\times 100$
$=\dfrac{6}{150}\times 100$
On simplifying we get,
Loss per cent= 4
Hence, the answer is 4%.
Note: We must always remember that Loss per cent of any number of items is equal but Loss varies with the number of items. Therefore, from the starting we were clear that SP and CP were selling price and cost price of one hen otherwise our calculations may contain an error as we proceeded. And when calculating loss per cent the denominator must be CP because whenever we calculate percentage the denominator is always the original value of the item and here the CP was our original value.
Recently Updated Pages
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Two charges are placed at a certain distance apart class 12 physics CBSE
Difference Between Plant Cell and Animal Cell
What organs are located on the left side of your body class 11 biology CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
The planet nearest to earth is A Mercury B Venus C class 6 social science CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
What is BLO What is the full form of BLO class 8 social science CBSE