Percentage and Profit & Loss

PrepBank · পাতা ১৫ / ১৭ · ১,৪০১–১,৫০০ / ১,৬৯৬

১,৪০১.

90 is 75 percent of which number given below?

ক
ক) 110
খ
খ) 80
গ
গ) 100
ঘ
ঘ) 120

ব্যাখ্যা

ধরি ,
x এর 75% = 90
x এর 75/100 = 90
3x/4 = 90
x = (90 × 4)/3 = 120

১,৪০২.

A retailer marked the price of a television at Taka 8000 and gave a discount of 15%. Calculate the selling price and the amount of discount.

ক
Taka 6600
খ
Taka 5800
গ
Taka 6000
ঘ
Taka 6800

ব্যাখ্যা

Question: A retailer marked the price of a television at Taka 8000 and gave a discount of 15%. Calculate the selling price and the amount of discount.

Solution:

Marked Price of the television = Taka 8000
Discount Percentage = 15%
Discount Amount = Discount Percentage × Marked Price = 15% × Taka 8000 = Taka 1200
Selling Price = Marked Price - Discount Amount = Taka 8000 - Taka 1200 = Taka 6800

১,৪০৩.

By selling 33 metres of cloth, one gains the selling price of 11 metres. Find the gain percent

ক
ক) 45%
খ
খ) 40%
গ
গ) 50%
ঘ
ঘ) 35%

ব্যাখ্যা

Here,
The selling price of 11m cloth is obtained as profit.
(S.P. of 33 m cloth) – (C.P. of 33 m cloth)= S.P pf 11 m cloth
The selling price of 22 m cloth = Cost Price of 33 m of cloth

Let the cost of each metre be Tk. 100.

Therefore,
the cost price of 22 m cloth = 22 × 100 = Tk. 2200 and
S.P. of 22 m cloth = Tk. 3300
Profit = 3300 - 2200 = 1100

Profit% = {(1100/2200) × 100}%
= 50%

১,৪০৪.

By Selling 45 lemons for Tk. 40, a man loses 20%. How many should he sell for Tk..24, to gain 20% in the transaction?

ক
22
খ
20
গ
18
ঘ
16

ব্যাখ্যা

Question: By Selling 45 lemons for Tk. 40, a man loses 20%. How many should he sell for Tk..24, to gain 20% in the transaction?

Solution:
SP per Lemons = 40/45
= Tk. 0.88.
Let, CP was Tk. X per Lemons.
SP = CP - 20% of CP
⇒ 0.88 = 0.8X
⇒ X = Tk. 1.11

To get 20% profit,
SP = 1.11 + 20% of 1.11 = Tk.1.33

Thus, he can sell = 24/1.33
= 18 Lemons in Tk. 24.

১,৪০৫.

There is a shopkeeper whose claim is that he sells a certain product at a cost of Tk 23/kg, which actually costs him Tk 25/kg. The shopkeeper says that he is taking the loss to let his customers get a better deal. When examined thoroughly, the constabulary find that the shopkeeper is actually using an 800 gms weight in place of a 1 kg weight. How much does he gain or lose?

ক
17% loss
খ
17% profit
গ
23.3% loss
ঘ
15% profit

ব্যাখ্যা

Question: There is a shopkeeper whose claim is that he sells a certain product at a cost of Tk 23/kg, which actually costs him Tk 25/kg. The shopkeeper says that he is taking the loss to let his customers get a better deal. When examined thoroughly, the constabulary find that the shopkeeper is actually using an 800 gms weight in place of a 1 kg weight. How much does he gain or lose?

Solution:
Selling price of 0.8 kg = 23 taka

Selling price of 1 kg = 23/0.8 taka
= 115/4 taka
= 28.75 taka

∴ Percentage profit = {(28.75 - 25)/25} × 100%
= (3.75/25) × 100%
= 15%

১,৪০৬.

1200 boys and 800 girls appeared in an examination. If 60% of the boys and 40% of the girls passed the examination, what is the percentage of candidates who failed in the examination?

ক
45%
খ
52%
গ
48%
ঘ
42%

ব্যাখ্যা

Question: 1200 boys and 800 girls appeared in an examination. If 60% of the boys and 40% of the girls passed the examination, what is the percentage of candidates who failed in the examination?

