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# 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=$$3\frac{1}{13}$$%.