Percentage and Profit & Loss

PrepBank · পাতা ১২ / ১৭ · ১,১০১–১,২০০ / ১,৬৯৬

১,১০১.

Out of 7,500 applications for a recruitment test, 1,500 failed to appear for the test. What percent of the total applicants did appear for the test?

ক
ক) 25
খ
খ) 50
গ
গ) 75
ঘ
ঘ) 80

ব্যাখ্যা

Question: Out of 7,500 applications for a recruitment test, 1,500 failed to appear for the test. What percent of the total applicants did appear for the test?

Solution:
পরীক্ষার্থী = ৭৫০০ জন
অনুপস্থিত = ১৫০০ জন
উপস্থিত = ৭৫০০ - ১৫০০ জন
= ৬০০০ জন

শতকরা উপস্থিত = ৬০০০ ×১০০%/৭৫০০
= ৮০%

১,১০২.

Rahim invested in all Tk. 2,600 in three different schemes at 8%, 4% and 6% per annum simple interest. At the end of the year, he received the same interest in all the three schemes. What is the money invested in scheme having 4% rate of interest?

ক
ক) Tk. 700
খ
খ) Tk. 800
গ
গ) Tk. 750
ঘ
ঘ) Tk. 1,200

ব্যাখ্যা

Question: Rahim invested in all Tk. 2,600 in three different schemes at 8%, 4% and 6% per annum simple interest. At the end of the year, he received the same interest in all the three schemes. What is the money invested in scheme having 4% rate of interest?

Solution:
Rahim invested Tk. 2600 at 4%, 6% and 8% respectively.
Let the three parts be x, y and z.

(x × 4 × 1)/100 = (y × 6 × 1)/100 = (z × 8 × 1)/100
4x =6y = 8z
2x = 3y = 4z

Now
2x = 3y
x/y = 3/2
x : y = 3 : 2

3y = 4z
y/z = 4/3
y : z = 4 : 3

x : y : Z = 6 : 4 : 3

Sum invested at 4%= Tk. (6 × 2600)/13
= Tk .1200

১,১০৩.

During an election, the victorious candidate received 70% of the votes and won with a margin of 60,000 votes. How many total votes were cast?

ক
170,000
খ
250,000
গ
130,000
ঘ
150,000

ব্যাখ্যা

Question: During an election, the victorious candidate received 70% of the votes and won with a margin of 60,000 votes. How many total votes were cast?

Solution:
Let, The victorious candidate secured 0.70x votes,
and the losing candidate secured 0.30x votes.

ATQ,
0.70x - 0.30x = 60,000
⇒ 0.40x = 60,000
⇒ x = 60,000 / 0.40
= 150,000

Thus, the total number of votes cast was 150,000.

১,১০৪.

A manufacturer sells three products i.e. X, Y and Z. Product X costs 250 and sells for 330, Product Y costs 150 and sells for 210. Product Z costs 100 and sells 120. On which product, he has maximum percentage of profit?

ক
X only
খ
Y only
গ
X and Y both
ঘ
Z only

ব্যাখ্যা

Question: A manufacturer sells three products i.e. X, Y and Z. Product X costs 250 and sells for 330, Product Y costs 150 and sells for 210. Product Z costs 100 and sells 120. On which product, he has maximum percentage of profit?

Solution:
We know that,
Profit Percentage = {(Selling Price − Cost Price)/Cost Price } × 100

Product X,
Profit = 330 − 250 = 80
Profit Percentage = (80/250) × 100 = 32%

Product Y,
Profit = 210 − 150 = 60
Profit Percentage = (60/150) × 100 = 40%

Product Z,
Profit = 120 − 100 =20
Profit Percentage = (20/100) × 100 = 20%

∴ Product Y has the highest profit percentage of 40%.

১,১০৫.

A reduction of 20% in the price of sugar enables a housewife to purchase 6 kg more for Tk. 240. What is original price per kg of sugar?

ক
Tk. 10
খ
Tk. 18
গ
Tk. 25
ঘ
Tk. 22

ব্যাখ্যা

Question: A reduction of 20% in the price of sugar enables a housewife to purchase 6 kg more for Tk. 240. What is original price per kg of sugar?

Solution:
Given that,
Price of sugar reduced by 20%.
With Rs. 240, she can buy 6 kg more sugar than before.
Let the original price per kg of sugar be x Rs.

Now,
Original quantity she could buy for Tk. 240,
∴ Quantity = 240/x kg

After 20% reduction, new price per kg = Tk. 0.8x
∴ Quantity = 240/0.8x = 240/(4x/5) = 1200/4x = 300/x kg

ATQ,
⇒ (300/x) - (240/x) = 6
⇒ (300 - 240)/x = 6
⇒ 60/x = 6
⇒ x = 60/6
∴ x = 10

So the original price per kg of sugar = Tk. 10

১,১০৬.

If 8% of x is the same as 4% of y, then 20% of x represents-

ক
50% of y
খ
10% of y
গ
70% of y
ঘ
40% of y

ব্যাখ্যা

Question: If 8% of x is the same as 4% of y, then 20% of x represents-

Solution:
Given that,
If 8% of x is the same as 4% of y

Now,
8% of x = 4% of y
⇒ (8/100)x = (4/100)y
⇒ x = 4y/8
⇒ x = y/2 .........(1)

Again,
We calculate,
= 20% of x
= 20% of y/2 ;[Substitute x = y/2]
= 20% × (y/2)
= 10% × y

Thus, 20% of x represents 10% of y.

১,১০৭.

A company pays rent of Tk. 20000 per month for office space to its owner. But if the company pays the annual rent at the beginning of the year the owner gives a discount of 5% on the total annual rent. What is the annual amount the company pays to the owner after the discount?

ক
ক) Tk. 225000
খ
খ) Tk. 228000
গ
গ) Tk. 227000
ঘ
ঘ) Tk. 226000

ব্যাখ্যা

Question: A company pays rent of Tk. 20000 per month for office space to its owner. But if the company pays the annual rent at the beginning of the year the owner gives a discount of 5% on the total annual rent. What is the annual amount the company pays to the owner after the discount?

Solution:
Total annual rent = Tk. (20000 × 12) = Tk. 240000
Discount = 5% of tk. 240000
= Tk. 12000
∴ Annual rent paid after discount = Tk. (240000 - 12000)
= Tk. 228000

১,১০৮.

A vendor bought 6 oranges for Tk. 10 and sold them at 4 for Tk. 6. Find his loss or gain percent.

ক
8% gain
খ
10% gain
গ
8% loss
ঘ
10% loss

ব্যাখ্যা

Question: A vendor bought 6 oranges for Tk. 10 and sold them at 4 for Tk. 6. Find his loss or gain percent.

Solution:
Suppose, number of oranges bought = LCM of 6 and 4 = 12
∴ CP of 12 oranges = (10/6) × 12 = Tk. 20
and SP of 12 oranges = (6/4) × 12 = Tk. 18
∴ Loss = 20 - 18 = 2

∴ Loss% = (2/20) × 100% = 10%

১,১০৯.

A man sells two articles at Tk.99 each. He gains 10% on one and loss 10% on the other. Then on overall basis he-

ক
ক) Tk. 1
খ
খ) Tk. 5
গ
গ) Tk. 10
ঘ
ঘ) Tk. 2

ব্যাখ্যা

Total Selling Price= Tk.(2×99)
= Tk.198
C.P. of first article = Tk. {(100/110) × 99}
= Tk. 90

C.P. of second article = Tk. {(100/90) × 99}
= Tk. 110
Total C.P.= Tk.(90 + 110)
= Tk. 200
∴Loss= Tk.(200−198)= Tk. 2

১,১১০.

A student mistakenly multiplied a number by 7/10 instead of 7/5. Find the percentage error in the result.

ক
5%
খ
50%
গ
10%
ঘ
12%

ব্যাখ্যা

Question: A student mistakenly multiplied a number by 7/10 instead of 7/5. Find the percentage error in the result.

Solution:
Let
The number is 100.

ATQ,
The actual calculation be: (7/5) × 100 = 140
and error calculation be: (7/10) × 100 = 70

∴ Difference = 140 - 70 = 70

∴ Percentage error = (70/140) × 100 = 50%

১,১১১.

A reduction of 20% in the price of chocolates enables a man to buy 20 chocolates more for Tk. 40. The price per chocolate before the reduction was

ক
40 paisa
খ
50 paisa
গ
1 taka
ঘ
1 taka 40 paisa

ব্যাখ্যা

Question: A reduction of 20% in the price of chocolates enables a man to buy 20 chocolates more for Tk. 40. The price per chocolate before the reduction was

Solution:
বর্তমান মূল্য ৮০ টাকা হলে পূর্বমূল্য ১০০ টাকা
বর্তমান মূল্য ১ টাকা হলে পূর্বমূল্য ১০০/৮০ টাকা
বর্তমান মূল্য ৪০ টাকা হলে পূর্বমূল্য ১০০ টাকা (১০০/৮০) × ৪০ টাকা
= ৫০ টাকা

২০ টি চকলেটের দাম (৫০ - ৪০) টাকা = ১০ টাকা
১ টি চকলেটের দাম = ১০/২০ টাকা
= ০.৫ টাকা
= ৫০ পয়সা

১,১১২.

A vendor purchased 45 dozen bananas for Tk. 250. Out of these 40 bananas were rotten and could not be sold. At what rate per dozen should he sell the remaining bananas to make a profit of 20%?

ক
ক) Tk. 5.5
খ
খ) Tk. 6
গ
গ) Tk. 7.2
ঘ
ঘ) Tk. 9

ব্যাখ্যা

Question: A vendor purchased 45 dozen bananas for Tk. 250. Out of these 40 bananas were rotten and could not be sold. At what rate per dozen should he sell the remaining bananas to make a profit of 20%?

