A man's annual income has increased by ₹ 5 la | vedclass

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Question

(C) Let the initial annual income be $x$ lakhs.The initial tax paid is $12 \%$ of $x = 0.12x$.The new income is $(x + 5)$ lakhs.The new tax paid is $1

Vedclass · Accepted Answer

$25$

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(C) Let the initial annual income be $x$ lakhs.The initial tax paid is $12 \%$ of $x = 0.12x$.The new income is $(x + 5)$ lakhs.The new tax paid is $10 \%$ of $(x + 5) = 0.10(x + 5) = 0.1x + 0.5$.According to the problem,the new tax is ₹ $10,000$ (which is $0.1$ lakh) more than the initial tax.So,$(0.1x + 0.5) - 0.12x = 0.1$.$-0.02x + 0.5 = 0.1$.$0.4 = 0.02x$.$x = \frac{0.4}{0.02} = 20$ lakhs.The question asks for the increased income,which is $x + 5 = 20 + 5 = 25$ lakhs.

$A$ man's annual income has increased by ₹ $5$ lakhs,but the tax on income that he has to pay has reduced from $12 \%$ to $10 \%$. He now pays ₹ $10,000$ more income tax. What is his initial income (in ₹ lakhs)?

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