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 \frac{10}{100}=6 =60-6=54

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

Saved=45

Amount he spent on food=9

45  \rightarrow  6750

9    \rightarrow  ?

\frac{9\times 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 \frac{20}{100}=0.8

4+0.8=4.8

He increases his expenditure by 10%

3\times \frac{10}{100}=0.3

3+0.3=3.3

Savings = 4.8-3.3=1.5

Percentage change = \frac{Final volume-initial volume}{initial volume}\times 100

= \frac{1.5-1}{1}\times 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 volume-initial volume}{initial volume}\times 100

=\frac{30-28}{30}\times 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 volume-initial volume}{initial volume}\times 100

= \frac{77-42}{42}\times 100

=83\tfrac{1}{3}%

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