Bank Job Recruitment Test Preparatory Program

MATH LECTURE - 10

Name:

CONTENTS
Percentage: Basic Concepts

Percentage Change

Successive Percentage Change

Consumption &Remaining

Cracking Word Problems

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Step 1: Concepts of Percentage
01. An NGO hired some volunteers. If 55% of the volunteers hired were male, and the remaining 180 were
female, how many volunteers were hired?
(A) 320 (B) 400 (C) 450 (D) 480 (E) none of these

02. If 75% of x is equal to 50% of y, then (x +y) = ?

(A) 1.25y (B) 1.80y (C) 2.25x (D) 2.50x (E) none
03. Boshid spent 20% of his salary for food, 30% for apartment rent, and 25% for other expenses. If the
remaining Tk. 3500 were his monthly savings, how much (Take) was his apartment rent?(W)
(A) 2400 (B) 3600 (C) 4200 (D) 4500 (E) none of these
04. Abir’s monthly salary is equal to 30% of Zahir’s monthly salary or 20% of Sohel’s monthly salary. If
the sum of Zahir’s monthly salary and Sohel’s monthly salary is Tk. 50,000, what is the monthly salary
of Abir?
(A) 6,000 (B) 7,500 (C) 8,500 (D) 10,500 (E) none
05. In 2009. Aslam’s salary was 25 percent higher than it was in 2008. In 2010, Aslam’s salary was fixed at
110 percent of 2008 annual salary. Aslam’s salary in 2010 was what percent less than his salary in
2009?
(A) 12 (B) 13 (C) 15 (D) 20 (E) none of these
06. The number of marbles in box X is 42% of the number of marbles in box Y. The number of marbles in box
Y is approximately what percent of the total number of marbles in boxes X and Y?
(A) 58 (B) 68.4 (C) 70.4 (D) 72.5 (E) 75
07. A survey of x people found 60% preferred brand A. An additional y people were surveyed who all
preferred brand A. Seventy percent of the total people surveyed preferred brand A. Find y in terms of x.
(A) x/3 (B) x/6 (C) x/2 (D) x/4 (E) none of these
08. Jar Y has 10% more marbles than Jar X . What percent of marbles from Jar Y need to be moved into X
so that both jars have equal marbles
(A) 4.54% (B) 9.09% (C) 10% (D) 11% (E) 12.25 %

09. If 15% of x is same as 20 % of y then x : y is

(A) 6 : 5 (B) 3 : 4 (C) 5 : 4 (D) 4 : 3 (E) 5:6

10. If 10% of x is 3 times 15% of y, then find x : y.

(A) 8 : 3 (B) 11 : 4 (C) 9 : 2 (D) 7 : 2 (E) 5:6

11. Given A is 50% larger than C and B is 25% larger than C, then A is what percent larger than B ?

(A) 75% (B) 20% (C) 25% (D) 50% (E) 60%

Bank Job Recruitment Test Preparatory ProgramMath Lecture No.-10©MasterClass Page 1

12. 0.01 is what per cent of 0.1?

(A) 100 (B) 1/100 (C) 10 (D) 1/10 (E) 1/1000

13. If 8% of x is the same as 4% of y, then 20% of x is the same as:

(A) 80% of y (B) 50% of y (C) 10% of y (D) 16% of y (E) 20% of y

3 5
14. A student multiplied a number by 5 instead of . What is the percentage error in the calculation ?
3

(A) 54% (B) 64% (C) 44% (D) 34% (E) 60%

15. In a college, 40% of the students were allotted group A, 75% of the remaining were given group B and
the remaining 12 students were given group C. Then the number of students who applied for the group is