Solution:
Total bananas = 45 × 12 = 540
Total good bananas = 540 - 40 = 500
Cost price of 540 bananas = Tk. 250

At 20% profit selling price of 500 bananas = 120% of 250 = Tk. 300
∴ Selling price of 1 banana = (300/500) = 3/5
∴ The selling price of 12 bananas = (3/5) × 12 = Tk. 7.2

So, the selling price of 1 dozen bananas is Tk. 7.2

১,১১৩.

A candidate scoring 25% marks in an examination fails by 10 marks while another candidate who score 50% marks get 15 marks more than the minimum pass marks. What is the minimum pass mark?

ক
35
খ
45
গ
50
ঘ
65
ঙ
100

ব্যাখ্যা

Question: A candidate scoring 25% marks in an examination fails by 10 marks while another candidate who score 50% marks get 15 marks more than the minimum pass marks. What is the minimum pass mark?

Solution:
Let total mark = m

ATQ,
(m × 25%) + 10 = (m × 50%) – 15
⇒ (m/4) + 10 = (m/2) - 15
⇒ (m/2) - (m/4) = 15 + 10
⇒ m/4 = 25
⇒ m = 100

∴ minimum pass mark = (m/4) + 10
= (100/4) + 10
= 25 + 10
= 35

১,১১৪.

Akash multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?

ক
50%
খ
57%
গ
64%
ঘ
68%

ব্যাখ্যা

Question: Akash multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?

Solution:
Let the number be x

Error = (5x/3) - (3x/5)
= (25x - 9x)/15
= 16x/15

% Error ={(16x/15) × (3/5x) × 100}% = 64%

১,১১৫.

A school has only four classes having 10, 20, 30 and 40 students respectively with pass percentage of 20%, 30%, 60% and 100% respectively. Find the pass percentage of the entire school.

ক
ক) 56%
খ
খ) 76%
গ
গ) 34%
ঘ
ঘ) 66%

ব্যাখ্যা

Pass Candidates of first class
= 20% of 10
= 2

Pass Candidates of second class
= 30% of 20
= 6

Pass Candidates of third class
= 60% of 30
= 18

Pass Candidates of fourth class
= 100% of 40
= 40

Total Pass Candidate
= 2 + 6 + 18 + 40
= 66

Total no of Student
= 10 + 20 + 30 + 40
= 100

Pass %
= (66/100) × 100
= 66%

১,১১৬.

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

ক
54%
খ
34%
গ
44%
ঘ
64%

ব্যাখ্যা

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

Solution:
Let, the number be x.
Then, error = (5/3)x - (3/5)x
= (25x - 9x)/15
= 16x/15

Error% = {(16x/15) × (3/5x) × 100}%
= 64%

১,১১৭.

A sells an article to B at gain of 25% B sells it to C at a gain of 20% and C sells it to D at a gain 10%. If D pays Tk. 330 for it, how much did it cost to A?

ক
Tk. 180
খ
Tk. 200
গ
Tk. 225
ঘ
Tk. 250

ব্যাখ্যা

Question: A sells an article to B at gain of 25% B sells it to C at a gain of 20% and C sells it to D at a gain 10%. If D pays Tk. 330 for it, how much did it cost to A?

Solution:
Let,
Cost Price for A was = 100

Then, CP for B = (100 + 25% of 100) = 125
CP for C = (125 + 20% of 125) = 150
CP for D = (150 + 10% of 150 ) = 165

But, D pay Tk. 660. Then it must be equal to,
165 = 330
1 = 330/165
∴ 100 = {330 × (100/165)} = 200

So, CP for A = Tk. 200

১,১১৮.

An item sells for 250 taka and includes a 25% profit. How much did it originally cost?

ক
Tk. 200
খ
Tk. 180
গ
Tk. 220
ঘ
Tk. 160

ব্যাখ্যা

Question: An item sells for 250 taka and includes a 25% profit. How much did it originally cost?

Solution:
ধরি,
ক্রয়মূল্য = 100 টাকা
∴ 25% লাভে বিক্রয়মূল্য = 100 + (100 এর 25%) = 100 + 25 = 125 টাকা

দেওয়া আছে,
বিক্রয়মূল্য = 250 টাকা

এখন,
বিক্রয়মূল্য 125 টাকা হলে ক্রয়মূল্য = 100 টাকা
∴ বিক্রয়মূল্য 1 টাকা হলে ক্রয়মূল্য = 100/125 টাকা
∴ বিক্রয়মুল্য 250 টাকা হলে ক্রয়মূল্য = (100 × 250)/125 = 200 টাকা

১,১১৯.

If the price of gasoline increases by 25% and Ron intends to spend only 15% more on gasoline, by how much % should he reduce the quantity of gasoline that he buys?

ক
ক) 10%
খ
খ) 12%
গ
গ) 8%
ঘ
ঘ) 6.66%

ব্যাখ্যা

Question: If the price of gasoline increases by 25% and Ron intends to spend only 15% more on gasoline, by how much % should he reduce the quantity of gasoline that he buys?

Solution:
25% বৃদ্ধিতে,
গ্যাসোলিনের মূল্য 25% বৃদ্ধিতে, বর্তমান মূল্য = 100 + 25 = 125 টাকা

15% বৃদ্ধিতে,
গ্যাসোলিনের মূল্য 15% বৃদ্ধিতে, বর্তমান মূল্য = 100 + 15= 115 টাকা

বর্তমান মূল্য 125 টাকা হলে পূর্বমূল্য 100 টাকা
বর্তমান মূল্য 1 টাকা হলে পূর্বমূল্য 100/125 টাকা
বর্তমান মূল্য 115 টাকা হলে পূর্বমূল্য (100 × 115)/125 টাকা
=92 টাকা
গ্যাসোলিনের ক্রয় কমাতে হবে = (100 - 92) = 8%

১,১২০.

A man purchases two clocks A and B at a total cost of Tk. 650. He sells A with a 20% profit and B at a loss of 25% and gets the same selling price for both clocks. What are the purchasing prices of A and B respectively?

ক
225, 425
খ
275, 375
গ
300, 350
ঘ
250, 400

ব্যাখ্যা

Question: A man purchases two clocks A and B at a total cost of Tk. 650. He sells A with a 20% profit and B at a loss of 25% and gets the same selling price for both clocks. What are the purchasing prices of A and B respectively?

Solution:
Let
selling price for both clocks is x taka

Purchasing price of A is = x/1.2 taka
Purchasing price of B is = x/0.75 taka

Now
(x/1.2) + (x/0.75 ) = 650
⇒ (100x/120) + (100x/75) = 650
⇒ x/120 + x/75 = 650/100
⇒ x (5 + 8)/600 = 650/100
⇒ x = (650 × 600)/ (100 × 13)
= 300 Taka

Purchasing price of A is = x/1.2 taka = 300/1.2 taka = 250 taka
Purchasing price of B is = x/0.75 taka = 300/0.75 = 400 taka

১,১২১.

(a% of b) + (b% of a) is equal to:

ক
a% of b
খ
2% of ab
গ
2% of 100ab
ঘ
100% of ab

ব্যাখ্যা

Question: (a% of b) + (b% of a) is equal to:

Solution:
According to question
(a% of b) + (b% of a)
= b × (a/100) + a × (b/100)
= (ab/100) + (ab/100)
= 2ab/100
= 2% of ab

১,১২২.

Jalal bought a mobile phone for Taka. 8000 and then sold it at a loss of Taka. 1200. What was the selling price of the mobile phone?

ক
Taka. 5800
খ
Taka. 6800
গ
Taka. 7000
ঘ
Taka. 5600

ব্যাখ্যা

Question: Jalal bought a mobile phone for Taka. 8000 and then sold it at a loss of Taka. 1200. What was the selling price of the mobile phone?

Answer:
Given,
Cost Price (CP) = 8000 Taka
Loss = 1200 Taka
Using Formula
Selling Price (SP) = Cost Price - Loss
⇒ Selling Price (SP) = Taka. 8000 - Taka. 1200
⇒ Selling Price (SP) = Taka. 6800
Therefore, selling price of the mobile phone is Taka. 6800.

১,১২৩.

x% of y is y% of what-

ক
x
খ
10x
গ
100x
ঘ
x/100

ব্যাখ্যা

Question: x% of y is y% of what-

Solution:
let, the number p

x% of y = y% of p
⇒ xy/100 = py/100
∴ p = x

১,১২৪.

If the cost price of 120 mangoes is equal to the selling price of 100 mangoes, what is the profit percent in this transaction?

ক
21%
খ
20%
গ
17%
ঘ
15%

ব্যাখ্যা

Question: If the cost price of 120 mangoes is equal to the selling price of 100 mangoes, what is the profit percent in this transaction?

Solution:
Let the C.P. of 120 mangoes be Tk. 120
As per question,
S.P. of 100 mangoes = Tk. 120

C.P. of 100 mangoes would be = Tk. 100
∴ Profit = (S.P. - C.P.) = 120 - 100 = 20

Profit percent = (20/100) × 100%
= 20%

১,১২৫.

A book is listed at Tk. 920. A customer pays Tk. 742.90 for it after receiving two successive discounts. If the first discount is 15%, what is the rate of the second discount?

ক
5%
খ
7%
গ
8%
ঘ
3%
ঙ
None

ব্যাখ্যা

Question: A book is listed at Tk. 920. A customer pays Tk. 742.90 for it after receiving two successive discounts. If the first discount is 15%, what is the rate of the second discount?

