Ex.8.3 Q1 Compairing Quantities - NCERT Maths Class 7

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Question

Tell what the profit or loss in the following transactions is. Also find profit per cent or loss per cent in each case.

a) Gardening shears bought for \(\rm Rs\, 250\) and sold for \(\rm Rs \,325.\)

b) A refrigerator bought for \(\rm Rs \,12,000\) and sold at \(\rm Rs\, 13,500.\)

c) A cupboard bought for \(\rm Rs \,2,500\) and sold at \(\rm Rs \,3,000.\) 

d) A skirt bought for \(\rm Rs \,250\) and sold at \(\rm Rs \,150.\)

 Video Solution
Comparing Quantities
Ex 8.3 | Question 1

Text Solution

What is Known?

Cost price and selling price of different items.

What is Unknown?

Profit and Loss percent in each case.

Reasoning:

Cost price is the price on which the product is bought. Selling price is the price at which the product is sold. If selling price is greater than the cost price, then there is profit and if cost price is greater than selling price then there is loss. This can be represented as

Profit \(=\) Selling price \(–\) Cost price

And Loss \(=\) Cost price \(–\) Selling price

Also, to find percentage profit/loss, we will divide the profit or loss with cost and then multiply it by \(100.\)

Profit\(/\)Loss \(\%\) 

\[=\frac{{{\text{Profit}}\;{\text{(or}}\;{\text{Loss)}}}}{{{\text{Cost}}\;{\text{Price}}}}\times{\text{100}}\]

Steps:

(a) In this question gardening shears are bought for \(\rm Rs \,250\) and sold for \(\rm Rs \,325.\) Since sale price is greater than cost price, so there is a profit

 Profit \(=\) Selling price \(-\) Cost price 

\[\begin{align} &=  325 -250\\\rm &= \rm{ Rs}\, 75\end{align}\]

And, Profit \(\%\) 

\[\begin{align}&= \frac{\text{Profit}}{\text{Cost Price}}\times 100\\ &= \frac{75}{250} \times 100\\ &= \frac{750}{25}\\ &= 30\% \end{align}\]

(b) In this question refrigerator bought for \(\rm Rs \,12,000\) and sold at \(\rm Rs \,13,500.\) Since sale price is greater than cost price so there is a profit.

 Profit \(=\) Selling price \(-\) Cost price 

\[\begin{align}&= 13500\, - 12000\,\\&= \rm{Rs} 1500\end{align}\]

And, Profit\(\%\) 

\[\begin{align} &= \frac{\text{Profit}} {\text{Cost Price}} \times 100\\&= \frac{1500}{12000} \times 100\\ &= \frac{150000}{12000}\\ &= 12.5\% \end{align}\]

(c) In this question sale price of cupboard is \(\rm Rs \,2,500\) and cost price is \(\rm Rs \,3,000.\) Since sale price is greater than cost price so there is profit

Profit  \(=\) Selling price \(-\) Cost price 

\[\begin{align}&= 3000 - 2500 \\&= \rm{Rs} 500\end{align}\]

 And,Profit\(\%\) 

\[\begin{align}\rm &= \frac{{{\rm{Profit}}\;}}{{{\rm{Cost}}\;{\rm{Price}}}} \times {\rm{100}}\\&= \frac{{500}}{{2500}} \times 100\\&= 20\% \end{align}\]

(d) Cost price of skirt is \(\rm Rs \,250\) and sale price is \(\rm Rs \,150.\) Since, cost price is greater than sale price so there is Loss

Loss \(=\) Cost price \(-\) Sale price 

\[\begin{align}&=  250 - 150\\&=  \text{Rs}100\end{align}\]

 And Loss\( \%\) 

\[\begin{align}&= \,\frac{{\;{\rm{Loss}}}}{{{\rm{Cost}}\;{\rm{Price}}}} \times {\rm{100}}\\&= \frac{{100}}{{250}} \times 100\\&= 40\% \end{align}\]