(A) 80 (B) 92 (C) 100 (D) 60 (E) 75

b +a
16. If 120% of a is equal to 80% of b, then is equal to
b −a

(A) 7 (B) 8 (C) 5 (D) 6 (E) 9

17. If 90% of A = 30% of B and B = 2x% of A, then the value of x is

(A) 300 (B) 150 (C) 450 (D) 400 (E) 120

18. 0.005 is equivalent to

(A) 0.05% (B) 0.5% (C) 50% (D) 5% (E) 500%

Step 2: Percentage Change

19. An economist estimates that the cost of living will increase by 8.50 percent over the next three years. How
much should a piece of candy cost in three years if it cost Tk. 1.50 today?
(A) Tk 12.75 (B) Tk 0.1275 (C) Tk 1.37
(D) Tk 1.63 (E) None of these
20. In January, 55 percent of a hospital’s 300 patients were women. In February, 30 percent of its 440 patients
were women. What was the percent change in the number of women patients from January to February?
(A) decrease of 20% (B) increase of 20% (C) decrease of 25%
(D) increase of 25% (E) none of these

Bank Job Recruitment Test Preparatory ProgramMath Lecture No.-10©MasterClass Page 2

21. A number is divided by 3/7 and then multiplied by 5/8. The net effect (approx) is
(A) the number decreases by 22%
(B) the number increases by 46%
(C) the number decreases by 33%
(D) the number increases by 33%
(E) none of these
22. A box contains 24 red socks and 43 green socks. How many green socks must be removed from the box so
that 60% of the socks in the box will be green?
(A) 6 (B) 7 (C) 8 (D) 9 (E) none of these
23. When the per unit production cost of an item is Tk 80 and other costs per unit is Tk 20, the producer makes a
profit of 15% on his total cost. If the production cost decreases by 20% and the selling price remains the
same, calculate the profit in Tk.
(A) 31 (B) 34 (C) 35 (D) 43 (E) none of these
24. If A = x% of y and B = y% of x, then which of the following is true?
(A) A is smaller than B.
(B) A is greater 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) None of the above

25. The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase
of population per year is:

(A) 4.37% (B) 5% (C) 6% (D)8.75% (E) 5.25%

26. The annual report for Basundhara Group stated that profits were up 10 percent over the previous year,
although profits as a percent of sales were down 10 percent. Total sales for that year were approximately
what percent of sales for the previous year?
(A) 78% (B) 90% (C) 110% (D) 122% (E) 190%

27. In a certain year the price of rice rose by 20% during January, fell by 20% during February, rose by 25%
during March, and fell by x% during April. The price of rice at the end of April was the same as it had
been at the beginning of January. To the nearest integer, what is x?

(A) 12 (B) 17 (C) 20 (D) 25 (E) 35

Bank Job Recruitment Test Preparatory ProgramMath Lecture No.-10©MasterClass Page 3

28. CDA expects Chittagong’s population to increase by 10% per year over the next two years. If that
projection were to come true, the population two years from now would be exactly double the population
of one year ago. Which of the following is closest to the percent population increase in Chittagong over
the last year?

(A) 20% (B) 40% (C) 50% (D) 65% (E) 75%

29. If m > 0 and x is m percent of y, then, in terms of m, y is what percent of x?

(A) 100m (B) 1/100m (C) 1/m (D) 10/m (E) 10000/m

Step 3: Successive Increase/Decrease in Percent

30. The potato traders have increased the original price of potatoes by 20% by creating a false shortage of
supply. Govt. intervened into the scene and forced the traders to reduce their price by 20% of new price and
stick to that. Currently the traders are selling potatoes with a loss/gain of what percentage over the original
price?
(A) 4% loss (B) 4% gain (C) 5.5% gain
(D) 6% loss (E) neither gain nor loss
31. A colony of 15,000 ants increased by 50% after being fed. Then after 4 weeks without food, the number of
ants dropped by 60%. What percentage decline did the original population undergo?
(A) 72.5 (B) 75 (C) 90 (D) 95.5 (E) none of these
32. The price of sugar increases by 20%. By what percent must a housewife reduce the consumption of sugar,
so that the expenditure on sugar is the same as before?
(A) 80 (B) 20 (C) 16.66 (D) 83.33 (E) 15
33. If the length of each side of an equilateral triangle were increased by 50 percent, what would be the
percent increase in the area?
(A) 75% (B) 100% (C) 125% (D) 150% (E) 225%
34. A number is decreased by 10% and the resulting number is again decreased by 20%. What is the final
percentage of decrease?
(A) 26% (B) 28% (C) 27% (D) 25% (E) 30%
35. Salary of a person is first increased by 20%, then it is decreased by 20%. Percentage change in his salary
is :
(A) 4% increased (B) 20% increased (C) 8% decreased (D) 4% decreased

