Question

A man spends 75% of his income. This income is increased by 20% and he increases his expenditure by 10%. By what per cent are his savings increased ?

Comments

Let the income be 100.
Income.           Expenditure.              Savings
100                    75                                  25
120                     82.5(i.e; 75+7.5)        37.5
So, percent increase in savings= ((37.5-25)/25)*100 = 50%

Answer 1

Let the income of the person be Rs x.

Then, his savings = Rs \(\frac{X}{4}\)

Expenditure = x - \(\frac{X}{4}\) = Rs \(\frac{3X}{4}\)

Increased income = \(\frac{120}{100}\) x x = Rs \(\frac{6X}{5}\)

Increased expenditure = \(\frac{110}{100}\) x \(\frac{3X}{4}\) = Rs \(\frac{33X}{40}\)

\(\therefore\) Increased savings = \(\frac{6X}{5}\) - \(\frac{33X}{40}\) = \(\frac{48X-33X}{40}\) = \(\frac{3X}{8}\)

\(\therefore\) % increase in savings = \(\frac{\Big(\frac{3X}{8}-\frac{X}{4}\Big)}{\frac{X}{4}}\)x 100

= \(\Big(\frac{X}{8}\times\frac{4}{X}\times100\Big)\)% = 50 %.