Solution:
MP = 920
After first discount Marked Price (MP) become,
= 920 - 15% of 920 = 782

The Selling Price (SP) = 742.90

Let,
second discount was x% on 782
⇒ 782 - x% of 782 = 742.90
⇒ 782x/100 = 39.1
⇒ 782x = 3910
⇒ x = 5%

∴ Second Discount = 5%

১,১২৬.

Even after reducing the marked price of a T.V by Tk. 320, a shopkeeper makes a profit of 15%. If the cost price be Tk. 3200, what percentage of profit would he have made if he had sold the T.V at the marked price?

ক
10%
খ
20%
গ
25%
ঘ
16(2/3) %
ঙ
50%

ব্যাখ্যা

15% of 3200 = 480
MP = 3200 + 480 + 320 = 4000

P = 4000 - 3200 = 800
P% = 8003200 × 100

১,১২৭.

A shopkeeper sells one shirt for Tk.840 at a gain of 20% and another for Tk.960 at a loss of 4%. His total gain or loss percent is-

ক
ক) 80/17%
খ
খ) 50/17%
গ
গ) 100/17%
ঘ
ঘ) 200/17%

ব্যাখ্যা

Question: A shopkeeper sells one shirt for Tk.840 at a gain of 20% and another for Tk.960 at a loss of 4%. His total gain or loss percent is-

Solution:
C.P. of 1^stshirt=Tk.(100 × 840)/120=Tk.700.
C.P. of 2^nd shirt=Tk.(100 × 960)/96=Tk.1000

So, total C.P.=Tk.(700 + 1000)=Tk.1700.
Total S.P.=Tk.(840 + 960)=Tk.1800.

∴Gain% =((100 × 100)/1700}% =100/17%

১,১২৮.

A retailer purchases a TV at a discount of 25% from the wholesaler. He marks it up by 50% on the discounted price and then offers a discount of 20% to the customer. What is his percentage profit?

ক
22%
খ
20%
গ
32%
ঘ
27%
ঙ
30%

ব্যাখ্যা

Question: A retailer purchases a TV at a discount of 25% from the wholesaler. He marks it up by 50% on the discounted price and then offers a discount of 20% to the customer. What is his percentage profit?

Solution:
Let the original price of the TV be 1000 Taka.

Wholesaler’s discount = 25%
Retailer’s purchase price:
1000 − 25% of 1000 = 1000−250 = 750 Taka

Retailer’s markup = 50% on Taka 750
New marked price:
750 + 50% of 750 = 750 + 375 = 1125 Taka

Customer’s discount = 20% on Taka 1125
Selling price:
1125 − 20% of 1125 = 1125 − 225 = 900 Taka

So, Profit = {(900 - 750)/750} × 100%
= 20%

১,১২৯.

A pen marked at Tk. 85 is sold for Tk. 68. The rate of discount is-

ক
ক) 10%
খ
খ) 15%
গ
গ) 18%
ঘ
ঘ) 20%

ব্যাখ্যা

Discount = 85 - 68
= 17
Discount Rate = (17/85) × 100
= 20%

১,১৩০.

Find the value of 25% of 10% of Tk. 800.

ক
25
খ
20
গ
30
ঘ
35

ব্যাখ্যা

Question: Find the value of 25% of 10% of Tk. 800.

Solution:
25% of 10% of 800
= (25/100) × (10/100) × 800
= 20

১,১৩১.

A hat seller had some hats. He sells 55% hats and still has 90 hats. Originally, he had:

ক
175
খ
180
গ
200
ঘ
225

ব্যাখ্যা

Question: A hat seller had some hats. He sells 55% hats and still has 90 hats. Originally, he had:

Solution:
Let,
The hat seller had = x hats.

ATQ,
(100 - 55)% of x = 90
⇒ 45% of x = 90
⇒ 45x/100 = 90
⇒ 9x/20 = 90
⇒ x = (90 × 20)/9
∴ x = 200

∴ Originally, he had 200 hats

১,১৩২.

If the price of an item is increased by 10% and then decreased by 10% , the net effect on the price of the item is -

ক
an increase of 9%
খ
a decrease of 1%
গ
an increase of 7%
ঘ
No Change

ব্যাখ্যা

Question: If the price of an item is increased by 10% and then decreased by 10% , the net effect on the price of the item is -

Solution:
Let,
The price of an item is 100 Tk.

If the price increased by 10%,
So, the new price will be after increased = 100 + {100 × (10/100)} Tk.
= 100 + 10 Tk.
= 110 Tk.

Then the new price decreased by 10%,
So, the new price will be after decreased = 110 - {110 × (10/100)} Tk.
= 110 - 11 Tk.
= 99 Tk.

∴ The net effect on the price of the item is = (100 - 99) Tk. decreased
= 1 Tk. decreased

১,১৩৩.

On Dhaka- Sylhet highway 5% of the drivers are fined for exceeding the speed limit. However, 80% of the drivers who exceed the speed limit are not fined. What percentage of drivers on this highway exceed the speed limit?

ক
10
খ
15
গ
20
ঘ
25
ঙ
None of these

ব্যাখ্যা

প্রশ্ন: On Dhaka- Sylhet highway 5% of the drivers are fined for exceeding the speed limit. However, 80% of the drivers who exceed the speed limit are not fined. What percentage of drivers on this highway exceed the speed limit?

সমাধান:
ধরি,
হাইওয়েতে 100 জন চালক ছিল।

এখন,
গতিসীমা অতিক্রম করার জন্য 5% চালককে জরিমানা করা হয়।
∴ 100 জন চালকের 5% বা 5 জন চালককে জরিমানা করা হয়।

আবার,
চালকদের মধ্যে যারা গতিসীমা অতিক্রম করেছিল তাদের মধ্যে 80% চালককে জরিমানা করা হয়নি।
∴ চালকদের মধ্যে যারা গতিসীমা অতিক্রম করেছিল তাদের মধ্যে 20% চালককে জরিমানা করা হয়।

প্রশ্নমতে,
20% = 5
∴ 1% = 5/20
∴ 100% = (5 × 100)/20
= 25

১,১৩৪.

By what percentage above the cost price, a fan should be sold if a shopkeeper wants to make a profit of Tk. 500 and the marked price of the article is Tk 6000 which is 50% above the cost price?

ক
ক) 9.82%
খ
খ) 12.5%
গ
গ) 15.4%
ঘ
ঘ) 16.4%

ব্যাখ্যা

Question: By what percentage above the cost price, a fan should be sold if a shopkeeper wants to make a profit of Tk. 500 and the marked price of the article is Tk 6000 which is 50% above the cost price?

Solution:

Marked Price, MP = Tk. 6000, যা ক্রয়মূল্য (CP) এর ৫০ শতাংশ বেশি।
প্রশ্নমতে,

MP = CP + CP × 50%

=>MP = CP (1 + 50%)

=>MP = CP × 150/100

=>MP = CP × 1.5

=>6000 = CP × 1.5

=>CP= 6000 /1.5

=>CP= 4000

Cost price = Tk. 4000
Profit = Tk. 500

=> Profit%= 500 × 100%/4000 =12.5%

১,১৩৫.

What number divided by 50 gives 3.6%?

ক
ক) 1.8
খ
খ) 18
গ
গ) 180
ঘ
ঘ) None

ব্যাখ্যা

Question: What number divided by 50 gives 3.6%?

Solution:
3.6%
= 3.6/100
= 0.036

let, the number x

x / 50 = 0.036
⇒ x = 50 × 0.036
= 1.8

১,১৩৬.

A acquired an article at Tk. 200 and sold it to B with a 20% markup. B then sold it to C at a 10% markup. Find the amount C paid.

ক
Tk. 150
খ
Tk. 198
গ
Tk. 224
ঘ
Tk. 264

ব্যাখ্যা

Question: A acquired an article at Tk. 200 and sold it to B with a 20% markup. B then sold it to C at a 10% markup. Find the amount C paid.

Solution:
Price paid by B = 200 + (200/100 × 20) = 200 + 40 = 240

∴ Price paid by C = 240 + (240/100 × 10) = 240 + 24 = 264

Hence, Thus, the price at which C bought the article from B is: Tk. 264

১,১৩৭.

The price of a book is Tk. 200. Its price is increased by 15% and then decreased by 20%. What is the present price of the book?

ক
Tk. 184
খ
Tk. 154
গ
Tk. 164
ঘ
Tk. 170

ব্যাখ্যা

Question: The price of a book is Tk. 200. Its price is increased by 15% and then decreased by 20%. What is the present price of the book?

Solution:
Initial Cost = Tk. 200
After 15% increase in the cost, it becomes,
(200 + 15% of 200)
= 200 + 30
= Tk. 230

Now, Cost is decreased by 20%, So cost will become,
(230 - 20% of 230)
= 230 - 46
= Tk. 184

So, present cost is Tk. 184.

১,১৩৮.

If the selling price is doubled, the profit triples. Find the profit percent.

ক
120%
খ
100 %
গ
130%
ঘ
140%

ব্যাখ্যা

Question: If the selling price is doubled, the profit triples. Find the profit percent.

Answer:
Let, Cost price = x taka
Selling price = y taka
Then, 3(y-x) = 2y-x
→ 3y- 2y = 3x- x
→ y = 2x
Then, Profit = (y- x) Taka = (2x- x) Taka
= x Taka
Profit percent =

= 100 %

১,১৩৯.

A family made a down payment of Tk. 7500 and borrowed the balance on a set of encyclopedias that cost Tk. 40000. The balance with interest was paid in 23 monthly payments of Tk. 1600 each and a final payment of Tk. 900. The amount of interest paid was what percent of the amount borrowed?