Step 4: Consumption & Remaining

36. The price of petrol is increased by 25%. By how much per cent a car owner should reduce his
consumption of petrol so that the expenditure on petrol would not be increased ?
(A) 20% (B) 30% (C) 25% (D) 50% (E) 45%

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37. Price of sugar rises by 20%. By how much percent should the consumption of sugar be reduced so that
the expenditure does not change?
2
(A) 15% (B) 10% (C) 20% (D) 163% (E) 25%

38. Price of a commodity has increased by 60%. By what per cent must a consumer reduce the consumption
of the commodity so as not to increase the expenditure?
(A) 60% (B) 37.5% (C) 37% (D) 40.5% (E) 45%

39. If food prices go up by 10%, by how much should a man reduce his consumption so as not to increase
his expenditure?

1 1
(A) The data is not sufficient (B) 10% (C) 9 11 % (D) 11 9% (E) 25%

40. If the price of rice be raised by 25%, the percent by which a house-holder must reduce his consumption
of rice so as not to increase his expenditure on rice is

(A) 20% (B) 25.75% (C) 225% (D) 25% (E) 40%

Step 5: Written Problems

01. The population of a village is 25,000. One fifth are females and the rest are males. 5% of males and 40%
of females are uneducated. What percentage on the whole are educated?

02. If 50% of (x – y) = 30% of (x + y), then what per cent of x is y?

2A − 3B
03 If 40% of (A + B) = 60% of (A – B) then find the value of .
A +B

04. If 50% of (P – Q) = 30% of (P + Q) and Q = x% of P, then find the value of x.

05. Out of two numbers, 40% of the greater number is equal to 60% of the smaller. If the sum of the
numbers is 150, then find the greater number.

06. A man spends 75% of his income. His income increases by 20% and his expenditure also increases by
10%. What is the percentage of increase in his savings?

Bank Job Recruitment Test Preparatory ProgramMath Lecture No.-10©MasterClass Page 5

 Review of Concepts

Percentages
A percent is just a shorthand way of expressing a fraction whose denominator is 100. Percent means “per
100”, “out of 100”, or “divided by 100”. For example, 25% = 25/100 = 0.25 and 0.3% = 0.3/100 = 0.003. In
terms of money, 50 cents out of a dollar is 50 cents out of 100, which is 50/100 of a dollar or 50% of a
dollar.
To find a percentage of something, the percents must be converted to decimals and then multiplied by
some number. Never directly add and/or subtract percent’s; must you first multiply them by something?
When finding percentages, convert the sentence into a mathematical equation. For example, “5 is what
percent of 100” can be converted into “5 = x (100)” where x is the percent you are looking for.
When working with percents, it is usually necessary to convert percents to decimals before performing
computations with them. Since a percent is just a fraction with denominator 100, you convert a percent to a
decimal by moving the decimal point two places from right to left. For example, 6% is equivalent to (.06).
In the following example, it is necessary to convert the percent to a decimal.

Example 1:
What is 30 percent of 200?
To find 30% of 200, convert 30% to .30. Then multiply 200 by .30, which results in 60. Hence, 60 is 30% of
200.
To convert a decimal to a percent, move the decimal point two places from left to right and add a % sign.
For example, 0.8 = 80% and 0.02 = 2%.
To convert a percent to a fraction, just make the percent the numerator of a fraction with denominator 100 and
reduce the fraction. For example, 40% = 40/100 = 4/10 = 2/5.
To convert a fraction to a percent, divide the numerator by the denominator and move the decimal point
two places to the right.
Example 2:
Express 4/5 as a percent.
To do so, use long division and move the decimal point. 5 divided into 4 is 0.8 which is equivalent to 80%.
Hence, 4/5 = 0.8 = 80%.
Successive Increase/Decrease in Percent
If a number is increased by a% and then it is decreased by b%, then resultant change in percentage will be:

ab
(a− b− 100 )%

Consumption & Remaining

If the quantity of one variable is A% more than another variable, then quantity of another variable is less in
comparison to the 1st variable by
A
((100+A)×100)%

