Solve the given questions on Percentage and get solutions with detailed explanations. All the Questions on Percentages are primarily based on calculating percentages along with its applications. Enhance your Conceptual Knowledge taking the help of the Solved Questions on Percentage. Identify the knowledge gap and practice the questions accordingly thereby score better grades in your exams.
1. 30 % of a number is 10 less than two-third of that number. Find the number?
Solution:
Let the number be x
From the given data (2/3)*x – 30% of x = 10
(2/3)*x – (30/100)*x = 10
x(2/3- 30/100) = 10
x((6-90)/300) = 10
x(-84/300) = 10
x = (10*300/-84)
= 3000/-84
= -250/7
2. When 50 is subtracted from a number; it reduces to 40 %. Find the three-fifth of that number?
Solution:
Let the number be x
From given data 50 subtracted from a number reduced to 40% which means
x- 50 = (40/100)*x
x- (40/100)x = 50
x(1-40/100) = 50
x(60/100) = 50
x= (50*100)/60
= 250/3
3. If 10% of x is equal to 5% of y, then 14% of x will be equal to how much % of y?
Solution:
From given data, we can write the equation as such
10% of x = 5% of y
14% of x = ? % of y
(10/100)*x = (5/100)*y
(1/10)*x = (1/20)*y
x/y = (1/20)/(1/10)
= 1/20*10/1
= 1/2
x/ y = 1/2
From this ratio, we can say that 14% of x = 7% of y
4. A shopkeeper marks the price of his goods at 20% higher than the original price. After that, he allows for a discount of 10%. What profit or loss does he get?
Solution:
Let the Cost Price of the goods be 100
Since the shopkeeper marked it 20% higher the price becomes 120.
Later the shopkeeper allows a discount of 10% i.e. 120 – 10 = 110
Since the Shopkeeper sold it for a higher price than the original price he will get a profit.
Profit % = ((Selling Price – Original Price)/Original Price)*100
= ((110-100)/100)*100
= 10%
Therefore, shopkeeper makes a profit of 10%.
5. A number is reduced by 50%. Its present value is 230. What was its original value?
Solution:
Let the number be x
The number reduced by price = x – 50/100*x
x -50/100*x = 230
x(1-50/100) = 230
x(50/100) = 230
x = (230*100)/50
= 460
Original Value is 460.
6. A student multiplied a number by 5/7 instead of 7/5, What is the percentage error in the calculation?
Solution:
Let the number be x
Ideally, the Number Multiplied by 7/5 is (7/5)x = 7x/5
Number Multiplied by 5/7 is (5/7)x = 5x/7
Error = (7x/5 – 5x/7)
= (49x -25x)/35
= 24x/35
Error % = (Error/True Value)*100
= ((24x/35)/(7x/5))*100
= (24x/35*5/7x)*100
= (120/245)*100
= 48.97%
7. Ram gets 45 % of total valid votes in an election. If the total votes were 9000, what is the number of valid votes that Ram got?
Solution:
Total number of votes cast = 9000
Ram got 45% of Votes i.e. 45/100*9000
= 45*90
= 4050
8. In a plot of 4000 sq. m., only 2500 sq. m. is allowed for construction. What percent of the plot is to be left without construction?
Solution:
Percentage of Plot allowed for construction = (2500/4000)*100
= 62.5%
Percentage of Plot not allowed for construction = (1500/4000)*100
= 37.5%