# CRE 2 - Percentage Change | Arithmetic - Percentage

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**CRE 2 - Percentage Change | Arithmetic - Percentage**

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 = $\frac{Finalvalue-Initialvalue}{Initialvalue}\times 100\%$ = $\frac{5100-4200}{4200}\times 100\%$ = 21.42 = approx 21%

Hence, option (e).

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**CRE 2 - Percentage Change | Arithmetic - Percentage**

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).

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**CRE 2 - Percentage Change | Arithmetic - Percentage**

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, $\frac{{\displaystyle \frac{35x}{6}}}{6x}\times 100$ = $\frac{35x}{36x}\times 100$ = 97%

Hence, option (b).

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**CRE 2 - Percentage Change | Arithmetic - Percentage**

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).

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**CRE 2 - Percentage Change | Arithmetic - Percentage**

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).

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**CRE 2 - Percentage Change | Arithmetic - Percentage**

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).

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**CRE 2 - Percentage Change | Arithmetic - Percentage**

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).

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**CRE 2 - Percentage Change | Arithmetic - Percentage**

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).

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**CRE 2 - Percentage Change | Arithmetic - Percentage**

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).

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**CRE 2 - Percentage Change | Arithmetic - Percentage**

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).

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**CRE 2 - Percentage Change | Arithmetic - Percentage**

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

∴ $\frac{x+50\%ofx}{y-20\%ofy}=\frac{3}{10}$

⇒ $\frac{1.5x}{0.8y}=\frac{3}{10}$

⇒ x/y = 4/25

Hence, option (e).

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**CRE 2 - Percentage Change | Arithmetic - Percentage**

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).

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**CRE 2 - Percentage Change | Arithmetic - Percentage**

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).

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**CRE 2 - Percentage Change | Arithmetic - Percentage**

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.

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**CRE 2 - Percentage Change | Arithmetic - Percentage**

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).

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**CRE 2 - Percentage Change | Arithmetic - Percentage**

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).

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**CRE 2 - Percentage Change | Arithmetic - Percentage**

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).

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**CRE 2 - Percentage Change | Arithmetic - Percentage**

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).

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