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 Answer Keys:
01. B 02. D 03. C 04. A 05. A 06. C 07. A 08. A 09. D 10. C
11. B 12. C 13. C 14. B 15. A 16. C 17. B 18. B 19. D 20. A
21. B 22. B 23. A 24. E 25. B 26. D 27. B 28. D 29. E 30. A
31. E 32. C 33. C 34. B 35. D 36. A 37. D 38. B 39. C 40. A

Written Problems
𝟕
01. 88% 02. 25% 03. 04. 25 05. 90 06. 50%
𝟔

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 Basic Discussions

𝟏
Per Cent = 𝟏𝟎𝟎 = %

𝟏
𝟏𝟎𝟎 % = 𝟏𝟎𝟎 × =𝟏
𝟏𝟎𝟎

How to convert fraction to percentage:

𝟏 𝟏 𝟏
= ×𝟏 = × 𝟏𝟎𝟎% = 𝟓𝟎%
𝟐 𝟐 𝟐

Bank Job Recruitment Test Preparatory ProgramMath Lecture No.-10©MasterClass Page 8

04. Abir’s monthly salary is equal to 30% of Zahir’s monthly salary or 20% of Sohel’s monthly
salary. If the sum of Zahir’s monthly salary and Sohel’s monthly salary is Tk. 50,000, what is the
monthly salary of Abir?
(A) 6,000 (B) 7,500 (C) 8,500 (D) 10,500 (E) none
Solution:
Let,
Zahir’s monthly salary = 𝑇𝑘 𝑥
And, Sohel’s monthly salary = 𝑇𝑘 𝑦
According to the 1st condition,
𝑥 × 30% = 𝑦 × 20%
30 20
𝑥 × =𝑦 ×
100 100
3 1
𝑥 × =𝑦 ×
10 5
3𝑥
=𝑦
2

3𝑥
∴𝑦=
2
According to the 2nd condition,
𝑥 + 𝑦 = 50000
3𝑥
𝑥+ = 50000
2
2𝑥+3𝑥
= 50000
2

5𝑥 = 100000

∴ 𝑥 = 20000
Hence,
Abir’s monthly salary = 𝑇𝑘 (20000 × 30%)
3
= 𝑇𝑘 ( 20000 × )
10
= 𝑇𝑘 6000
Answer: A
07. A survey of x people found 60% preferred brand A. An additional y people were surveyed who all
preferred brand A. Seventy percent of the total people surveyed preferred brand A. Find y in
terms of x.
(A) x/3 (B) x/6 (C) x/2 (D) x/4 (E) none of these

Bank Job Recruitment Test Preparatory ProgramMath Lecture No.-10©MasterClass Page 9

Solution:
According to the question,
𝑥 × 60% + 𝑦 = (𝑥 + 𝑦) × 70%
3 7
𝑥 × 5 + 𝑦 = 𝑥 + 𝑦 × 10
3𝑥 7𝑥+7𝑦
+𝑦 =
5 10
3𝑥+5𝑦 7𝑥+7𝑦
=
5 10
7𝑥+7𝑦
3𝑥 + 5𝑦 = 2

7𝑥 + 7𝑦 = 6𝑥 + 10𝑦
7𝑥 − 6𝑥 = 10𝑦 − 7𝑦
𝑥 = 3𝑦
𝑥
∴𝑦=
3
Answer: A

12. 0.01 is what per cent of 0.1?