Solution:
Number of students failed = 40% of boys (1200) + 60% of girls (800)
= (40 × 1200)/100 + (60 × 800)/100
= 480 + 480
= 960

Total number of students = 1200 + 800 = 2000

∴ Percentage of candidates failed = (960/2000) × 100
= 48%

১,৪০৭.

A shopkeeper lost 7.5% by selling an article. If he had bought it at 10% less and sold it for tk. 31 more, he would have gained 20%. Find the cost price of the article.

ক
50 tk.
খ
125 tk.
গ
200 tk.
ঘ
300 tk.
ঙ
370 tk.

ব্যাখ্যা

Let, Cost price be tk. 100,
At the loss of 7.5%, the selling price would be tk. (100-7.5)=92.5
At 10% less Cost price would be tk. (100-10) =90
if he gained 20% the selling price would be tk (90+20% of 90) tk (90+18) Etk. 108
Difference of selling price = tk (108 - 92.50) tk 15.50

So when the difference value is 15.50, then the actual value of difference = 31
when the value is 1, then the actual value = 31/15.50
when the value of CP is 100, then the actual value of CP is = 31/15.50 x 100 = 200 TK

১,৪০৮.

The price of a pen is 25% more than the price of a book. The price of a pen holder is 50% more than the price of the book. How much is the price of the pen holder more than the price of the pen?

ক
20%
খ
25%
গ
35%
ঘ
15%

ব্যাখ্যা

Let price of book = 100tk

Price of pen = 100 + 100 × 25% = 125 tk
Price of pen-holder = 100 + 100 × 50% = 150 tk

Difference is = 150 -125 = 25 tk

∴ Percentage = (25 × 100)/125 = 20%

১,৪০৯.

5.6 can be expressed in terms of percentage as

ক
ক) 56%
খ
খ) 5.6%
গ
গ) 560%
ঘ
ঘ) 0.56%

ব্যাখ্যা

5.6 × 100/100
⇒ (5.6 × 100) × (1/100)
= (5.6 × 100)%
= 560%

∴ 5.6 is 560%.

১,৪১০.

A shopkeeper marks the price of an article at Tk. 80. What will be the selling price, if he allows two successive discounts of 5% each?

ক
ক) Tk. 72
খ
খ) Tk. 85
গ
গ) Tk. 72.2
ঘ
ঘ) Tk. 7.2

ব্যাখ্যা

At 5% discount for the first time = 80 × 95/100 = Tk. 76
At 5% discount for second time = 76 × 95/100 = Tk. 72.20

১,৪১১.

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

ক
ক) 100%
খ
খ) 64%
গ
গ) 74%
ঘ
ঘ) 70%

ব্যাখ্যা

প্রশ্ন: A person multiplied a number by 3/5 instead of 5/3, What is the percentage error in the calculation?

সমাধান:
ধরি,
সংখ্যাটি = ক

৩/৫ দ্বারা গুণ করলে হবে = ৩ক/৫
৫/৩ দ্বারা গুণ করলে হবে = ৫ক/৩

হিসাবের ভুল = (৫ক/৩ - ৩ক/৫)
= (২৫ক - ৯ক)/১৫
= ১৬ক/১৫

৫ক/৩ এ ভুল হয় = ১৬ক/১৫
∴ ১ এ ভুল হয় = (১৬ক/১৫) × (৩/৫ক) = ১৬/২৫
∴ ১০০ এ ভুল হয় = (১৬/২৫) × ১০০
= ৬৪

১,৪১২.

Bottles A and B contain alcohol-water solutions in ratios of 1:3 and 4:1 respectively. X liters of the solution from bottle A are to be mixed with Y liters of the solution from bottle B. What will be the percentage of alcohol in the resultant solution?

ক
{(5X + 10Y)/(X + Y)}%
খ
{(25X + 16Y)/(X + Y)}%
গ
{(25X + 80Y)/(X + Y)}%
ঘ
{(5X + 16Y)/(X + Y)}%

ব্যাখ্যা

Question: Bottles A and B contain alcohol-water solutions in ratios of 1:3 and 4:1 respectively. X liters of the solution from bottle A are to be mixed with Y liters of the solution from bottle B. What will be the percentage of alcohol in the resultant solution?

Solution:
In bottle A,
alcohol = 1/4
so, in X liters of bottle A contains alcohol = X/4

in bottle B,
alcohol = 4/5
so, in Y liters of bottle B contains alcohol = 4Y/5

total alcohol in X + Y liters solution = X/4 + 4Y/5
= (5X + 16Y)/20

∴ percentage = [{(5X + 16Y)/20}/(X + Y)] × 100%
= {(25X + 80Y)/(X + Y)}%

১,৪১৩.

