Table of Contents

    Percentage

    Rumman Ansari August 06, 2024 481 views

    Percentage Formulas

    Percentage

    A percentage is a fraction of 100.

    \[ \text{Percentage} = \left( \frac{\text{Value}}{\text{Total Value}} \right) \times 100 \]

    Percentage Increase

    To calculate the percentage increase from an initial value to a final value:

    \[ \text{Percentage Increase} = \left( \frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}} \right) \times 100 \]

    Percentage Decrease

    To calculate the percentage decrease from an initial value to a final value:

    \[ \text{Percentage Decrease} = \left( \frac{\text{Initial Value} - \text{Final Value}}{\text{Initial Value}} \right) \times 100 \]

    Finding the Value when Percentage is Known

    To find the value when a percentage of it and the percentage are known:

    \[ \text{Value} = \left( \frac{\text{Percentage}}{100} \right) \times \text{Total Value} \]

    Finding the Value when Percentage is Known

    To find the value when a percentage of it and the percentage are known:

    \[ \text{Value} = \left( \frac{\text{Percentage}}{100} \right) \times \text{Total Value} \]

    Example:

    Suppose you know that 30% of a number is 60. To find the total value:

    Let \( \text{Percentage} = 30 \) and \( \text{Value} = 60 \). We need to find \( \text{Total Value} \).

    \[ \text{Total Value} = \frac{\text{Value}}{\left( \frac{\text{Percentage}}{100} \right)} \]

    \[ \text{Total Value} = \frac{60}{\left( \frac{30}{100} \right)} = \frac{60}{0.30} = 200 \]

    Therefore, the total value is 200.

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    MCQ Section

    MCQ 1
    The quantity of water in milk constitutes 5 parts for every 15 parts of the mixture. What is the percentage of water in the mixture?
    MCQ 2
    If A's income is 25% more than B's income then by what percentage is B's income less than A's?
    MCQ 3
    If the price of petrol is increased by 20% and subsequently 40%, what is the final price if the original price is Rs. 25?
    MCQ 4
    Formula For Successive increase or decrease of percentage
    MCQ 5
    Formula for Percentage reduction in consumption
    MCQ 6
    The formula for Successive Discount:
    If two successive discounts of a% and b% are offered then the net discount offered is
    MCQ 7
    Find the net discount offered on two successive discounts of 20% and 30%?
    MCQ 8
    What is the number if 65% of it is 21 less than 4/5 of the number?
    MCQ 9
    Find the percentage error in expressing the length 810472 km with three significant digits as accurately as possible.
    MCQ 10
    If 50% of the difference between x and y is equal to 30% of the sum of x and y, what percentage of x is y?
    MCQ 11
    Mr. Jones initially had an unknown amount of money. He gave 40% of this amount to his wife, and then gave 20% of the remaining amount to his three sons. After this, he spent half of the remaining amount on miscellaneous items and deposited the remaining Rs. 12,000 in the bank. How much money did Mr. Jones have initially?
    MCQ 12
    After Raman's salary was decreased by 50% and then increased by 50%, what is the percentage change in his salary compared to its original amount?
    MCQ 13
    What was the impact on total revenue when the price of a product was decreased by 10% and the number sold increased by 30%?
    MCQ 14
    If the numerator of a fraction is increased by 15% and its denominator is decreased by 8%, and the resulting fraction has a value of 15/16, what is the original fraction?
    MCQ 15
    In a village, 10% of the inhabitants died of cholera, causing panic among the remaining inhabitants. As a result, 25% of the remaining inhabitants left the village, reducing the population to 4050. How many original inhabitants were there in the village?
    MCQ 16
    A salesman receives a commission of 5% on all sales up to Rs. 10,000, and a commission of 4% on all sales above this amount. He sends a total of Rs. 31,100 to his parent company after deducting his commission. What is the total amount of sales that the salesman made?
    MCQ 17
    Paulson's income was increased by 20% and he increased his expenditure by 10%. If Paulson spends 75% of his income, what is the percentage increase in his savings after these changes?
    MCQ 18
    If a person's salary was reduced by 10%, what percentage increase is needed to bring the reduced salary back to the original amount?
    MCQ 19
    In the new budget, the price of kerosene oil has increased by 25%. To prevent an increase in expenditure on it, by what percentage must a person reduce their consumption?
    MCQ 20
    What will the population of a town be in two years if it has a current population of 1,76,400 and grows at a rate of 5% per year, and what was the population of the town two years ago?
    MCQ 21
    80 is what percent of 64?
    MCQ 22
    If the population of a town increased by 5% over the course of one year, and the total population at the end of the second year is 9975, then what was the population size at the beginning of the first year?
    MCQ 23
    Is 80% of 40 greater than 4/5 of 25?
    MCQ 24
    What number is 40% more than 20% of 650 and 190?
    MCQ 25
    If A and B's salaries amount to Rs. 2,000 and A spends 95% of his salary while B spends 85% of his, and now their savings are the same, what is A's salary
    MCQ 26
    If 5% of the people in a village in Sri Lanka died by bombardment and 15% of the remainder left the village out of fear, and the population is now reduced to 3553, what was the population in the beginning?
    MCQ 27
    In a factory where 40% of the workers are technicians and 60% are non-technicians, and 60% of the technicians and 40% of the non-technicians are permanent employees, what is the percentage of workers who are temporary?
    MCQ 28
    If 12% of x is equal to 6% of y, what percentage of y is equal to 18% of x?
    MCQ 29
    If the two given numbers are 7% and 28% of a third number, respectively, what percentage of the second number is the first number?
    MCQ 30
    If two numbers are 40% and 30% more than a third number, respectively, what percentage of the first number is the second number (approximately)?
    MCQ 31
    If one number is 20% more than another number, what percentage is the smaller number less than the greater number?
    MCQ 32
    If two numbers are less than a third number by 40% and 47% respectively, approximately what percentage is the second number less than the first?
    MCQ 33
    If a man's wages were decreased by 50% and then increased by 50%, what was his loss?
    MCQ 34
    If the price of cooking oil has increased by 25%, what percentage reduction in the use of cooking oil should a family make in order to avoid increasing expenditure on this account?
    MCQ 35
    If a number is increased by 20% and then decreased by 20%, what is the final value of the number?
    MCQ 36
    A batsman scored 120 runs, including 3 boundaries and 8 sixes. What percentage of his total score did he make by running between the wickets?
    MCQ 37
    A shopkeeper marks the price of his goods at 25% higher than the original price. After that, he allows a discount of 12%. What profit or loss does he get?
    MCQ 38
    Since 4 x pi x radius x radius = surface area. Therefore, net % change in area = ( x + y + xy/100) % = [10 + 10 + (10 x 10)/100]% or 21%.
    MCQ 39
    If the price of an article is reduced by 30% and the sales of the article increase by 50%, what is the percentage change in the total amount of receipts?
    MCQ 40
    If the side of a square is increased by 55%, what is the increase in its area?
    MCQ 41
    If the length and breadth of a square are increased by 40% and 30% respectively, how much does the area of the resulting rectangle exceed the area of the original square?