Then Value of the machine after n years = P((1R)/100))n
If the present value of a machine = P and it depreciates at the rate of R% per annum,
Solved Examples
1. If A = x% of y and B = y% of x, then which of the following is true?  
A. None of these  B. A is smaller than B. 
C. Relationship between A and B cannot be determined.  D. If x is smaller than y, then A is greater than B. 
E. A is greater than B. 
Answer : Option A
Explanation :
A = xy/100 ………….(Equation 1)
B = yx/100.................(Equation 2)
From these equations, it is clear that A = B
2. If 20% of a = b, then b% of 20 is the same as:  
A. None of these  B. 10% of a 
C. 4% of a  D. 20% of a 
Answer : Option C
Explanation :
20% of a = b
=> b = 20a/100
b% of 20 = 20b/100=(20a/100) × 20/100
=(20×20×a)/(100×100)=4a/100 = 4% of a
3. Two numbers A and B are such that the sum of 5% of A and 4% of B is twothird of the sum of 6% of A and 8% of B. Find the ratio of A : B.  
A. 2 : 1  B. 1 : 2 
C. 1 : 1  D. 4 : 3 
Answer : Option D
Explanation :
5% of A + 4% of B = 2/3(6% of A + 8% of B)
5A/100+4B/100=2/3(6A/100+8B/100)
⇒5A+4B=2/3(6A+8B)
⇒15A+12B=12A+16B
⇒3A=4B
⇒AB=43⇒A:B=4:3
4. The population of a town increased from 1,75,000 to 2,62,500 in a decade. What is the average percent increase of population per year?  
A. 4%  B. 6% 
C. 5%  D. 50% 
Answer : Option C
Explanation :
Increase in the population in 10 years = 2,62,500  1,75,000 = 87500
% increase in the population in 10 years = (87500/175000)×100=8750/175=50%
Average % increase of population per year = 50%/10=5%
5. Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?  
A. 57%  B. 50% 
C. 52%  D. 60% 
Answer : Option A
Explanation :
Votes received by the winning candidate = 11628
Total votes = 1136 + 7636 + 11628 = 20400
Required percentage = (11628/20400)×100=11628/204=2907/51=969/17=57%
6. A fruit seller had some oranges. He sells 40% oranges and still has 420 oranges. How many oranges he had originally?  
A. 420  B. 700 
C. 220  D. 400 
Answer : Option B
Explanation :
He sells 40% of oranges and still there are 420 oranges remaining
=> 60% of oranges = 420
⇒(60×Total Oranges)/100=420
⇒Total Oranges/100=7
⇒ Total Oranges = 7×100=700
7. A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?  
A. 499/11 %  B. 45 % 
C. 500/11 %  D. 489/11 % 
Answer : Option C
Explanation :
Total runs scored = 110
Total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60
Total runs scored by running between the wickets = 110  60 = 50
Required % = (50/110)×100=500/11%
8. What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?  
A. 2023%  B. 20% 
C. 21%  D. 2223% 
Answer : Option B
Explanation :
Total numbers = 70
Total numbers in 1 to 70 which has 1 in the unit digit = 7
Total numbers in 1 to 70 which has 9 in the unit digit = 7
Total numbers in 1 to 70 which has 1 or 9 in the unit digit = 7 + 7 = 14
Required percentage = (14/70)×100=140/7=20%
9. In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, what was the number of valid votes that the other candidate got?  
A. 2800  B. 2700 
C. 2100  D. 2500 
Answer : Option B
Explanation :
Total number of votes = 7500
Given that 20% of Percentage votes were invalid
=> Valid votes = 80%
Total valid votes = (7500×80)/100
1^{st} candidate got 55% of the total valid votes.
Hence the 2nd candidate should have got 45% of the total valid votes
=> Valid votes that 2nd candidate got = (total valid votes ×45)/100
=7500×(80/100)×(45/100)=75×(4/5)×45=75×4×9=300×9=2700
10. In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?  
A. 8200  B. 7500 
C. 7000  D. 8000 
Answer : Option D
Explanation :
State A and State B had an equal number of candidates appeared.
In state A, 6% candidates got selected from the total appeared candidates
In state B, 7% candidates got selected from the total appeared candidates
But in State B, 80 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 80
=> total appeared candidates in State B = 80 x 100 = 8000
=> total appeared candidates in State A = total appeared candidates in State B = 8000
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