By selling 20 oranges for one taka a man losses 4%. How many oranges for one taka should he sell to gain 20%?

ক
14
খ
16
গ
17
ঘ
18

ব্যাখ্যা

Question: By selling 20 oranges for one taka a man losses 4%. How many oranges for one taka should he sell to gain 20%?

Solution:
৪% ক্ষতিতে
ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য ৯৬ টাকা

বিক্রয়মূল্য ৯৬ টাকা হলে ক্রয়মূল্য ১০০ টাকা
বিক্রয়মূল্য ১ টাকা হলে ক্রয়মূল্য ১০০/৯৬ টাকা

২০% লাভে
ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য ১২০ টাকা
ক্রয়মূল্য ১ টাকা হলে বিক্রয়মূল্য ১২০/১০০ টাকা
ক্রয়মূল্য ১০০/৯৬ টাকা হলে বিক্রয়মূল্য (১২০/১০০) × (১০০/৯৬)টাকা
= ১০/৮
=৫/৪

৫/৪ টাকায় বিক্রয় করতে হবে ২০ টি কমলা
১ টাকায় বিক্রয় করতে হবে ২০× (৪/৫) টি কমলা
= ১৬ টি

১,৪১৪.

Mohan bought an article at 20% less of the marked price and sold it at 20% more than the marked price. Find the profit earned by him.

ক
50%
খ
55%
গ
57.3%
ঘ
52.3%

ব্যাখ্যা

Question: Mohan bought an article at 20% less of the marked price and sold it at 20% more than the marked price. Find the profit earned by him.

Solution:
Let the marked price be Tk. 100
∴ Cost Price = 100 - 20 = 80
And,
Selling Price = 100 + 20 = 120

Profit = 120 - 80 = 40

Profit % = (40/80) × 100% = 50%

১,৪১৫.

What is the original price of a T-shirt, if the sale price after 15% discount is 272?

ক
ক) 300
খ
খ) 280
গ
গ) 320
ঘ
ঘ) 314

ব্যাখ্যা

ATQ,
85% = 272
So, 100% = (272 × 100)/85 = 320

১,৪১৬.

(75% of 320) + (40% of 150) - ? = 170

ক
110
খ
120
গ
130
ঘ
140

ব্যাখ্যা

Question: (75% of 320) + (40% of 150) - ? = 170

Solution:
Let,
(75% of 320) + (40% of 150) - x = 170
⇒ {(75 × 320)/100} + {( 40 × 150)/100} - x = 170
⇒ 240 + 60 - x = 170
⇒ - x = 170 - 300
∴ x = 130

১,৪১৭.

At what profit percent must an article be sold so that by selling at half that price, there will a loss of 30%?

ক
25%
খ
36%
গ
42%
ঘ
40%

ব্যাখ্যা

Question: At what profit percent must an article be sold so that by selling at half that price, there will a loss of 30%?

Solution:
ধরি,
দ্রব্যটির ক্রয়মূল্য ১০০ টাকা
এবং লাভে দ্রব্যটির বিক্রয়মূল্য ক টাকা

এখন দ্রব্যটি ক এর অর্ধেক মূল্যে বিক্রয় করলে ৩০ টাকা ক্ষতি হয়।

∴ ১০০ - ক/২ = ৩০
বা, ২০০ - ক = ৬০
বা, ক = ২০০ - ৬০
∴ ক = ১৪০

∴ ক টাকা বিক্রয় করলে লাভ হয় = ক - ১০০ = ১৪০ - ১০০ = ৪০ টাকা

∴ ৪০% লাভে বিক্রয় করতে হবে।

১,৪১৮.

If you buy equal amounts of two types of chocolate at the rate of Tk. 1/4 and Tk. 1/6 respectively and sell all of them at the rate of Tk. 1/5, what will be your profit/loss?

ক
ক) 1% loss
খ
খ) 2% profit
গ
গ) 4% profit
ঘ
ঘ) 4% loss

ব্যাখ্যা

মনে করি,
প্রত্যেক ধরনের চকলেট কেনার হলো 60 টি করে।
তাহলে,
Total cost = 60 × (1/4) + 60 × (1/6)
= 25।
আবার, selling price = 60 × 2 × (1/5)
= 24।
কাজেই percentage loss = (25 - 24)/25 × 100
= 4%

১,৪১৯.

