Question

A person bought a watch for Rs. 500 and sold for Rs. 600. Another person bought another watch for Rs. 400 and sold for Rs. 500
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Answer 1

Step-by-step explanation:

Given that:

⬤A person bought a watch for Rs. 500 and sold for Rs. 600.

⬤Another person bought another watch for Rs. 400 and sold for Rs. 500

To find:

⬤The profit ℅ in both cases.

Solution:

⬤Profit in first case = ₹600 - ₹500 = ₹100

⬤Profit in second case = ₹500 - ₹400 = ₹100

Profit is the same in both cases. But the first case the has to spend ₹500 and second case only ₹400 to make the same profit.

So we calculate percentage of profit in each case to campare.

The first person spends ₹500 to earn a profit of ₹100.

$\tt \</strong><strong>g</strong><strong>r</strong><strong>e</strong><strong>e</strong><strong>n</strong><strong>{₹ \: 1 \: to \: earn \: profit \: of \: ₹ \frac{100}{500} }$

$\tt \</strong><strong>g</strong><strong>r</strong><strong>e</strong><strong>e</strong><strong>n</strong><strong>{₹ \: 100 \: to \: earn \: profit \: of \: ₹ \: \frac{100}{500} \times 100}$

$\: \: \: \: \: \: \: \tt</strong><strong>\</strong><strong>g</strong><strong>r</strong><strong>e</strong><strong>e</strong><strong>n</strong><strong>{ = ₹20}$

$\: \: \: \: \: \: \tt \</strong><strong>g</strong><strong>r</strong><strong>e</strong><strong>e</strong><strong>n</strong><strong>{ profit =20 \%}$

The second person spends ₹400 to earn a profit of 100

$\tt \</strong><strong>g</strong><strong>r</strong><strong>e</strong><strong>e</strong><strong>n</strong><strong>{₹ \: 1 \: to \: earn \: profit \: of \: ₹ \: \frac{100}{400}}$

$\tt \</strong><strong>g</strong><strong>r</strong><strong>e</strong><strong>e</strong><strong>n</strong><strong>{₹ \: 100 \: to \: earn \: profit \: of \: ₹ \: \frac{100}{400} \times 100}$

$\: \: \: \: \: \: \: \tt \</strong><strong>g</strong><strong>r</strong><strong>e</strong><strong>e</strong><strong>n</strong><strong>{= ₹ 25}$

$\: \: \: \: \: \tt \</strong><strong>g</strong><strong>r</strong><strong>e</strong><strong>e</strong><strong>n</strong><strong>{profit = 25\%}$

Thus we can say that the profit percentages are different.

formula

$\mathrm{\fbox{${\begin{array}{l}{\Pr{ofit}\hspace{0.33em}{percentage}{=}\frac{\Pr}{{Cost}\hspace{0.33em}{price}}\times{100}{\%}}\\{{Loss}\hspace{0.33em}{percentage}{=}\frac{Loss}{{Cost}\hspace{0.33em}{price}}\times{100}{\%}}\end{array}}$}}$

Note: Profit or loss percentage is always calculated on every ₹ 100 of the cost price.