7.A milkman sold two of his buffaloes for ₹ 20,000 each. On one he made a gain of 5% and on the other a loss of 10%. Find his overall gain or loss. [Hint: Find CP of each]

Given, SP of a buffalo=₹ 20,000.
And Gain=5%

∴ \(SP=CP\; (1+\frac{Gain}{100}\))

\(\Rightarrow 20000=CP\; (1+\frac{5}{100}\))

\(\Rightarrow 20000=CP\;\times (\frac{105}{100}\))

\(\Rightarrow CP=\frac{20000\times100}{105}\)

\(\Rightarrow CP=₹\;\frac{4,00,000}{21}\)

SP of another buffalo=₹ 20,000

And given loss=10%

∴ \(SP=CP\; (1-\frac{loss}{21}\))

\(\Rightarrow 20000=CP\; (1-\frac{10}{100}\))

\(\Rightarrow 20000=CP\;\times (\frac{90}{100}\))

\(\Rightarrow CP=\frac{20000\times100}{90}\)

\(\Rightarrow CP=₹\;\frac{2,00,000}{9}\)

So we have total CP=\(₹\;\frac{4,00,000}{21}\) +\(₹\;\frac{2,00,000}{9}\)

\(=₹\;\frac{12,00,000+14,00,000}{63}\)

\(=₹\;\frac{26,00,000}{63}\)

And we have total SP=₹ 20,000 + ₹ 20,000 =₹ 40,000

Here we see that,SP < CP i.e., it was a loss.

∴ Loss=CP-SP

\(=₹\;\frac{26,00,000}{63}-₹ 40,000\)

\(=₹\;\frac{26,00,000-25,20,000}{63}\)

\(=₹\;\frac{80,000}{63}=₹\;1,269.84\)

Therefore, %Loss=\(\frac{Loss}{CP}\)

=\(\frac{\frac{80,000}{63}}{\frac{26,00,000}{63}}\times 100\)

=\(\frac{80,000}{63}\times\frac{26,00,000}{63}\times100\)

=\(\frac{80}{26}\)%=\(\frac{40}{13}\)%=\(3\frac{1}{13}\)%

Hence, the complete percent loss=\(3\frac{1}{13}\)%.