(A) 100 (B) 1/100 (C) 10 (D) 1/10 (E) 1/1000

Solution:

is
× 100%
of
0.01
= × 100%
0.1
1
= %
0.1
1 × 10
= %
0.1 × 10

= 10 %

Answer: C

Alternative

Let,

0.01 is x percent of 0.1

Bank Job Recruitment Test Preparatory ProgramMath Lecture No.-10©MasterClass Page 10
According to the question,

0.1 × 𝑥 % = 0.01
0.1𝑥
= 0.01
100

0.1𝑥 = 1
1
𝑥 = 0.1

∴ 𝑥 = 10

Answer: C

𝟑 𝟓
14. A student multiplied a number by 𝟓 instead of . What is the percentage error in the calculation?
𝟑

(A) 54% (B) 64% (C) 44% (D) 34% (E) 60%

Solution:

Let,

The original number = 𝑥

5
Actual Multiplication = 𝑥 × 3

5𝑥
=
3
3
Student multiplied = 𝑥 × 5

3𝑥
=
5
5𝑥 3𝑥
∴ Error in calculation = 3
− 5

25𝑥 − 9𝑥
=
15

16𝑥
=
15

Hence,
16x
15
The percentage error in the calculation = ( 5x × 100)%
3

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 16𝑥 3
= × × 100 %
15 5𝑥

= 64 %

Answer: B

22. A box contains 24 red socks and 43 green socks. How many green socks must be removed from the
box so that 60% of the socks in the box will be green?
(A) 6 (B) 7 (C) 8 (D) 9 (E) none of these
Solution:
We need 60% green socks

∴ Obviously rest 100 − 60 % 𝑜𝑟 40% socks are red.

According to the question,
40% of total socks = 24
24
∴ 1% of total socks = 40
24 × 100
∴ 100% of total socks = 40
= 60

∴ The number of Green socks is = 60 − 24 = 36

Hence,
The number of green socks must be removed = 43 − 36 = 7
Answer: B
24. If A = x% of y and B = y% of x, then which of the following is true?
(A) A is smaller than B.
(B) A is greater 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) None of the above

Solution:

Given,

𝐴= 𝑦 ×𝑥%
𝑥
= 𝑦 ×
100
𝑥𝑦
=
100

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 And, 𝐵 = 𝑥 × 𝑦 %
𝑦
= 𝑥 ×
100
𝑥𝑦
=
100

∴𝐴=𝐵
Answer: E

26. The annual report for Basundhara Group stated that profits were up 10 percent over the previous
year, although profits as a percent of sales were down 10 percent. Total sales for that year were
approximately what percent of sales for the previous year?
(A) 78% (B) 90% (C) 110% (D) 122% (E) 190%

Question Explanation:

Last Year Profit = 100

This year profit = 110

Last year sales = 1000

This year sales = 2200

100
Last year profit as a percent of sales = 1000 × 100% = 10%

110
This year profit as a percent of sales = 2200 × 100% = 5%
Solution:

Let,

Last year profit = 100

∴ This year profit = 100 + (100 × 10%)

= 100 + 10

= 110

Again,

Let,

Last year sales = 100

And, This year sales = 𝑥

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 100
∴ Last year profit percent of sales = (100 × 100)%

= 100 %
110
∴ This year profit percent of sales = ( 𝑥
× 100 )%

11000
= %
𝑥
According to the question,

11000
100 − 10 =
𝑥
11000
90 = 𝑥

11000
𝑥= 90

∴ 𝑥 = 122.22
Therefore,
122.22
The sales this year is approximately × 100 % or 122.22 % of the sales last year.
100

Answer: D

27. In a certain year the price of rice rose by 20% during January, fell by 20% during February, rose
by 25% during March, and fell by x% during April. The price of rice at the end of April was the
same as it had been at the beginning of January. To the nearest integer, what is x?

(A) 12 (B) 17 (C) 20 (D) 25 (E) 35

Solution:

Let,

The price of rice at the beginning of January was = 𝑇𝑘 100

∴ The price of rice during January = 𝑇𝑘 {100 + (100 × 20%}

= 𝑇𝑘 120

∴ The price of rice during February = 𝑇𝑘 {120 − 120 × 20% }

= 𝑇𝑘 96

∴ The price of rice during March = 𝑇𝑘 {96 + 96 × 25% }

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 = 𝑇𝑘 120
According to the question,

120 − (120 × 𝑥 %) = 100

𝑥
120 − (120 × ) = 100
100

6𝑥
120 − = 100
5

6𝑥
= 120 − 100
5

6𝑥
= 20
5

∴ 𝑥 = 16.67% 𝑜𝑟 17%
Answer: B

28. CDA expects Chittagong’s population to increase by 10% per year over the next two years. If that
projection were to come true, the population two years from now would be exactly double the
population of one year ago. Which of the following is closest to the percent population increase in
Chittagong over the last year?