ক
16%
খ
14%
গ
12%
ঘ
6%

ব্যাখ্যা

Question: A family made a down payment of Tk. 7500 and borrowed the balance on a set of encyclopedias that cost Tk. 40000. The balance with interest was paid in 23 monthly payments of Tk. 1600 each and a final payment of Tk. 900. The amount of interest paid was what percent of the amount borrowed?

Solution:
Amount Borrowed = 40000 - 7500 = 32500

Total Balance with interest paid = 23 × 1600 + 900 = 37700
∴ Interest = 37700 - 32500 = 5200

∴ Percentage = (5200/32500) × 100 = 16%

১,১৪০.

Find the single discount equivalent to a series discount of 30%, 20% and 10%.

ক
46.9%
খ
51.07%
গ
56.49%
ঘ
50%
ঙ
49.6%

ব্যাখ্যা

Let marked price be Tk. 100

Therefore, selling price = 90%, 80% and 70% of Tk. 100

Selling price = (90/100) × (80/100) × (70/100) × 100 = 50.4

Selling Price = Tk. 50.4

Required discount = Marked Price – Selling Price

= 100 – 50.4

= 49.6%

১,১৪১.

A town's population increased by 1200 people, and then this new population decreased 11%. The town now had 32 less people than it did before the 1200 increase. Find the original population.

ক
10000
খ
11000
গ
12000
ঘ
13000

ব্যাখ্যা

Question: A town's population increased by 1200 people, and then this new population decreased 11%. The town now had 32 less people than it did before the 1200 increase. Find the original population.

Solution:
Let,
the population = P
So, the increased population will be = P + 1200
The population after 11% decrease in population becomes = P − 32

Therefore,
P − 32 = (P + 1200) − (11/100)(P + 1200)
⇒ p - 32 = (100p + 120000 - 11p - 13200)/100
⇒ 89p + 106800 = 100p - 3200
⇒ 89p - 100p = - 3200 - 106800
⇒ - 11p = - 110000
∴ p = 10000

So, the total population is 10000.

১,১৪২.

Sarah sold her bicycle for Taka. 5000 while making a profit of Taka. 570. Then what is the price at which she bought that cycle?

ক
3330 Taka
খ
3430 Taka
গ
4000 Taka
ঘ
4430 Taka

ব্যাখ্যা

Question: Sarah sold her bicycle for Taka. 5000 while making a profit of Taka. 570. Then what is the price at which she bought that cycle?

Solution:
Given,
Selling Price (SP) = Taka. 5000
Profit = 570 Taka
Thus, Cost Price = Selling Price - Profit
⇒ Cost Price = 5000 - 570
⇒ Cost Price = 4430 Taka
Thus, cost price of the bicycle is Taka 4430

১,১৪৩.

Seventy-two percent of a number is 30 less than three-fourths of that number. What is the number?

ক
1000
খ
850
গ
972
ঘ
1260

ব্যাখ্যা

Question: Seventy-two percent of a number is 30 less than three-fourths of that number. What is the number?

Solution:
Let, the number = x.

ATQ,
72% of x = (3/4) of x - 30
⇒ 72x/100 = (3x/4) - 30
⇒ 18x/25 = (3x/4) - 30
⇒ (3x/4) - (18x/25) = 30
⇒ (75x - 72x)/100 = 30
⇒ 3x/100 = 30
⇒ 3x = 3000
⇒ x = 3000/3
∴ x = 1000

So, the number is 1000

১,১৪৪.

Junayed purchased two articles at the same price and sold one at a profit of 20% and the other at a profit of 22.5%. If the difference between the two selling price is Tk. 150, what is the cost price of each of the articles?

ক
5000
খ
6000
গ
4000
ঘ
7000

ব্যাখ্যা

Question: Junayed purchased two articles at the same price and sold one at a profit of 20% and the other at a profit of 22.5%. If the difference between the two selling price is Tk. 150, what is the cost price of each of the articles?

Solution:
Let the cost price of each of the articles = 100.
The selling price of the first articles = 120
and the selling price of the second articles = 122.5
The difference in the selling price = 122.5 - 120 = 2.5

The difference in the selling price = 2.5 if the cost price = 100
If the difference in selling price = 150, then the cost price = (150 × 100)/2.5 = 6000

১,১৪৫.

Salma's average in four tests is 80%. What mark does she need to score in her fifth test to make her average 84%?

ক
100%
খ
94%
গ
84%
ঘ
96%
ঙ
None of these

ব্যাখ্যা

Question: Salma's average in four tests is 80%. What mark does she need to score in her fifth test to make her average 84%?

Solution:
Total score on 4 tests = 80 × 4 = 320
Total score on 5 tests = 84 × 5 = 420

The score in the fifth test is = 420 - 320
= 100 or 100%

১,১৪৬.

What percentage of the whole week does Rakibul spend in office, if his office hours are 9 am to 5 pm from Sunday to Thursday?

ক
23.81%
খ
33.33%
গ
42.23%
ঘ
25.5%

ব্যাখ্যা

Question: What percentage of the whole week does Rakibul spend in office, if his office hours are 9 am to 5 pm from Sunday to Thursday?

Solution:
Percentage = {(5 × 8)/(7 × 24)} × 100%
= (5/21) × 100%
= 23.81%

১,১৪৭.

A shopkeeper purchases 15 mangoes for Tk. 10 and sells them at 10 mangoes for Tk. 15. Thus, he earns a profit of ___ .

ক
ক) 50%
খ
খ) 75%
গ
গ) 80%
ঘ
ঘ) 125%

ব্যাখ্যা

15 টি আমের ক্রয়মূল্য = 10 টাকা
1 টি আমের ক্রয়মূল্য =10/15 =2/3 টাকা

আবার,
10 টি আমের বিক্রয়মূল্য = 15 টাকা
1 টি আমের বিক্রয়মূল্য = 15/10 টাকা
= 3/2 টাকা
লাভ = (3/2) - (2/3) টাকা
= (9 - 4)/6 টাকা
= 5/6 টাকা

শতকরা লাভ= [{(5/6)/(2/3)} × 100]%
= {(5/6) ×(3/2)× 100}%
= 125%

১,১৪৮.

If the price of an article is increased by 25% and then decreased by 20%, the net change in the price is -

ক
5% increase
খ
5% decrease
গ
2.5% increase
ঘ
No change

ব্যাখ্যা

Question: If the price of an article is increased by 25% and then decreased by 20%, the net change in the price is -

Solution:
Let,
The price of an article is 100 Tk.

If the price increased by 25%,
So, the new price will be after increase = 100 + {100 × (25/100)} Tk.
= 100 + 25 Tk.
= 125 Tk.

Then the new price decreased by 20%,
So, the new price will be after decrease = 125 - {125 × (20/100)} Tk.
= 125 - 25 Tk.
= 100 Tk.

∴ The net effect on the price of the article is = (100 - 100)
= 0 Taka

So, after both the increase and the decrease, the price remains the same.

১,১৪৯.

A shopkeeper earns a profit of 10% after allowing a discount of 20% on the marked price. What is the cost price of the article whose marked price is 880 taka?

ক
120 taka
খ
110 taka
গ
704 taka
ঘ
640 taka

ব্যাখ্যা

Market price of the article = 880 taka
After 20% discount,
if cost price is 100 taka, then selling price of the article= (880 × 80/100) taka = 704 taka
At 10% profit,
If the cost price 100 taka, selling price = (100 + 10) taka = 110 taka
Therefore, Cost price of the article = (704 × 100/110) taka = 640 taka

১,১৫০.

A car dealership has 40 cars on the lot, 30% of which are silver. If the dealership receives a new shipment of 80 cars, 40% of which are not silver, what percent of the total number of cars are silver?

ক
36.67%
খ
50%
গ
62%
ঘ
45%

ব্যাখ্যা

Question: A car dealership has 40 cars on the lot, 30% of which are silver. If the dealership receives a new shipment of 80 cars, 40% of which are not silver, what percent of the total number of cars are silver?

Solution:
old silver car = 30% of 40 = 12
new silver car = (100 - 40)% of 80
= 60% of 80
= 48

% silver car = {(12 + 48)/ (40 + 80)} × 100%
=(60/120)× 100%
= 1/2 × 100%
= 50%

১,১৫১.

The selling price of 40 items is equal to purchase price of 28 items. What is the profit or loss percent?

ক
20% loss
খ
30% loss
গ
30% profit
ঘ
20% profit

ব্যাখ্যা

Question: The selling price of 40 items is equal to purchase price of 28 items. What is the profit or loss percent?

Solution:
Let the price of each item 1 taka
Buying price = 40 tk
Selling price = 28 tk
∴ %loss = (40 - 28)/40 × (100 %)
= 30%

১,১৫২.

If books bought at prices ranging from Tk. 200 to Tk.350 are sold at prices ranging from Tk.300 to Tk. 425, what is the greatest possible profit that might be made in selling ten books?

ক
Tk.1800
খ
Tk.1200
গ
Tk.1620
ঘ
Tk.2250

ব্যাখ্যা

Question: If books bought at prices ranging from Tk. 200 to Tk.350 are sold at prices ranging from Tk.300 to Tk. 425, what is the greatest possible profit that might be made in selling ten books?

Solution:
সর্বনিম্ন ক্রয়মূল্য = 10 × 200 = 2000 টাকা
সর্বোচ্চ বিক্রয়মূল্য = 10 × 425 =4250 টাকা

∴ সর্বোচ্চ লাভ = 4250 - 2000 = 2250 টাকা

১,১৫৩.

A lamp is manufactured to sell for $ 35.00, which yields a profit of 25% of cost. If the profit is to be reduced to 15% of the cost, what will be the new retail price of the lamp?