Rifat sold an article for Tk. 528 alter allowing a discount of 12% on its marked price. What was the marked price of the article?

ক
ক) 820 Tk.
খ
খ) 650 Tk.
গ
গ) 700 Tk.
ঘ
ঘ) 600 Tk.

ব্যাখ্যা

Question: Rifat sold an article for Tk. 528 alter allowing a discount of 12% on its marked price. What was the marked price of the article?

Solution:
Marked price of a article be x
According to the question
x88/100 = 528
88x = 528 × 100
x = (528 × 100)/88
x= 600

১,৪২০.

An article is sold at a 25% discount, resulting in a 20% profit. If the discount is reduced to 15%, what will be the new profit percentage?

ক
39%
খ
22%
গ
35%
ঘ
36%

ব্যাখ্যা

Question: An article is sold at a 25% discount, resulting in a 20% profit. If the discount is reduced to 15%, what will be the new profit percentage?

Solution:
Let the cost price (CP) be Tk. 100

With 20% profit:
Selling Price (SP) = CP + 20% profit
= 100 + 20
= Tk. 120

This SP is after 25% discount on Marked Price (MP).
∴ SP = 75% of MP
⇒ 120 = 0.75 × MP
⇒ MP = 120 / 0.75
= Tk. 160

Now, with reduced discount of 15%:
New Selling Price = 85% of Marked Price
= 0.85 × 160
= Tk. 136

∴ New profit = New Selling Price – Cost Price
= 136 – 100
= Tk. 36

∴ New profit percentage = (36 / 100) × 100% = 36%

১,৪২১.

The length of a rectangle is increased by 25%. By what percentage should the width be decreased so that the area of the rectangle remains unchanged?

ক
30%
খ
25%
গ
20%
ঘ
35%

ব্যাখ্যা

Question: The length of a rectangle is increased by 25%. By what percentage should the width be decreased so that the area of the rectangle remains unchanged?

Solution:
We can let the original length = 4, and the original width = 10.
So the original area is 40.

When the length increases by 25% we have 4 × 1.25 = 5
Thus, for the area to remain 40, the width must be 8.

Since {(8 - 10)/10} × 100 = - 20, we see that 8 is 20 percent less than 10. In other words, the width has to decrease by 20%.

১,৪২২.

The ratio, in which tea costs Tk. 192 per kg is to be mixed with tea costing Tk. 150 per kg so that the mixed tea when sold for Tk. 194.40 per kg, gives a profit of 20%

ক
2 : 5
খ
3 : 5
গ
5 : 3
ঘ
5 : 2

ব্যাখ্যা

CP of first tea = Tk. 192 per kg.
CP of Second tea = Tk. 150 per kg.
The mixture is to be sold in Tk. 194.40 per kg, which has included 20% profit. So,
SP of Mixture = Tk. 194.40 per kg.

Let the CP of Mixture be Tk. X per kg. Therefore,
X + 20% of X = SP
6x/5 = 194.40
6X = 194.40 × 5
X = Tk. 162 per kg.

Let N kg of first tea and M kg of second tea be added.

Now, Using Alligation,
We get,
N/M = 12/30
N/M = 2 : 5

১,৪২৩.

If the selling price is tripled, the profit becomes eight times. Find the profit percent.

ক
25%
খ
40%
গ
50%
ঘ
55%

ব্যাখ্যা

Question: If the selling price is tripled, the profit becomes eight times. Find the profit percent.

Solution:
Let,
The cost price be Tk.100 and sell price be Tk. x,

Then,
The profit is = (x - 100)

Now, The sell price is doubled, then the new sell price is 3x
New profit is = (3x - 100)

ATQ,
8(x - 100) = 3x - 100
⇒ 8x - 800 = 3x - 100
⇒ 8x - 3x = 800 - 100
⇒ 5x = 700
∴ x = 140

Then, the Profit = (140 - 100) = 40
Hence the profit percentage is = (40/100) × 100%
= 40%

১,৪২৪.

25% of the candidates failed in English and 35% failed in Math. If 15% failed in both subjects, what percentage passed both English and Math?