(A) 20% (B) 40% (C) 50% (D) 65% (E) 75%

Solution:

Let,

The population of Chittagong this year = 100

∴ The population of Chittagong after 1 year = 100 + (100 × 10%)

= 110

∴ The population of Chittagong after 2 years = 110 + (110 × 10%)

= 121
121
∴ The population of Chittagong 1 year ago = 2

= 60.5
∴ The population of Chittagong increased over the last year = 100 − 60.5
= 39.5

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Hence,
39.5
The percent of population increased over the last year = ( × 100 )%
60

= 65.29 %
Answer: D

Successive Increase/Decrease in percent:

Problem Number: 30, 31, 33, 34, 35

𝐀 ×𝐁
𝐀+𝐁 +
𝟏𝟎𝟎
Increase = +
Decrease = −

30. The potato traders have increased the original price of potatoes by 20% by creating a false shortage of
supply. Govt. intervened into the scene and forced the traders to reduce their price by 20% of new
price and stick to that. Currently the traders are selling potatoes with a loss/gain of what percentage
over the original price?
(A) 4% loss (B) 4% gain (C) 5.5% gain (D) 6% loss
Solution:
We know,
𝐴 ×𝐵
𝐴+𝐵 +
100
20 × (−20)
= 20 + (−20) +
100
= −4

Answer: A

Written Format
Let,
The original price of potatoes = 𝑇𝑘 100
After 20% increase in price,
The present price of potatoes = 𝑇𝑘 {100 + (100 × 20%)}
= 𝑇𝑘 120

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Again,
After 20% decrease in price,
The present price of potatoes = 𝑇𝑘 {120 − (120 × 20%)}
= 𝑇𝑘 96
Hence,
100−96
Loss percentage = ( × 100)%
100

= 4%
Answer: A

Consumption & Remaining:

Problem Number: 32, 36, 37, 38, 39, 40

𝟏𝟎𝟎 × 𝐑
𝐑𝐞𝐪𝐮𝐢𝐫𝐞𝐝 𝐏𝐞𝐫𝐜𝐞𝐧𝐭𝐚𝐠𝐞 =
𝟏𝟎𝟎 ± 𝐑
Increase = +
Decrease = −

32. The price of sugar increases by 20%. By what percent must a housewife reduce the consumption of
sugar, so that the expenditure on sugar is the same as before?
(A) 80 (B) 20 (C) 16.66 (D) 83.33 (E) 15
Solution:
We Know,
100 × 𝑅
𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 =
100 + 𝑅
100 × 20
=
100 + 20
100 × 20
=
120
= 16.67 %
Answer: C
Written Format
Let,
The previous price of sugar was = Tk 100

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After 20% increase,
The new price of sugar is = 𝑇𝑘 {100 + 100 × 20% }
= 𝑇𝑘 120

∴ Price of sugar increased = 𝑇𝑘 (120 − 100)

= 𝑇𝑘 20

∴ In Tk 120 the use of sugar should be decreased = Tk 20

20
∴ In Tk 1 the use of sugar should be decreased = Tk 120
20×100
∴ In Tk 100 the use of sugar should be decreased = Tk 120

= 𝑇𝑘 16.67
Answer: C

Extra Math: When the price of rice is reduced by 25%, then at what percent should the
use of rice be increased so that there will be no change in the expenditure for the use of
rice?
Solution:
We Know,
100 × 𝑅
𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 =
100 − 𝑅
100 × 25
=
100 − 25
100 × 25
=
75
= 33.33 %
Answer: 33.33 %
Written Format
Let,
The previous price of rice was = Tk 100
After 20% reduced,
The new price of rice is = 𝑇𝑘 {100 − 100 × 25% }
= 𝑇𝑘 75

∴ Price of rice reduced = 𝑇𝑘 (100 − 75)

