CRE 2 - Percentage Change | Arithmetic - Percentage
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The population of a town increases from 4200 to 5100. What is the approximate percentage increase?
- (a)
10%
- (b)
12%
- (c)
25%
- (d)
20%
- (e)
21%
Answer: Option E
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Explanation :
Percentage increase = = = 21.42 = approx 21%
Hence, option (e).
Workspace:
A number increases by 40 when added to 20% of itself. The number is
- (a)
200
- (b)
60
- (c)
80
- (d)
320
Answer: Option A
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Explanation :
Let the number be N.
Number increases by 40 due to 20% of itself.
⇒ 20% of N = 40
⇒ 20/100 × N = 40
⇒ N = 200.
Hence, option (a).
Workspace:
A positive number was by mistake divided by 6 instead of being multiplied by 6. What is the % error on the basis of correct answer?
- (a)
3
- (b)
97
- (c)
17
- (d)
83
Answer: Option B
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Explanation :
Let x be the unknown positive number. Then, correct answer = 6x
Wrong answer = x/6
Error = 6x – x/6 = 35x/6
With respect to correct answer, % error can be found as, = = 97%
Hence, option (b).
Workspace:
A candidate who gets 30% of the marks fails by 50 marks. But another candidate who gets 45% marks gets 25 marks more than necessary for passing. Find the number of marks for passing:
- (a)
150
- (b)
200
- (c)
250
- (d)
275
Answer: Option B
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Explanation :
Let aggregate score be M and pass marks be x.
Then, by conditions of the problem, 0.3M = x – 50,
and, 0.45M = x + 25
Solving these simultaneous equations we get x = 200 marks
Hence, option (b).
Workspace:
Two numbers are 50% and 60% less than a third number. How much per cent is the second number less than the first?
- (a)
15%
- (b)
20%
- (c)
10%
- (d)
25%
Answer: Option B
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Explanation :
Let the third number be x
Then, first number = 0.5x and second number = 0.4x
Second number is less than first by (0.5x – 0.4x) i.e. 0.1x
In terms of %age: 0.1x/0.5x × 100 = 20%
Hence, option (b).
Workspace:
A student needs 40% marks to pass in an exam. He got 240 marks and failed by 40 marks. Find the total marks?
- (a)
700
- (b)
800
- (c)
400
- (d)
300
- (e)
None of these
Answer: Option A
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Explanation :
Let total marks = x
∴ Pass marks = 40% of x
Also pass marks = 240 + 40 = 280
∴ 40% of x = 280
x = 280/(40%) = 700
Hence, option (a).
Workspace:
A earns 20% more than B but 25% less than C. If B earns Rs. 900 less than C, find the earnings of C :
- (a)
Rs. 2500
- (b)
Rs. 1600
- (c)
Rs. 1500
- (d)
Rs. 2400
Answer: Option D
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Explanation :
Let the earnings of C be 'c'.
⇒ Earnings of A = 25% less than earnings of C = 3/4 × c
⇒ Earnings of A = 20% more than earnings of B
⇒ 3/4 × c = 6/5 × earnings of B
⇒ Earnings of B = 5/8 × c
Givne, c - 5/8 × c = 900
⇒ 3/8 × c = 900
⇒ c = 2400
Hence, option (d).
Workspace:
After 38 litres of petrol were poured into an empty tank, it was still 5% empty. How much petrol more must be poured into the tank in order to fill it?
- (a)
38 liters
- (b)
40 liters
- (c)
38.5 liters
- (d)
2 liters
Answer: Option D
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Explanation :
Let the capacity of tank be C liters
Then, 0.95 C = 38 liters
∴ C = 38/0.95 = 40 liters
Now, (40 - 38=) 2 liters of petrol must be poured to fill the tank.
Hence, option (d).
Workspace:
If 17% is lost in grinding wheat, a country has to import 6 lakhs tonnes of wheat but can maintain from its resources if only 5% is lost in grinding. The quantity of wheat grown in the country is
- (a)
5000 tonnes
- (b)
50,000 tonnes
- (c)
5,00,000 tonnes
- (d)
50,00,000 tonnes
Answer: Option D
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Explanation :
Let x lakh tones wheat is produced in the country.
When 17% of it is lost in grinding, the country needs to import 6 lakhs tonnes.
⇒ Consumption of wheat (in lakh tones) = 0.83x + 6 ...(1)
When 5% of it is lost in grinding, the country does not need to import.
⇒ Consumption of wheat = 0.95x ...(2)
From (1) and (2)
0.83x + 6 = 0.95x
⇒ 0.12x = 6 or
x = 50 lakh tonnes = 50,00,000 tonnes
Alternately,
Due to saving (17 - 5 = ) 12% of wheat produced, the country need not import 6 lakh tones of wheat.
⇒ 12% of Wheat produced = 6 lakh tones
⇒ 12/100 × Wheat produced = 6 lakh tones
⇒ Wheat produced = 50 lakh tones
Hence, option (d).