ক
30%
খ
45%
গ
55%
ঘ
60%

ব্যাখ্যা

Question: 25% of the candidates failed in English and 35% failed in Math. If 15% failed in both subjects, what percentage passed both English and Math?
(২৫% প্রার্থীর ইংরেজি পরীক্ষায় এবং ৩৫% গণিত পরীক্ষায় ফেল হয়েছে। ১৫% প্রার্থী উভয় বিষয়েই ফেল করেছে, তাহলে কত শতাংশ প্রার্থী ইংরেজি ও গণিত উভয় বিষয়েই পাস করেছে?)

Solution:
ইংরেজি এবং গণিত উভয় বিষয়ে ফেল করেছেন = 15%
শুধুমাত্র ইংরেজিতে ফেল করেছেন = (25 - 15)% = 10%
শুধুমাত্র গণিতে ফেল করেছেন = (35 - 15)% = 20%

∴ এক বা দুটি বিষয়ে ফেল করা প্রার্থী সংখ্যা = 15% + 10% + 20%
= 45%

∴ উভয় বিষয়েই পাশ করা প্রার্থী সংখ্যা = (100 - 45)% = 55%

১,৪২৫.

A student scores 55% marks in 8 papers of 100 marks each. He scores 15% of the total marks in Bangla How much does he score in Bangla?

ক
62
খ
66
গ
68
ঘ
72

ব্যাখ্যা

Question: A student scores 55% marks in 8 papers of 100 marks each. He scores 15% of the total marks in Bangla How much does he score in Bangla?

Solution:
৮ টি বিষয়ে মোট নম্বর = 8 × 100 = 800
সে নম্বর পেয়েছে = 800 এর 55%
= 800 এর 55/100
= 440

সে বাংলায় নম্বর পেয়েছে = 440 এর 15%
= 440 এর 15/100
= 66

১,৪২৬.

The price of the sugar rise by 25%. If a family wants to keep their expenses on sugar the same as earlier, the family will have to decrease its consumption of sugar by-

ক
10%
খ
12%
গ
20%
ঘ
25%

ব্যাখ্যা

Question: The price of the sugar rise by 25%. If a family wants to keep their expenses on sugar the same as earlier, the family will have to decrease its consumption of sugar by-

Solution:
২৫% বৃদ্ধিতে দাম = (১০০ + ২৫) = ১২৫টাকা।

১২৫ টাকায় চিনি খাওয়া কমে = ১২৫ - ১০০ = ২৫ টাকা
∴ ১ টাকায় চিনি খাওয়া কমে = ২৫/১২৫ টাকা
∴ ১০০ টাকায় চিনি খাওয়া কমে = (২৫ × ১০০)/১২৫
= ২০ টাকা

অর্থাৎ, শতকরা ২০% কমিয়েছিল

১,৪২৭.

An employer pays 3 workers X, Y and Z a total of TK. 36600 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
9000
খ
10800
গ
11700
ঘ
12000

ব্যাখ্যা

Question: An employer pays 3 workers X, Y and Z a total of TK. 36600 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:
X = 125% of Y
⇒ X = 125Y/100
⇒ X/Y = 125/100
∴ X : Y = 5 : 4 = 5 × 4 : 4 × 4 = 20 : 16

X = 80% of Z
⇒ X = 80Z/100
⇒ X/Z = 80/100
∴ X : Z = 4 : 5 = 4 × 5 : 5 × 5 = 20 : 25

∴ X : Y : Z = 20 : 16 : 25

X makes the week = (20/61) × 36600
= 12000

১,৪২৮.

A fruit seller purchases guavas at the rate of 2 guavas for 1 taka and sells them at the rate of 5 guavas for 3 taka. What is his gain percentage?

ক
22%
খ
18%
গ
15%
ঘ
20%
ঙ
None

ব্যাখ্যা

Question: A fruit seller purchases guavas at the rate of 2 guavas for 1 taka and sells them at the rate of 5 guavas for 3 taka. What is his gain percentage?

Solution:
2 guavas cost 1 tk
So 1 lemon costs 1/2 tk

For comparing,
let's calculate CP (Cost Price) for 10 guavas
∴ CP of 10 guavas = 10 × (1/2) = 5 tk

Now,
Let's find the selling price (SP) of guavas:
5 guavas cost 3 tk
∴ 10 guavas will cost = (10/5) × 3 = 6 tk

∴ Gain = SP - CP = 6 - 5 = 1 tk
∴ Gain percentage = (Gain/CP) × 100
= (1/5) × 100
= 20%

১,৪২৯.

