A man's working hours a day were increased by $20\%$ and his wages per hour were increased by $15\%$. By how much percent was his daily earning increased? (R.R.B., 2008)
Answer
Answer (as printed):
Explanation
Let the original number of working hours a day be $x$ and original wages per hour be ₹ $y$. Then, original daily earning $=₹(xy)$. Increased working hours $=120\%$ of $x=\frac{6x}{5}$. Increased wages per hour $=115\%$ of ₹$y=₹\frac{23y}{20}$. New daily earning $=₹\left(\frac{6x}{5}\times\frac{23y}{20}\right)=₹\left(\frac{69xy}{50}\right)$. Increase in daily earning $=₹\left(\frac{69xy}{50}-xy\right)=₹\left(\frac{19xy}{50}\right)$. Increase $\%=\left(\frac{19xy}{50}\times\frac{1}{xy}\times 100\right)\%=38\%$.
Explanation as extracted from the printed page; notation may be imperfect.