Question

The income of a company increases 20% per
annum. If its income is F 26,64,000 in the year
2012, then its income in the year 2010 was :​

Answer 1

Step-by-step explanation:

Let the income of 2010 be " x ".

Hence,

$income \: of \: 2011 = x + 20\% \: of \: x \\income \: of \: 2011 = x + \frac{20x}{100} \\ income \: of \: 2011 = \frac{100x + 20x}{100} \\ income \: of \: 2011 = \frac{120x}{100} \\ income \: of \: 2011 = \frac{12x}{10}$

Now,

$income \: of \: 2012 = \frac{12x}{10} + 20\% \: of \: \frac{12x}{10} \\ income \: of \: 2012 = \frac{12x}{10} + \frac{20 \times 12x}{100 \times 10} \\income \: of \: 2012 = \frac{12x}{10} + \frac{6x}{25} \\ income \: of \: 2012 = \frac{60x + 12x}{50} \\ income \: of \: 2012 = \frac{72x}{50} \\ income \: of \: 2012 = \frac{36x}{25}$

From the question, we know that income of 2012 = Rs 26,64,000.

Therefore,

$\frac{36x}{25} = rs \: 2664000 \\ x = \frac{rs \: 2664000 \times 25}{36} = rs \: 1850000$

Hence, the income of the company in 2010 was Rs. 18,50,000.