by selling bananas at the rate of ₹72 per dozen, what would be the percent age of his gain or loss? if he sold at ₹700 per hundred
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CBSE
Mathematics
Grade 9
Profit and Loss
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By selling oranges at the rate of Rs 72 per dozen, Suhel loses 10% of his investment. What would be the percentage of her gain or loss, if she sold them at Rs 600 per hundred?
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Hint: Firstly, we have to find the selling price (SP) of 1 orange using the unitary method. Then, we will assume the cost price (CP) of one orange will be x. We will find the value of x by substituting the values in the formula for percentage of loss which is given by %Loss=(CP−SP)CP×100 . Then, we will find the CP of 100 oranges by multiplying the value of x by 100. We will then check whether the SP of 100 oranges is less than or greater than the CP of 100 oranges. If the SP is less than CP, then loss has been incurred. If the SP is greater than CP, then profit has occurred. Finally, we have to find the percentage of loss or percentage of gain accordingly.
Step-by-step explanation:
Complete step by step answer:
We are given that the selling price (SP) of a dozen oranges, that is, 12 oranges is Rs 72.
⇒SP of 12 oranges=Rs.72
Therefore, by unitary method, we can find the SP of 1 orange. We have to divide 72 by 12.
⇒SP of 1 orange=Rs.7212⇒SP of 1 orange=Rs.6
We are given the percentage of loss as 10%.
⇒loss
Let the cost price (CP) of one orange be x. We know that percentage of loss is given by
%Loss=(CP−SP)CP×100...(i)
Let us substitute the values in the above formula.
⇒10=(x−6)x×100
We have to find the value of x. Let us take the denominator of the RHS to the LHS.
⇒10x=(x−6)100
We have to apply distributive property on the RHS.
⇒10x=100x−600
Let us collect like terms on one side and unlike terms on the other.
⇒600=100x−10x⇒600=90x
We have to move the coefficient of x to the RHS.
⇒60090=x⇒x=203
Therefore, the CP of 1 orange is 203 . Let us find the CP of 100 oranges by multiplying 203 by 100.
⇒CP of 100 oranges=203×100⇒CP of 100 oranges=20003
We are given that SP of 100 oranges is Rs 600. We can see that the SP of 100 oranges is less than CP of 100 oranges. Therefore, Suhel got a loss. Let us find the percentage of loss. By substituting the values in the formula (i).
⇒%Loss=(20003−600)20003×100⇒%Loss=2000−1800320003×100⇒%Loss=200320003×100⇒%Loss=2003×32000×100
Let us cancel the common factors and terms.
⇒%Loss=2003×3200010×100⇒%Loss=10%
Hence, the percentage of loss is 10%.