# Percentages Part 4

Income and expenditure concept

Problem 1: A person spends 40% of his salary on house rent, on remaining 10%  spends on travels, on remaining $16\tfrac{2}{3}$% spends on food and remaining is saved. If he saved RS 6750 what amount he spent on food?

Solution : Assume total income=100

40% spends on salary=100-40=60

on remaining 10% spends on travels=$60\times&space;\frac{10}{100}=6$ =60-6=54

On remaining $16\tfrac{2}{3}$% spends on food=$54\times&space;\frac{1}{6}=9$ =54-9=45

Saved=45

Amount he spent on food=9

45  $\rightarrow$  6750

9    $\rightarrow$  ?

$\frac{9\times&space;6750}{45}=1350$

The amount spent on food is 1350

Observe the below figure

Assume income =100

Problem 2: A man spends 75% of his income. His income is increased by 20% and he increased his expenditure by 10%. Are his savings increased by?

Solution: A man sends his income  is 75%

The fractional value of 75%=$\frac{3}{4}$

Here 4 is the actual income and 3 is the expenditure

Savings are 4-3=1

He increases his income by 20%

$4\times&space;\frac{20}{100}=0.8$

4+0.8=4.8

He increases his expenditure by 10%

$3\times&space;\frac{10}{100}=0.3$

3+0.3=3.3

Savings = 4.8-3.3=1.5

Percentage change = $\frac{Final&space;volume-initial&space;volume}{initial&space;volume}\times&space;100$

= $\frac{1.5-1}{1}\times&space;100$

=50%

Observe the below figure

Problem 3: The price of sugar is increased by $16\tfrac{2}{3}$% and the consumption of a family is decreased by 20%. Find the percentage change in expenditure?

Solution :$16\tfrac{2}{3}$%=$\frac{1}{6}$       20%=$\frac{1}{5}$

Actual price is 6 and increased price is 7

Actual consumption is 5 and decreased consumption is 4

Price * Consumption = Expenditure

6*5=30        7*4=28

Percentage change=$\frac{Final&space;volume-initial&space;volume}{initial&space;volume}\times&space;100$

=$\frac{30-28}{30}\times&space;100=6.66$%

Observe the below figure

Problem 4: The sale of a cinema ticket is increased by $57\tfrac{1}{7}$% and the price of a ticket is increased by $16\tfrac{2}{3}$%. Find the change in the return?

Solution:   $57\tfrac{1}{7}$%=$\frac{4}{7}$         $16\tfrac{2}{3}$%=$\frac{1}{6}$

Percentage change = $\frac{Final&space;volume-initial&space;volume}{initial&space;volume}\times&space;100$

= $\frac{77-42}{42}\times&space;100$

=$83\tfrac{1}{3}$%