Friday, 31 March 2017

Percentage Problems for Bank Exams - Part I

percentage problems

The quantitative aptitude section in SBI PO and IBPS PO definitely would include questions from the topic, percentage. We had earlier discussed what is percentage and the basic concepts related to percentage.

Let us now provide you with a guide on how to solve percentage problems for bank exams. This guide has been divided into 18 models for easier understanding. These are essentially the 18 different types of percentage related questions that one can encounter when writing any bank exam.

Model 1: One of the common questions that you would face in any bank exam is to find the total salary of the person based on his monthly budget. 

Example 1: Sameer spends 20% of his monthly salary on house rent, 25% on food, 10% on transportation, 15% on the education of his children, and 18% on other household expenses. He saves the remaining amount of ₨. 4800 at the end of the month. What is his monthly salary?

Solution:
Monthly Salary = Total value = 100%
Monthly Expenditure = 20% + 25% + 10% + 15% + 18% = 88%
Monthly Savings = 100% - 88% = 12% = 4800

Monthly Salary = 12% = 4800
100% = x
By Cross multiplication, x = (4800* 100)/12 = Rs. 40,000

Similarly, in the same problem, we can use cross multiplication to find any of his expenditure; house rent, food, transportation etc.

Example 2: Gaurav spends 40% of his allowance on hostel expenses, 20% on books and stationary, and 50% of the remaining on transport. He saves Rs. 450, which is half of the remaining amount after spending on the hostel expenses, books and stationary and transport. How much is his allowance?

Solution:
Monthly allowance = Total value = 100%
HE + BS = 40% + 20% = 60%
Remaining amt = 100% - 60% = 40%
Transport = 50% of remaining = 50% of 40% = 20%
Total Expenditure = 60% + 20% = 80%
Remaining amt = 100% - 80% = 20%

Half of remaining ⇒ 50% of 20% = 10% = 450
Total allowance  100% = x
By Cross multiplication, x = (450* 100)/10 = Rs. 4500

The trick to solving percentage questions on monthly salary or expenditure is by considering the total amount to be 100% and then, finding the remaining amount, or whatever value is required according to the question.

Model 2: The next most common type of question that you would face in any bank exam is to calculate the percentage of a percentage.

Example 1: Prerna decided to donate 30% of her monthly income to orphanages. But on the day of donation, she changed her mind and donated Rs. 4200, which is 70% of what she had earlier decided. What should be her actual donation as per her earlier decision?

Solution: 
70% of 30% = 4200
⇒ (70*30/100)% 
⇒ 21% = 4200
⇒ 30% = x
By Cross multiplication, x = (30 * 4200)/21 = Rs. 6000

Example 2: The price of a car is Rs. 5,00,000. It was insured for 90% of its price. The car got completely damaged and the insurance company paid only 80% of the insured amount. What is the price of the difference between the price of the car and the amount of insurance received?

Solution:
Total value = 100% = 5,00,000
Insurance received (B) = 80% of insured amt
⇒ 80% of 90%
⇒ (80*90/100)% = 72%

Price of the car (A) = 100%
Difference% of A – B = 28%
Difference amt = 28% = x
100% = 5,00,000
By Cross multiplication, x = (28*5,00,000)/100 = Rs. 1,40,000

Model 3: Another common frequently asked questions in bank exams related to the concept of percentage is election between two or more people

Example 1: In an election between two candidates, the winner secured 58% of the total votes cast and wins by a majority of 2400 votes. How many votes did the losing candidate get?

Solution:
Total votes cast = 100%
Winner gets = 58%
Loser gets = 100 – 58 = 42%

Majority = Votes secured by winner – Votes secured by loser
⇒ 58% - 42% = 16% = 2400
Votes by the losing candidate = x = 42%
By Cross multiplication, x = (42 * 2400)/16 = 6300 votes

Example 2: In a college election between 2 students, 10% of the votes cast is invalid. The winner gets 70% of the valid votes and defeats the loser by 1800 votes. How many votes were cast in total?

Solution:
Total votes cast = 100%
Invalid votes = 10%
Valid votes = 100 – 10 = 90%

Winner gets = 70% of 90%
⇒ (70 * 90)/100% = 63%
Loser gets = Valid votes – Winner votes
⇒ 90% - 63% = 27%

Majority = Votes secured by winner – Votes secured by loser
⇒ 63% - 27% = 36% = 1800
Total votes cast = 100% = x 
By Cross multiplication, x = (100 * 1800)/36 = 5000 votes

Similarly, we can also find out the number of valid votes cast, since we have the value of one percentage.

Point to remember:
When a question like this mentions a percent of a percent, like here, the winner gets 70% of the 90%, it is easy to confuse the votes secured by the loser to be 90% minus 70%. One must remember that the difference of 20% is not an indication of the total percentage of votes secured by the loser.

Because it is 20% of the valid votes and not the total votes cast.

There are 15 more different types of percentage problems that we have identified as frequently-asked questions for any bank exams. Check out our next blog to know more about how to solve various percentage problems for bank exams. And never stop practicing!

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