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Question: These questions are based on the following pre-chart Arun’s monthly income is Rs \(21,000\) If t...

These questions are based on the following pre-chart
Arun’s monthly income is Rs 21,00021,000
If the rent is increased by {\text{5% }} and the other expenditure and income are the same. So then by what percent does saving decrease?

{\text{a)60% }}
{\text{b)75% }}
{\text{c)25% }}
{\text{d)40% }}

Explanation

Solution

First, we have to find the original saving percentage by subtracting all the other expenses.
Then, we have to increase the rent by {\text{5% }} and find a new saving percentage.
With that, we will have to apply a formula to find the decreased percentage of savings.

Formula used: Change in percentage =old value - new valueold value×100 = \dfrac{{{\text{old value - new value}}}}{{{\text{old value}}}} \times 100

Complete step-by-step solution:
It is given that the pie chart stated as,
Rent = 150∘{\text{150}}^\circ
Food = 120∘{\text{120}}^\circ
Petrol = 50∘{\text{50}}^\circ
Medicines = 30∘{\text{30}}^\circ
Here, we will find the original old savings percentage.
As we know, the full circle is 360∘{\text{360}}^\circ and savings percentage is one among the 360∘{\text{360}}^\circ
So we can write it as,
Old Savings = 360∘−{\text{360}}^\circ - rent – food – petrol – medicines.
On putting the values and we get
⇒360∘−150∘−120∘−50∘−30∘\Rightarrow 360^\circ - 150^\circ - 120^\circ - 50^\circ - 30^\circ
On simplifying we get
Old savings =10∘= 10^\circ
Now, it is given that the rent is increased by {\text{5% }}
We have to find the increased percentage of rent,
Old rent = 150∘{\text{150}}^\circ
Increased percent = {\text{5% }}
∴\therefore Increased rent percent = 150×5100150 \times \dfrac{5}{{100}}
⇒750100\Rightarrow \dfrac{{750}}{{100}}
On dividing we get,
⇒7.5∘\Rightarrow 7.5^\circ
So the new rent = 150∘+7.5∘=157.5∘{\text{150}}^\circ + 7.5^\circ = 157.5^\circ
Now we have to find out the new savings = 360∘−{\text{360}}^\circ - new rent – food – petrol – medicines.
⇒360∘−157.5∘−120∘−50∘−30∘\Rightarrow 360^\circ - 157.5^\circ - 120^\circ - 50^\circ - 30^\circ
On simplifying we get
New savings =2.5∘= 2.5^\circ
Now, we have both the old and new savings, from this we will find the decreased percent of savings.
Change in percentage =old value - new valueold value×100 = \dfrac{{{\text{old value - new value}}}}{{{\text{old value}}}} \times 100
Putting the values and we get
∴\therefore Decreased savings percent =10 - 2.510×100 = \dfrac{{{\text{10 - 2}}{\text{.5}}}}{{{\text{10}}}} \times 100
Let us subtract the numerator term and we get,
⇒7.510×100\Rightarrow \dfrac{{7.5}}{{10}} \times 100
Let us multiply the terms and we get
=75010=75= \dfrac{{750}}{{10}} = 75%
Therefore, the savings percent is decreased by 7575%

Hence the correct option is (B)\left( B \right).

Note: Basically when we convert numbers into percentages or any data into percentages, nature will change, numbers have no end but percentage does have an end (e.g. {\text{100% }}).
When we simply subtract or add the changes, the base (or end) will change (e.g. {\text{100% }} will change either below {\text{100% }} or above {\text{100% }}).