ক
ক) $31.50
খ
খ) $28.00
গ
গ) $21.00
ঘ
ঘ) $32.20

ব্যাখ্যা

Question: A lamp is manufactured to sell for $ 35.00, which yields a profit of 25% of cost. If the profit is to be reduced to 15% of the cost, what will be the new retail price of the lamp?

Solution:
২৫% লাভে খরচ ১০০ টাকা হলে বিক্রয়মূল্য = ১২৫ টাকা
বিক্রয়মূল্য ১২৫ টাকা হলে খরচ ১০০ টাকা
বিক্রয়মূল্য ৩৫ টাকা হলে খরচ = (১০০ × ৩৫)/১২৫ টাকা
= ২৮ টাকা

আবার, ১৫% লাভে নতুন বিক্রয়মূল্য = ১১৫ টাকা

খরচ ১০০ তাকা হলে বিক্রয়মূল্য = ১১৫ টাকা
খরচ ২৮ টাকা হলে বিক্রয়মূল্য = (১১৫ × ২৮)/১০০ টাকা
= ৩২.২ টাকা

১,১৫৪.

A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price.The ratio of the cost price and the printed price of the book is:

ক
ক) 44 : 57
খ
খ) 45 : 56
গ
গ) 41 : 52
ঘ
ঘ) 40 : 59

ব্যাখ্যা

Let
The CP be 100
Hence,
SP= 100 + 12% of 100
=112
If the marked price be x,
then
90% of x = 112
⇒x = 112 × 100/90
⇒x = 1120/9

Hence, Required ratio = 100 :1120/9
= 900 : 1120
= 45 : 56

১,১৫৫.

A manufacturer sells a pair of shoes to a wholesale dealer at a profit of 20%. Wholesalers sell them to retailers at a profit of 25%. The shoes are again sold to the customer for Tk. 50.50, thereby earning a profit of 30%. Find the cost price of the manufacturer.

ক
ক) Tk. 20.36
খ
খ) Tk. 22.90
গ
গ) Tk. 25.89
ঘ
ঘ) Tk. 30.50

ব্যাখ্যা

Profit earned by manufacturer = 20%
Profit earned by wholesaler = 25%
Profit earned by retailer = 30%
S.P. of shoes = Tk. 50

Therefore, 130% of 125% of 120% of x = 50.50
⇒ 120/100 × 125/100 × 130/100 × x = 5050/100
⇒ (195/100) x = 5050/100
⇒ x = (5050 × 100)/(195 × 100)
⇒ x = 25.89
Cost price of shoes = Tk. 25.89

১,১৫৬.

The length and breadth of a square are increased by 40% and 30% respectively. The area of the resulting rectangle exceeds the area of the square by:

ক
50%
খ
76%
গ
82%
ঘ
41%

ব্যাখ্যা

Question: The length and breadth of a square are increased by 40% and 30% respectively. The area of the resulting rectangle exceeds the area of the square by:

Solution:
Let, old length 100 m and breadth 100m
Old area = 100 × 100 m²
= 10000 m²

New length = 100 + 40
= 140 m
New breadth = 100 + 30
= 130 m

New area = 140 × 130 m²
= 18200 m²

The area of the resulting rectangle exceeds the area of the square by = {(18200 - 10000)/10000} × 100%
= (8200/10000)× 100%
= 83%

১,১৫৭.

A person buys certain number of gems at 20 per taka and an equal number at 30 per taka. He mixes them and sells them at 25 per taka. His gain or loss in the transaction is-

ক
6% gain
খ
5% loss
গ
4% loss
ঘ
2% gain

ব্যাখ্যা

Question: A person buys certain number of gems at 20 per taka and an equal number at 30 per taka. He mixes them and sells them at 25 per taka. His gain or loss in the transaction is-

Solution:
The cost price of each gem is 20 per Tk. = Tk. 1/20
The price of each gem is 30 per Tk. = Tk. 1/30

∴ Average cost of gem = {(1/20) + (1/30)}/2
= (3 + 2)/(2 × 60)
= 5/120
= 1/24

The selling price of mixed gem = Tk. 1/25

∴ Loss = (1/24) - (1/25) = 1/600

Cost price 1/24 then loss Tk. 1/600
Cost price 1 then loss Tk. (1/600)/(1/24)

∴ Cost price 1 then loss Tk. {(1/600)/(1/24)} × 100
= 4%

∴ There is a loss of 4%

১,১৫৮.

If 18 is 15% of 50% of a certain number, what is the number?

ক
ক) 360
খ
খ) 120
গ
গ) 240
ঘ
ঘ) 900

ব্যাখ্যা

ধরি,
সংখ্যাটি x

এখানে,
x এর 50% = 50x /100 = x /2

x/2 এর 15% = x/2 এর 15/100 = 3x/40

প্রশ্নমতে,
3x/40 = 18
x = (18 × 40)/3
= 240

১,১৫৯.

If A's income is 20% less than that of B, then by what percent is B's income more than that of A?

ক
20%
খ
25%
গ
30%
ঘ
35%

ব্যাখ্যা

Question: If A's income is 20% less than that of B, then by what percent is B's income more than that of A?

Solution:
Let B’s income be Tk. x
∴ A's income = x - 20% of x
= x - 0.20x
= 0.80x
So, A's icome = 0.80x

Difference between B's and A's income,
= x - 0.80x
= 0.20x

∴ Percentage = (Difference/A's income) × 100%
= (0.20x/0.80x) × 100%
= (1/4) × 100%
= 25%

১,১৬০.

On selling 12 balls at Tk. 720 there is a loss equal to the cost price of 4 balls. The cost price of a ball is-

ক
Tk. 72
খ
Tk. 84
গ
Tk. 90
ঘ
Tk. 110

ব্যাখ্যা

Question: On selling 12 balls at Tk. 720 there is a loss equal to the cost price of 4 balls. The cost price of a ball is-

Solution:
Let,
The cost price of 1 ball is = Tk. x
The cost price of 12 balls is = Tk. 12x

We know,
Cost price - Selling price = Loss
⇒ 12x - 720 = 4x
⇒ 8x = 720
⇒ x = 720/8
∴ x = 90

∴ The cost price of 1 ball is Tk. 90

১,১৬১.

A farmer harvested a crop of apples. 15% of them were damaged during transportation. He sold 70% of the remaining good apples to a market. If he has 255 apples left, how many apples did he originally harvest?

ক
1280
খ
1000
গ
960
ঘ
850

ব্যাখ্যা

Question: A farmer harvested a crop of apples. 15% of them were damaged during transportation. He sold 70% of the remaining good apples to a market. If he has 255 apples left, how many apples did he originally harvest?

Solution:
Let the original number of apples be x

ATQ,
⇒ x × 85% × 30% = 255
⇒ (x × 85 × 30)/(100 × 100) = 255
⇒ x = (255 × 100 × 100)/(85 × 30)
⇒ x = (255 × 1000)/255
∴ x = 1000

So the farmer originally harvested 1,000 apples.

১,১৬২.

A company's profits have doubled for each of the last 4 years . If the total profits for the last 4 years were Tk. 30 lacs. What were the profits in the first year?

ক
Tk. 200000
খ
Tk. 250000
গ
Tk. 20000
ঘ
Tk. 315000
ঙ
Tk. 400000

ব্যাখ্যা

Question: A company's profits have doubled for each of the last 4 years . If the total profits for the last 4 years were Tk. 30 lacs. What were the profits in the first year?

Solution:
Let the profit in the first year is P (in Tk. lacs).
Since the profits double each year.

ATQ,
⇒ p + 2p + 4p + 8p = 3000000
⇒ 15p = 3000000
⇒ p = 3000000/15
∴ p = 200000

Thus, the profit in the first year is Tk. 200000

১,১৬৩.

A sells an article which costs him Tk. 400 to B at a profit of 20%. B then sells it to C, making a profit of 10% on the price he paid to A. How much dose C pay to B?

ক
Tk. 472
খ
Tk. 476
গ
Tk. 528
ঘ
Tk. 532

ব্যাখ্যা

Question: A sells an article which costs him Tk. 400 to B at a profit of 20%. B then sells it to C, making a profit of 10% on the price he paid to A. How much dose C pay to B?

Solution:
A এর 20% লাভে বিক্রয়মূল্য = 400 + 400 এর 20%
= 400 + 400 এর 20/100
= 400 + 80
= 480

A এর বিক্রয়মূল্য = B এর ক্রয়মূল্য

B এর 10% লাভে বিক্রয়মূল্য = 480 + 480 এর 10%
= 480 + 480 এর 10/100
= 480 + 48
= 528

B এর বিক্রয়মূল্য = C এর ক্রয়মূল্য = 528 টাকা

১,১৬৪.

The marked price of a mobile is 20% more than its cost price. If a discount of 10% is given on the marked price, the profit percent is:

ক
8%
খ
10%
গ
12%
ঘ
20%
ঙ
None

ব্যাখ্যা

Question: The marked price of a mobile is 20% more than its cost price. If a discount of 10% is given on the marked price, the profit percent is:

Solution:

Let,

Cost price = Tk.100

Market price = 100 + 20% of 100

= 100 + (100 × 20/100)

= Tk. 120

Now,

Selling price = 120 - 10% of 120

= 120 - (120 × 10)/100

= Tk. 108

Profit = 108 - 100 = Tk. 8

∴ Profit % = (8 × 100)/100

= 8%

১,১৬৫.

A book store earns 5% on its first Tk 1000 sale per day and 4% on all sales in excess of Tk 1000 for that day. What would be the profit of the book store in a day when sales are TK. 12000?