Workspace:
In a town, there are 3000 men and 3000 women. If men increased by 20% and women decreased by 40%, women as a percent of men now is:
- (a)
50%
- (b)
66.66%
- (c)
80%
- (d)
83.33%
- (e)
None of these
Answer: Option A
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Explanation :
After 20% increase, men = 3000 × 1.2 = 3600
After 40% decrease, women = 3000 × 0.6 = 1800
So women as a percentage of men =1800/3600 × 100 = 50%
Hence, option (a).
Workspace:
If the numerator of a fraction is increased by 50% and denominator decreased by 20%, the new value is 3/10. What was the original fraction?
- (a)
3/5
- (b)
4/5
- (c)
7/8
- (d)
3/2
- (e)
None of these
Answer: Option E
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Explanation :
Let the original fraction = x/y
∴
⇒
⇒ x/y = 4/25
Hence, option (e).
Workspace:
A 'laddoo' is made of 60% flour, 20% sugar and the rest is 'ghee'. What is the quantity of 'ghee' in two kg laddoos?
- (a)
400 gms
- (b)
2 kgs
- (c)
100 gms
- (d)
450 gms
- (e)
None of these
Answer: Option A
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Explanation :
If 60% is flour, 20% is sugar. So ghee = (100 - 60 - 20) = 20%.
So quantity of ghee in 2 kg laddoos = 20% of 2000 gms = 400 gms.
Hence, option (a).
Workspace:
If A's income is 50% more than B's, then B's income is what percent of A's income?
- (a)
66.66%
- (b)
80%
- (c)
90%
- (d)
125%
- (e)
None of these
Answer: Option A
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Explanation :
A’s income = 1.50 of B’s income = 3/2 × B’s income
B’s income = 2/3 of A’s income = 66.66% of A’s income.
Hence, option (a).
Workspace:
A number when increased by 36.36% becomes 180. Find the number?
Answer: 132
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Explanation :
Let the initial number be N.
Final number (F) = 180.
Percentage change= 36.36% = 4/11
∴ multiplication factor (mf) = 1 + 4/11 = 15/11
⇒ N = F/mf = 180/15/11 = 180 × 11/15 = 132.
Hence, 132.
Workspace:
A number is doubled. By what % must it be reduced to get back the original number.
- (a)
33.33%
- (b)
40%
- (c)
50%
- (d)
None of these
Answer: Option C
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Explanation :
Let the initial number be 100.
After doubling, the number becomes 200.
Now, 200 should reduce to 100.
∴ % change = (200 - 100)/200 × 100% = 50%
Alternately,
If the number is multiplied with 2 (doubled), it should be multiplied with 1/2 (reciprocal) to get back the original number.
∴ multiplication factor when reducing = 1/2
⇒ % change = (mf - 1) × 100% = (1/2 - 1) × 100% = - 50% [- indicated % decrease.]
Hence, option (c).
Workspace:
Match the percenetage change with its corresponding multiplication factor.
- (a)
1 - (a), 2 - (b), 3 - (c), 4 - (d)
- (b)
1 - (c), 2 - (d), 3 - (a), 4 - (b)
- (c)
1 - (c), 2 - (d), 3 - (b), 4 - (a)
- (d)
None of these
Answer: Option B
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Explanation :
44.44% = 4/9
∴ mf = 1 - 4/9 = 5/9
16.67% = 1/6
∴ mf = 1 + 1/6= 7/6
28.56% = 2/7
∴ mf = 1 - 2/7 = 5/7
15.38% = 2/13
∴ mf = 1 + 2/13 = 15/13
Hence, option (b).
Workspace:
A number is first doubled and then reduced to one-third of its new value. What is the overall percentage change in the value of the number?
- (a)
- 32.5%
- (b)
- 25%
- (c)
- 40%
- (d)
- 33.33%
Answer: Option D
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Explanation :
Let the number initially be x.
First the number is doubled, hence it becomes 2x.
Next, the number is reduced to 1/3rd of its new value, hence it becomes 2x/3.
So, the number changes from x to 2x/3, i.e., the multiplication factor is 2/3.
∴ Overall percentage change = (2/3 - 1) × 100% = - 33.33%
Hence, option (d).
Workspace:
A number is increased by 37.5%. By what % should it be decreased to get back the original number?
- (a)
37.5%
- (b)
25%
- (c)
20%
- (d)
None of these
Answer: Option D
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Explanation :
Let the number initially be 100.
New number after 37.5% increase = 137.5
Now, to get back the original number 100, new number 137.5 should be decreased by 37.5
∴ percentage change = (37.5/137.5) × 1000% = 27.27%
Alternately,
Multiplication factor for an increase of 37.5% (3/8) = 1 + 3/8 = 11/8
∴ Multiplication factor to get back the original number = Reciprocal of 11/85 = 8/11
∴ percentage change = (8/11 - 1) × 100% = -3/11 × 100% = - 27.27%
⇒ Decrease of 27.27%
Hence, option (d).
Workspace:
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