Here are some solved examples of Percentage :
Example. 1 : 28% of 450 + 45% of 280 = ?
Solution :
28% of 450 + 45% of 280 = 28/100 of 450 + 45/100 of 280
= 126 + 126 = 252
Example. 2 : 65% of anumber is 21 less than four-fifth of that number. Find the number ?
Solution :
Let the number be, X.
Then, 65% of X = .65X and 4/5 of X = .8X
According to the question, .8X - .65X = 21
or, .15X = 21
or, X = 2100/15 = 140
Example. 3 : If the income of Ram is 25% more than that of Shyam's income. Then how much % Shyam's income is less than that of Ram's income ?
Solution :
Let the Shyam's income be Rs. 100
Then Ram's income = Rs. 125
.·. Shyam's income is Rs. 25 less by Ram's income
.·. Shyam's income is( 25/125) × 100 % less than that of Ram's income.
= 20%
Example. 4 : Subir spends 30% on foods, 20% on house loans, 15% on educations and 10% on travel. After all these expenditure he saved Rs. 12500. Find his total income and the amount spent on house loans ?
Solution :
Let the total income be Rs. X.
Total expenditure = X × (30% + 20% + 15% + 10%) = 3X/4
Then savings = X - 3X/4 = X/4
.·. X/4 = 12500
or, X = 12500 × 4 = 50000
.·. Subir's total income = Rs. 50000
and he spent on house loans = Rs. 50000 × 20%
= Rs. 50000 ×1/5 = Rs. 10000
Example. 5 : If the length of a rectangle is increased by 10% and breadth is decreased by 20%. Then Find the net percent change in the area of that rectangle ?
Solution :
We know the formula of net percent change
And its = X - Y -  [when X% increase and Y% decrease]
= 10 - 20 - 200/100
= - 10 - 2 = - 12
.·. The area of that rectangle is decreased by 12%
Example. 6 : In an election between two candidates, 75% of the voters cast their votes, out of which 2% of the votes were decleared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election ?
Solution :
Let the total number of votes enrolled be X. Then,
Number of votes cast = 75% of X = 3X/4
Valid votes = 98% of 3X/4 = 98/100 × 3X/4
According to the question, 3/4 × 98/100 × 3X/4 = 9261
or, X = (9261 × 4 × 4 × 100) /(3 × 98 × 3)
or, X = 16800
The total votes enrolled in that election = 16800
Example. 7 : When the price of a product is decreased by 10%, and the number of sold increased by 20%. Then what is effect on the total revenue ?
Solution :
Let the price of the product be Rs. 100 and let the sale be 100 pieces.
Then the total revenue = Rs. (100 × 100) = Rs. 10000
And the new revenue = Rs. (90 × 120) = Rs. 10800
.·. Increase in revenue = ( 800/10000 × 100) % = 8%
Example. 8 : The population of a town is 2,00,000. If it increases at the rate of 10% per annum, what will be its population 2 years hence ?
Solution :
We know the formula about population after n years = P(1 + R%)n
.·. Population after 2 years = Rs. 200000 (1 + 10%)2
= Rs. 200000 (110/100)2
= Rs. 200000 × 11/10 × 11/10
= Rs. 2000 × 121 = 242000
Example. 9 : The value of a machine depreciates at the rate of 10% per annum. If its present value is Rs. 150000, what will be its value after 2 years ?
Solution :
We know the formula of the depreciated value of a machine after n years
= P(1 - R%)n
The value of machine after 2 years =Rs. 150000(1 - 10%)2
= Rs. 150000 (90/100)2
= Rs. 150000 × 9/10 × 9/10
= Rs. 1500 × 81 = Rs. 121500
Example. 10 : In an examination, 30% of the total students failed in English, 40% failed in Hindi and 10% failed in both the subjects. Then find the percentage of those who passed in both the subjects ?
Solution :
Let A and B be the sets of students who failed in English and Hindi respectively.
Then n (A) = 30, n (B) = 40, n (A ∩ B) = 10
So, n (A U B) = n (A) + n (B) - n (A ∩ B) = ( 30 + 40 - 10) = 60
.·. Students failed in English or Hindi or Both = 60%
Hence, Students passed = (100 - 60)% = 40%
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