ক
Tk. 500
খ
Tk. 350
গ
Tk. 250
ঘ
Tk. 490

ব্যাখ্যা

Question: A book store earns 5% on its first Tk. 1000 sale per day and 4% on all sales in excess of Tk. 1000 for that day. What would be the profit of the book store in a day when sales are Tk. 12000?

Solution:
Profit for first Tk. 1000 = 1000(5/100)
= Tk. 50

Total sales excess of Tk. 1000 = (12000 - 1000)
= Tk. 11000

∴ Profit for excess of Tk. 1000 = 11000(4/100)
= Tk. 440

∴ Total Profit = (50 + 440)
= Tk. 490

১,১৬৬.

If 0.07 is x% of 0.7, then the value of x is-

ক
ক) 7
খ
খ) 70
গ
গ) 100
ঘ
ঘ) 10

ব্যাখ্যা

Question: If 0.07 is x% of 0.7, then the value of x is-

Solution:
x% of 0.7 = 0.07
⇒ (x/100) × 0.7 = 0.07
⇒ x = 0.07 × 100/0.70
⇒ x = 10

১,১৬৭.

Mamun purchased 20 dozen toys at the rate of Tk. 375 per dozen. He sold each one of them at the rate of Tk. 33. Find out his profit percentage.

ক
5.6%
খ
3.5%
গ
4.1%
ঘ
3.4%

ব্যাখ্যা

The cost price of 12 toys = Tk. 375
The selling price of 12 toys = 33 × 12
= Tk. 396
profit = 396 - 375
= Tk. 21
Profit percentage = (21 × 100)/375
= (7 × 100)/125
= (7 × 4)/5
= 5.6%

১,১৬৮.

A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of 392 Tk, what was his profit?

ক
48 Tk
খ
55 Tk
গ
58 Tk
ঘ
72 Tk

ব্যাখ্যা

Question: A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of 392 Tk, what was his profit?

Solution:
Given,
Selling price = 392 Tk
Cost price = (100/122.5) × 392 Tk
= (1000/1225) × 392 Tk
= 320 Tk

Therefore, Profit = 392 - 320 Tk
= 72 Tk

১,১৬৯.

0.35 represents what percent of 0.007?

ক
0.05%
খ
5%
গ
50%
ঘ
5000%

ব্যাখ্যা

Question: 0.35 represents what percent of 0.007?

Solution:
(0.35/0.007) × 100%
= {(350 × 100)/7}%
= 5000%

১,১৭০.

If an item whose marked price is Tk. 1,000 is sold after two successive discounts of 10% and 15%, then find the price at which the item is sold?

ক
Tk.745
খ
Tk.725
গ
Tk. 715.5
ঘ
Tk.765

ব্যাখ্যা

Question: If an item whose marked price is Tk. 1,000 is sold after two successive discounts of 10% and 15%, then find the price at which the item is sold?

Solution:
Marked price is Tk. 1,000

After 10% discount
= 1000 - 10 of 1000
= 1000 - 100
= 900

After 15% discount
= 900 - 15 of 900
= 900 - 135
= 765

১,১৭১.

An employer pays 3 workers X, Y and Z a total of Tk. 36,600 a week. X is paid 125% of the amount Y is paid and 80% of the amount Z is paid. How much does X make a week?

ক
ক) 9,000
খ
খ) 12,000
গ
গ) 10,800
ঘ
ঘ) 11,700

ব্যাখ্যা

Question: An employer pays 3 workers X, Y and Z a total of Tk. 36,600 a week. X is paid 125% of the amount Y is paid and 80% of the amount Z is paid. How much does X make a week?

Solution:
ধরি,
y পায় p টাকা
∴ x পায় p এর 125% = 5p/4
z পায় q টাকা
∴ x পায় q এর 80% = 4q/5

তাহলে,
5p/4 = 4q/5
q = 25p/16

প্রশ্নমতে,
x + y + z = 36600
(5p/4) + p + (25p/16) = 36600
61p/16 = 36600
p/16 = 600
p = 9600

∴ x পায় = 5p/4
= (5 × 9600)/4
= 12000 টাকা

১,১৭২.

A and B are two fixed points 5 cm apart and C is a point an AB such that AC is 3 cm. If the length of AC is increased by 6%, the length CB is decreased by-

ক
8%
খ
9%
গ
7%
ঘ
6%

ব্যাখ্যা

Question: A and B are two fixed points 5 cm apart and C is a point an AB such that AC is 3 cm. If the length of AC is increased by 6%, the length CB is decreased by-

Solution:

After increment of 6% new length of AC = 3 + {(3 × 6)/100}
= 3 + 0.18
= 3.18cm

Required % decrease = (0.18/2) × 100
= 9%

১,১৭৩.

A shopkeeper incurs a loss by selling an article for Tk 800. If he had sold it for Tk 1200, he would have made a profit which is four times the initial loss. At what price should he sell the article to make 25% profit?

ক
Tk. 890
খ
Tk. 1000
গ
Tk. 1100
ঘ
Tk. 1250

ব্যাখ্যা

Question: A shopkeeper incurs a loss by selling an article for Tk 800. If he had sold it for Tk 1200, he would have made a profit which is four times the initial loss. At what price should he sell the article to make 25% profit?

Solution:
ধরি, পণ্যের ক্রয়মূল্য = x টাকা
800 টাকায় বিক্রি করলে ক্ষতি = x - 800 টাকা
1200 টাকায় বিক্রি করলে লাভ = 1200 - x টাকা

প্রশ্নমতে,
1200 - x = 4(x - 800)
⇒ 1200 - x = 4x - 3200
⇒ 1200 + 3200 = 4x + x
⇒ 4400 = 5x
∴ x = 880 টাকা

এখন, 25% লাভে,
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য 125 টাকা
ক্রয়মূল্য 1 টাকা হলে বিক্রয়মূল্য 125/100 টাকা
∴ ক্রয়মূল্য 880 টাকা হলে বিক্রয়মূল্য = (125 × 880)/100 টাকা
= 1100 টাকা

∴ বিক্রয়মূল্য: Tk. 1100

১,১৭৪.

A shopkeeper sells a watch for Tk. 8,400 and makes a profit of 25%. If the profit is reduced to 15%, what will be the new selling price?

ক
7248 tk
খ
7456 tk
গ
7542 tk
ঘ
7728 tk

ব্যাখ্যা

Question: A shopkeeper sells a watch for Tk. 8,400 and makes a profit of 25%. If the profit is reduced to 15%, what will be the new selling price?

Solution:
Let Cost Price was x
ATQ,
x + 25% of x = 8400
⇒ x + (25x/100) = 8400
⇒ x + 0.25x = 8400
⇒ 1.25x = 8400
∴ x = 6720

So, Cost Price = 6720
Now, Selling Price When profit remains at 15%,
= 6720 + 15% of 6720
= 6720 + 1008
= 7728

১,১৭৫.

A fruit seller sells 20 oranges for Tk. 900 and suffers a loss equal to the cost price of 5 oranges. Find the cost price of one orange.

ক
Tk. 55
খ
Tk. 60
গ
Tk. 42
ঘ
Tk. 62

ব্যাখ্যা

Question: A fruit seller sells 20 oranges for Tk. 900 and suffers a loss equal to the cost price of 5 oranges. Find the cost price of one orange.

Solution:
Let,
cost price of 1 orange is = Tk. x
∴ cost price of 20 oranges is = Tk. 20x
∴ cost price of 5 oranges is = Tk. 5x

We know,
Cost price - Selling price = Loss
20x - 900 = 5x
⇒ 20x - 5x = 900
⇒ 15x = 900
⇒ x = 900/15
∴ x = 60

∴ Cost price of 1 orange is Tk. 60

১,১৭৬.

70 grams is what percentage of 20 kilograms?

ক
0.5%
খ
0.35%
গ
0.15%
ঘ
0.8%

ব্যাখ্যা

Question: 70 grams is what percentage of 20 kilograms?

Solution:
We know,
20 kg = 20 × 1000
= 20000 grams

∴ Percentage = (70 ÷ 20000) × 100
= 0.35%

∴ 70 grams is 0.35% of 20 kg.

১,১৭৭.

There are n students in a school. If r% among the students are 12 years or younger, which of the following expressions represents the number of students who are older than 12?

ক
ক) n(1 - r)
খ
খ) 100 (1 - r)n
গ
গ) n(1 - r)/100
ঘ
ঘ) n(100 - r)/100

ব্যাখ্যা

Question: There are n students in a school. If r% among the students are 12 years or younger, which of the following expressions represents the number of students who are older than 12?

Solution:
r% শিক্ষার্থীর বয়স ১২ বা তার কম হলে,

n - ( n এর r%) এর বয়স ১২ এর বেশি।
= n - (rn/100)
= (100n - rn)/100
= n(100 - r)/100

১,১৭৮.

The value of a machine is Tk. 6,250. Its value decreases by 10% during the first year, 20% during second year and 30% during the third year. What will be the value of the machine after 3 years?

ক
ক) 2650
খ
খ) 3050
গ
গ) 3150
ঘ
ঘ) 3750

ব্যাখ্যা

প্রশ্ন: The value of a machine is Tk. 6,250. Its value decreases by 10% during the first year, 20% during second year and 30% during the third year. What will be the value of the machine after 3 years?