= 𝑇𝑘 25

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∴ In Tk 75 the use of rice should be increased = Tk 25
25
∴ In Tk 1 the use of rice should be increased = Tk 75
25×100
∴ In Tk 100 the use of rice should be increased = Tk 75

= 𝑇𝑘 33.33
Answer: 33.33 %

33. If the length of each side of an equilateral triangle were increased by 50 percent, what would be the
percent increase in the area?
(A) 75% (B) 100% (C) 125% (D) 150% (E) 225%
Solution:
We know,
𝐴 ×𝐵
𝐴+𝐵 +
100
50 × 50
= 50 + 50 +
100
= 125

Answer: C
Written Format
Let,
The length of each side of an equilateral triangle = 𝑎 𝑢𝑛𝑖𝑡𝑠
3
∴ The area of the equilateral triangle = 𝑎2 𝑠𝑞𝑢𝑎𝑟𝑒 𝑢𝑛𝑖𝑡𝑠
4

After 50% increase,

The length of each side will be = 𝑎 + 𝑎 × 50% 𝑢𝑛𝑖𝑡s
𝑎
= 𝑎+ 𝑢𝑛𝑖𝑡𝑠
2
2𝑎 + 𝑎
= 𝑢𝑛𝑖𝑡𝑠
2
3𝑎
= 𝑢𝑛𝑖𝑡𝑠
2
3 3𝑎 2
∴ The area will be = { 4 × 2
} 𝑠𝑞𝑢𝑎𝑟𝑒 𝑢𝑛𝑖𝑡𝑠

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 9 3 2
= 𝑎 𝑠𝑞𝑢𝑎𝑟𝑒 𝑢𝑛𝑖𝑡𝑠
16
9 3 3
∴ The area increased = 𝑎2 − 𝑎2 𝑠𝑞𝑢𝑎𝑟𝑒 𝑢𝑛𝑖𝑡𝑠
16 4

9 3𝑎2 − 4 3𝑎2
= 𝑠𝑞𝑢𝑎𝑟𝑒 𝑢𝑛𝑖𝑡𝑠
16
5 3𝑎2
= 𝑠𝑞𝑢𝑎𝑟𝑒 𝑢𝑛𝑖𝑡𝑠
16
3a 2 5 3𝑎 2
∴ In 4
square units the area increased 16
square units

5 3a 2 ×4
∴ In 1 square unit the area increased 16× 3a 2
square units

5 3a 2 ×4×100
∴ In 100 square units the area increased 16× 3a 2
square units

= 125 square units

Answer: C

Written Problems
01. The population of a village is 25,000. One fifth are females and the rest are males. 5% of males
and 40% of females are uneducated. What percentage on the whole are educated?

Solution:

Given,

The number of Total Population = 25000

1
∴ The number of Females = 25000 × 5

= 5000

∴ The number of Males = 25000 − 5000

= 20000
∴ The number of uneducated males = 20000 × 5%
= 1000

∴ The number of uneducated females = 5000 × 40%

= 2000

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∴ The number of educated persons = 25000 − (1000 + 2000)
= 22000
22000
∴ The percentage of educated persons = ( 25000 × 100 )%
= 88 %

Answer: 88 %
06. A man spends 75% of his income. His income increases by 20% and his expenditure also increases
by 10%. What is the percentage of increase in his savings?
Solution:

Let,
His income = 𝑇𝑘 100

∴ His expense = 𝑇𝑘 (100 × 75%)

= 𝑇𝑘 75

∴ His savings = 𝑇𝑘 (100 − 75)

= 𝑇𝑘 25
After 20% increase,
His income will be = 𝑇𝑘 {100 + 100 × 20% }
= 𝑇𝑘 120
After 10% increase,
His expense will be = 𝑇𝑘 {75 + 75 × 10% }
= 𝑇𝑘 82.50

∴ His savings will be = 𝑇𝑘 (120 − 82.50)

= 𝑇𝑘 37.50

∴ His savings will increase = 𝑇𝑘 (37.50 − 25)

= 𝑇𝑘 12.50
Hence,
12.50
The percentage of increase in his savings = × 100 %
25

= 50 %
Answer: 50 %

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