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Question

# Tick (✓) the correct answer: If an article is sold at a gain of 5% instead of being sold at a loss of 5%, a man gets Rs 5 more. What is the cost price of the article? (a) Rs 50 (b) Rs 40 (c) Rs 60 (d) Rs 80

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Solution

## (a)​ Rs. 50 $\mathrm{Let}\mathrm{the}\mathrm{CP}\mathrm{be}\mathrm{Rs}x.\mathrm{Then},\mathrm{we}\mathrm{have}:\phantom{\rule{0ex}{0ex}}\left(105%\mathrm{of}\mathrm{x}\right)-\left(95%\mathrm{of}\mathrm{x}\right)=5\phantom{\rule{0ex}{0ex}}⇒\left(\frac{105}{100}×\mathrm{x}\right)-\left(\frac{95}{100}×\mathrm{x}\right)=5\phantom{\rule{0ex}{0ex}}⇒\left(\frac{105\mathrm{x}}{100}-\frac{95\mathrm{x}}{100}\right)=5\phantom{\rule{0ex}{0ex}}⇒\frac{\left(105\mathrm{x}-95\mathrm{x}\right)}{100}=5\phantom{\rule{0ex}{0ex}}⇒\frac{10\mathrm{x}}{100}=5\phantom{\rule{0ex}{0ex}}⇒\frac{\mathrm{x}}{10}=5\phantom{\rule{0ex}{0ex}}⇒\mathrm{x}=50\phantom{\rule{0ex}{0ex}}\therefore \mathrm{CP}=\mathrm{Rs}50$

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