সমাধান:
একটি মেশিনের মূল্য ৬২৫০ টাকা

প্রথম বছরে এর মূল্য ১০% হ্রাস পায়
প্রথম বছর পর এর মূল্য = ৬২৫০ - ৬২৫০ এর ১০%
= ৬২৫০ - (৬২৫০ ×১/১০)
= ৬২৫০ - ৬২৫ টাকা
= ৫৬২৫ টাকা

দ্বিতীয় বছরে এর মূল্য ২০% হ্রাস পায়
দ্বিতীয় বছর শেষে মূল্য = ৫৬২৫ - ৫৬২৫ এর ২০%
= ৫৬২৫ - ১১২৫ টাকা
= ৪৫০০ টাকা

তৃতীয় বছরে, এর মূল্য ৩০% হ্রাস পায়
∴ তৃতীয় বছর শেষে এর মূল্য = ৪৫০০ - ৪৫০০ এর ৩০%
= ৪৫০০ - ১৩৫০ টাকা
= ৩১৫০ টাকা

১,১৭৯.

A person sold a book at a gain of 15%. Had he bought it for 25% less and sold it for Tk. 600 less, he would have made a profit of 32%. The cost price of the book was:

ক
ক) Tk. 2250
খ
খ) Tk. 2750
গ
গ) Tk. 2550
ঘ
ঘ) Tk. 3750

ব্যাখ্যা

Question: A person sold a book at a gain of 15%. Had he bought it for 25% less and sold it for Tk. 600 less, he would have made a profit of 32%. The cost price of the book was:

Solution:
Let the original cost price = Tk. x

Selling price = x + 15% of x
= 115x/100
= 23x/20

Cost price = x - 25% of x
= x - (25x/100)
= 75x/100
= 3x/4

Selling price = (3x/4) + 32% of (3x/4)
= (3x/4) + (32/100) × (3x/4)
= 99x/100

ATQ,
(23x/20) - (99x/100) = 600
⇒ (115x - 99x)/100 = 600
⇒ 16x = 600 × 100
⇒ x = (600 × 100)/16
∴ x = 3750

১,১৮০.

৫৫০ এর ৯২.৫% সমান কত?

ক
৫০৮.৭৫
খ
৫০৬.৪৮
গ
৫২১.৫৫
ঘ
৫০২.৭৮
ঙ
৫০৭

ব্যাখ্যা

প্রশ্ন: ৫৫০ এর ৯২.৫% সমান কত?

সমাধান:
৫৫০ এর ৯২.৫%
= ৫৫০ × (৯২.৫/১০০)
= ৫৫০ × (৯২৫/১০০০)
= ৫০৮.৭৫

১,১৮১.

If the radius of a circle is doubled, its area is increased by-

ক
ক) 200%
খ
খ) 100%
গ
গ) 300%
ঘ
ঘ) 50%

ব্যাখ্যা

Let
Radius of the circle = r
then Area of the circle = πr²
if we doubled the radius then radius = 2r
and Area of the circle = π(2r)² = 4πr²

Increased Area = 4πr²- πr²=3πr²
Increase % = (3πr²/πr²) ×100}%
= 300%

১,১৮২.

69% of the students of a certain class took Mathematics and 47% took Biology. If each student took Biology or Mathematics and 44 took both, what is the total number of students in the class?

ক
150
খ
250
গ
300
ঘ
275

ব্যাখ্যা

Question: 69% of the students of a certain class took Mathematics and 47% took Biology. If each' student took Biology or Mathematics and 44 took both, what is the total number of students in the class?

Solution:
দেওয়া আছে,
গণিত নিয়েছে = 69%
জীববিজ্ঞান নিয়েছে = 47%
উভয় বিষয় নিয়েছে = 44 জন

ধরি,
উভয় বিষয় নিয়েছে = x জন

প্রশ্নমতে,
(69% - x) + x + (47% - x) = 100%
⇒ 116% - x = 100%
⇒ x = (116 - 100)%
⇒ x = 16%

আবার,
শর্তমতে,
মোট শিক্ষার্থী × 16% = 44
⇒ মোট শিক্ষার্থী × (16/100) = 44
⇒ মোট শিক্ষার্থী = (44 × 100)/16
⇒ মোট শিক্ষার্থী = 275

∴ মোট শিক্ষার্থীর সংখ্যা = 275 জন

১,১৮৩.

Pabel and Khalil started a business in the ratio of 2 : 3. After 2 years Pabel left the business but Khalil continued. After 3 years he had a profit of Tk 26000. What was the profit of Pabel?

ক
Tk. 8000
খ
Tk. 15600
গ
Tk.18000
ঘ
No Profit

ব্যাখ্যা

Question: Pabel and Khalil started a business in the ratio of 2 : 3. After 2 years Pabel left the business but Khalil continued. After 3 years he had a profit of Tk 26000. What was the profit of Pabel?

Solution:
Let,
the initial capital of Pabel and Khalil be Tk. 2x and Tk. 3x respectively.

Then, ratio of profits = (2x × 24) : (3x × 36)
= (2x × 2) : (3x × 3)
= 4x : 9x
= 4 : 9

∴ Profit of Pabel = 26000 × (4/13)
= 2000 × 4
= Tk. 8000

১,১৮৪.

A shopkeeper sells a badminton racket, whose marked price is Tk.800, at a discount of 15% and gives a shuttle cock costing Tk.20 free with each racket. Even then he makes a profit of 25%. His cost price per racket is-

ক
488 Tk
খ
528 Tk
গ
552Tk
ঘ
None of the above

ব্যাখ্যা

Question: A shopkeeper sells a badminton racket, whose marked price is Tk.800, at a discount of 15% and gives a shuttle cock costing Tk.20 free with each racket. Even then he makes a profit of 25%. His cost price per racket is-

Solution:
Marked price = 800 tk
After 15% discount selling price = (100 - 15)% of 800
= 85% of 800
= (85/100) × 800
= 680
cost of shuttle cock = 20 Tk

So, actual selling price = (680 - 20) tk
= 660 tk

let, cost price per racket is = x tk
at 25% profit, selling price = 1.25x tk

Now,
1.25x = 660
⇒ x = 660/1.25
= 528 Tk

His cost price per racket is 528 Tk.

১,১৮৫.

What is the original price of a T-shirt, if the sale price after 16% discount Is 264?

ক
ক) 300
খ
খ) 214
গ
গ) 320
ঘ
ঘ) 314

ব্যাখ্যা

84% = 264
So, 100% = (264 × 100) / 84
= 314.29 ≈ 314

১,১৮৬.

If the side of a square is increased by 20%, by what percent will the area be increased?

ক
21%
খ
42%
গ
44%
ঘ
20%

ব্যাখ্যা

Question: If the side of a square is increased by 20%, by what percent will the area be increased?

Solution:
Let the original side length = 10 units.

∴ Area = 10 × 10 = 100 square units

Again,
After a 20% increase, the new side length = 10 + (20% of 10)
= 10 + 2 = 12 units

∴ New area = 12 × 12 = 144 square units

∴ Increase in area = (144 - 100) square units
= 44 square units

∴ Percentage increase in area = (44/100) × 100%
= 44%

So the area will increase by 44%

১,১৮৭.

If w is 10% less than x, and y is 30% less than z, than wy is what percent less than xz ?

ক
ক) 10%
খ
খ) 15%
গ
গ) 24%
ঘ
ঘ) 37%

ব্যাখ্যা

ধরি, x = 100
w = 100 - 100 এর 10% = 100 - 10 = 90
আবার,
z = 100
y = 100 - 100 এর 30% = 100 - 30 = 70

wy = 90 × 70 = 630
xz = 100 × 100 = 10000

wy , xz এর চেয়ে কম = 10000 - 6300 = 3700
wy , xz এর চেয়ে শতকরা কম ={(3700/10000) × 100}% = 37%

১,১৮৮.

The percentage of metal extracted from a mine of lead ore is 50%. Now the percentage of gold is 4/5% of the metal and the rest is lead. If the mass of ore extracted from the mine is 6000kg, the mass of the lead is-

ক
48 kg
খ
1976 kg
গ
2998 kg
ঘ
2976 kg

ব্যাখ্যা

Question: The percentage of metal extracted from a mine of lead ore is 50%. Now the percentage of gold is 4/5% of the metal and the rest is lead. If the mass of ore extracted from the mine is 6000kg, the mass of the lead is-

Solution:
Given mass of lead ore = 6000 kg
Mass of metal is 50% of 6000 = 3000 kg
Mass of gold is 4/5% of 3000 = (4 × 3000)/(5 × 100) = 24 kg

Mass of lead = Mass of metal - Mass of gold
⇒ Mass of lead = 3000 - 24 = 2976 kg

১,১৮৯.

হাসান একটি পণ্য বিক্রি করে ২০% লাভ করে। যদি সে উক্ত পণ্যটি ১০% কম দামে কিনত এবং ৪০% লাভে বিক্রি করত, তাহলে সে ২৪ টাকা বেশি পেত। তাঁর প্রকৃত বিক্রয়মূল্য কত ছিল?

ক
৪২০ টাকা
খ
৪৪০ টাকা
গ
৪৮০ টাকা
ঘ
৫০০ টাকা
ঙ
কোনটিই নয়

ব্যাখ্যা

প্রশ্ন: হাসান একটি পণ্য বিক্রি করে ২০% লাভ করে। যদি সে উক্ত পণ্যটি ১০% কম দামে কিনত এবং ৪০% লাভে বিক্রি করত, তাহলে সে ২৪ টাকা বেশি পেত। তাঁর প্রকৃত বিক্রয়মূল্য কত ছিল?

সমাধান:
ধরি, প্রকৃত ক্রয়মূল্য = x টাকা
∴ ২০% লাভে বিক্রয়মূল্য = x + x এর ২০%
= x + ২০x/১০০
= ১২০x/১০০
= ১২x/১০
= ৬x/৫

নতুন ক্রয়মূল্য = x − x এর ১০%
= x − ১০x/১০০
= ৯০x/১০০
= ৯x/১০

৪০% লাভে নতুন বিক্রয়মূল্য = (৯x/১০) + (৯x/১০) এর ৪০%
= (৯x/১০) + (৩৬x/১০০)
= (৯০x + ৩৬x)/১০০
= ১২৬x/১০০
= ৬৩x/৫০

প্রশ্নমতে,
নতুন বিক্রয়মূল্য − পূর্ব বিক্রয়মূল্য = ২৪
⇒ ৬৩x/৫০ − ৬x/৫ = ২৪
⇒ (৬৩x - ৬০x)/৫০ = ২৪
⇒ ৩x/৫০ = ২৪
⇒ ৩x = ২৪ × ৫০
⇒ x = (২৪ × ৫০)/৩
∴ x = ৪০০

∴ প্রকৃত বিক্রয়মূল্য = ৬x/৫ = (৬×৪০০)/৫
= ৪৮০ টাকা

১,১৯০.

25% of A's income is equal to 35% of B's income. The ratio of the incomes of A and B is-

ক
ক) 5 : 7
খ
খ) 7 : 5
গ
গ) 13 : 15
ঘ
ঘ) 15 : 13
ঙ
ঙ) 7 : 13

ব্যাখ্যা

25% of A = 35% of B
⇒ (25/100)A = (35/100)B
⇒ A/4 = 7B/20
⇒ A/B = (7/20)×4 = 7/5
⇒ A:B = 7:5

১,১৯১.

A jacket is sold after providing two successive discounts of 15%. If the marked price of the jacket is Tk. 400, find the selling price.

ক
Tk. 270
খ
Tk. 276
গ
Tk. 281
ঘ
Tk. 289

ব্যাখ্যা

Question: A jacket is sold after providing two successive discounts of 15%. If the marked price of the jacket is Tk. 400, find the selling price.

Solution:
First Discount:
Discount 1 = 400 × (15/100) = Tk. 60
Selling Price after 1st Discount = 400 - 60 = Tk. 340

Second Discount:
Discount 2 = 340 × (15/100) = Tk. 51
Selling Price after 2nd Discount = 340 - 51 = Tk. 289

So, the selling price of the jacket after two successive discounts of 15% is Tk. 289.

১,১৯২.

In a factory, there are workers, executives and clerks. 70% of the employees are workers, 596 are executives and the remaining 334 employees are clerks. How many employees are there in the factory?

ক
3100
খ
2100
গ
2720
ঘ
3390

ব্যাখ্যা

Question: In a factory, there are workers, executives and clerks. 70% of the employees are workers, 596 are executives and the remaining 334 employees are clerks. How many employees are there in the factory?

Solution:
Let
Total employee 100%
Executive and clerks (100 - 70)% = 30%

executive and clerks employee = 596 + 334 = 930

Now
30% employee = 930
∴ 1% employee = 930/30
∴ 100% employee = ( 930 × 100)/30 = 3100

১,১৯৩.

Three partners shared the profit in a business in the ratio 3 : 4 : 5. They had partnered for 8 months, 6 months and 4 months respectively. What was the ratio of their investments?

ক
9 : 16 : 30
খ
9 : 18 : 30
গ
8 : 16 : 30
ঘ
9 : 16 : 24
ঙ
9 : 16 : 8

ব্যাখ্যা

Let their investments be x taka for 8 months,
y taka for 6 months
and z taka for 4 months respectively.

Then, 8x : 6y : 4z = 3 : 4 : 5.
or, 8x/6y = 3/4
or, y = 16x/9
and 8x/4z = 3/5.
or, z = 10x/3

x : y : z = x : 16x/9 : 10x/3 = 9 : 16 : 30

১,১৯৪.

The value of a machine depreciates every year by 10%. If its present value is Tk. 50000 then the value of the machine after 2 years is?

ক
Tk. 40000
খ
Tk. 45500
গ
Tk. 35500
ঘ
Tk. 40500

ব্যাখ্যা

Question: The value of a machine depreciates every year by 10%. If its present value is Tk. 50000 then the value of the machine after 2 years is?

solution:
Given that,
Present value of machine = 50000
Depreciation rate = 10%
And year = 2

Now,
After first year value of machine = (100 - 10)% of 50000 = (90/100) × 50000 = Tk. 45000
And after 2 years value of machine = (100 - 10)% of 45000 = (90/100) × 45000 = Tk. 40500

∴ value of machine after 2 years is Tk. 40500

১,১৯৫.

Asif bought 5 apples at Taka 15 and sold 3 apples at Taka 15. What will be the rate of profit-

ক
66.67%
খ
26.75%
গ
50%
ঘ
33.33%

ব্যাখ্যা

Question: Asif bought 5 apples at Taka 15 and sold 3 apples at Taka 15. What will be the rate of profit-

Solution:
5 টি আপেলের ক্রয়মূল্য 15 টাকা
1 টি আপেলের ক্রয়মূল্য 15/5 = 3 টাকা

আবার,
3 টি আপেলের বিক্রয়মূল্য 15 টাকা
1 টি আপেলের বিক্রয়মূল্য 15/3 = 5 টাকা

∴ লাভ = 5 - 3 = 2 টাকা

∴ 3 টাকায় লাভ হয় 2 টাকা
1 টাকায় লাভ হয় 2/3 টাকা
100 টাকায় লাভ হয় 200/3 = 66.67 টাকা

∴ লাভ 66.67%

১,১৯৬.

In an election 4% of votes cast are invalid. A candidate gets 55% of casted votes and wins the election by 4800 votes. Find the total number of votes casted.

ক
40000
খ
45000
গ
55000
ঘ
50000

ব্যাখ্যা

Question: In an election 4% of votes cast are invalid. A candidate gets 55% of casted votes and wins the election by 4800 votes. Find the total number of votes casted.

Solution:
বিজয়ী প্রার্থী ভোট পায়= 55%
বৈধ ভোট = (100 - 4)% = 96%

বিজয়ী প্রার্থী বৈধ ভোটের শতকরা পায় = (55 × 96)/100
= 52.8%

পরাজিত প্রার্থী ভোট পায় = (96 - 52.8)%
= 43.2%

বিজয়ী প্রার্থী ও পরাজিত প্রার্থীর ভোটের পার্থক্য = (52.8 - 43.2)%
= 9.6%

প্রশ্নমতে
9.6% = 4800
1% = 4800/9.6
100% = (4800 × 100)/9.6
= 50000

১,১৯৭.

A shopkeeper sells a pair of sunglasses at a profit of 25%. If he had bought it at 25% less and sold it for Tk. 10 less, he would have gained 40%. Determine the cost price of the pair of sunglasses.

ক
Tk. 40
খ
Tk. 50
গ
Tk. 55
ঘ
Tk. 60

ব্যাখ্যা

Question: A shopkeeper sells a pair of sunglasses at a profit of 25%. If he had bought it at 25% less and sold it for Tk. 10 less, he would have gained 40%. Determine the cost price of the pair of sunglasses.

Solution:
ধরি,
ক্রয়মূল্য = 100 টাকা
25% লাভে বিক্রয়মূল্য = 100 + 25 = 125 টাকা
25% কমে ক্রয়মূল্য = 100 - 25 = 75 টাকা

আবার,
40% লাভে বিক্রয়মূল্য = {75 + 75 × (40/100)}
= 105 টাকা
বিক্রয়মূল্য কম হয় = (125 - 105) টাকা
= 20 টাকা

এখন,
২০ টাকা বিক্রয়মূল্য কম হয় ক্রয়মূল্য = 100 টাকায়
∴ 10 টাকা বিক্রয়মূল্য কম হয় ক্রয়মূল্য = (100 × 10)/20 টাকায়
= 50 টাকা

১,১৯৮.

Alom invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 years is the same as the simple interest earned on the second part at 12% per annum for 3 years. Then, the percentage of his savings invested in the first part is

ক
30%
খ
32.3%
গ
37.5%
ঘ
None of these

ব্যাখ্যা

Question: Alom invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 years is the same as the simple interest earned on the second part at 12% per annum for 3 years. Then, the percentage of his savings invested in the first part is

Solution:
let, Alom invest x taka at 15% per annum for 4 years and y taka at 12% per annum for 3 years

ATQ,
x × 0.15 × 4 = y × 0.12 × 3
⇒ x/y = 0.36/.6 = 3/5
⇒ x : y = 3 : 5

%percentage = (3/8) × 100%
= 37.5%

১,১৯৯.

A retailer bought a glass at wholesale and marked it up 80% to its initial retail price of Tk.45. By how many more taka does he need to increase the price to achieve a 100% markup?

ক
Tk. 3
খ
Tk. 5
গ
Tk. 7
ঘ
Tk. 9

ব্যাখ্যা

Question: A retailer bought a glass at wholesale and marked it up 80% to its initial retail price of Tk.45. By how many more taka does he need to increase the price to achieve a 100% markup?

Solution:
let, wholesale price x

1.8x = 45
⇒ x = 45/1.8
∴ x = 25 taka

to achieve a 100% markup retail price = 25 + 25 = 50 taka

he needs to increase = 50 - 45 taka
= Tk. 5

১,২০০.

A coat was sold for Tk 75. The coat was sold for 150% of the cost of the coat. How much did the coat cost?

ক
Tk. 150
খ
Tk. 45
গ
Tk. 50
ঘ
Tk. 60
ঙ
None of these

ব্যাখ্যা

Question: A coat was sold for Tk. 75. The coat was sold for 150% of the cost of the coat. How much did the coat cost?

Solution:
Let,
The cost price of coat = x

ATQ,
150% of x = 75
⇒ (150/100) × x = 75
⇒ x = (75 × 100)/150
∴ x = 50