A mobile phone is sold for Tk. 9,600, and the seller makes a profit of 25% on the cost price. What will be the new selling price if he reduces the profit to 10%?

ক
7575 Tk.
খ
8448 Tk.
গ
1056 Tk.
ঘ
8652 Tk.

ব্যাখ্যা

Question: A mobile phone is sold for Tk. 9,600, and the seller makes a profit of 25% on the cost price. What will be the new selling price if he reduces the profit to 10%?

Solution:
At 25% profit,
Selling Price = 125% of Cost Price
∴ Cost Price = (100/125) × Selling Price
= (100/125) × 9,600
= 7,680 Tk.

Now, if the seller wants 10% profit,
∴ New Selling Price = 7,680 + (10% of 7,680)
= 7,680 + {(10/100) × 7,680}
= 7,680 + 768
= 8,448 Tk.

১,৪৩০.

Nazrul saved Tk. 2.50 in buying an item on sale. If he spent Tk. 25 for the item, approximately how much percent did he save in the transaction?

ক
8%
খ
(100/9)%
গ
(100/11)%
ঘ
None of these

ব্যাখ্যা

Question: Nazrul saved Tk. 2.50 in buying an item on sale. If he spent Tk. 25 for the item, approximately how much percent did he save in the transaction?

Solution:
cost price = 25 + 2.5 = 27.5 taka

Approximate save = (2.5/27.5) × 100%
= (100/11)%

১,৪৩১.

A man buys a cycle for Tk.1400 and sells it at a loss of 15%. What is the selling price of the cycle?

ক
ক) Tk.1290
খ
খ) Tk.1190
গ
গ) Tk.1090
ঘ
ঘ) Tk.1390

ব্যাখ্যা

S.P. = 85% of Tk.1400
= Tk. (85 × 1400)/100
= Tk.1190

১,৪৩২.

After paying a 10 percent tax on all income over Tk. 3,000, a person had a net income of Tk. 12,000. What was the income before taxes?

ক
Tk. 13,000
খ
Tk. 12900
গ
Tk. 10000
ঘ
Tk. 9000

ব্যাখ্যা

Question: After paying a 10 percent tax on all income over Tk. 3,000, a person had a net income of Tk. 12,000. What was the income before taxes?

Solution:
প্রশ্নে ৩০০০ টাকা পর্যন্ত আয়ের উপর কোন কর দেয়া লাগে না এবং ৩০০০ টাকার উপর আয় করলে বাকি টাকার উপর কর দিতে হয়।

ধরি,
আয়ের করযুক্ত অংশ ক টাকা

∴ ক - ক এর ১০% + ৩০০০ = ১২০০০
বা, ক - (১০ক)/১০০ + ৩০০০ = ১২০০০
বা, ক - ক/১০ = ৯০০০
বা, ১০ক - ক = ৯০০০০
বা, ৯ক = ৯০০০০
∴ ক = ১০০০০

∴ করযুক্ত টাকা ১০০০০ এবং করমুক্ত টাকা ৩০০০
∴ মোট টাকা (১০০০০ + ৩০০০) = ১৩০০০ টাকা

∴ যদি কর না দিত তাহলে তাঁর আয় ১৩০০০ টাকা হত। কিন্তু ১০০০ টাকা কর দিয়ে দেয়ায় তার আয় থাকে ১২০০০ টাকা

১,৪৩৩.

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. 9
খ
Tk. 6
গ
Tk. 5
ঘ
Tk. 4

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

১,৪৩৪.

If selling a chair for 720 Taka causes a 10% loss, determine the selling price required to earn a 20% profit on the same item.

ক
Tk. 760
খ
Tk. 800
গ
Tk. 920
ঘ
Tk. 960

ব্যাখ্যা

Question: If selling a chair for 720 Taka causes a 10% loss, determine the selling price required to earn a 20% profit on the same item.

Solution:

১,৪৩৫.

Find the rate of discount when the marked price is Tk.1880 and selling price is Tk. 1598.

ক
ক) 12%
খ
খ) 18%
গ
গ) 8%
ঘ
ঘ) 15%

ব্যাখ্যা

Question: Find the rate of discount when the marked price is Tk.1880 and selling price is Tk. 1598.

Solution:

বইয়ের লিখিত মূল্য, x = Tk. 1880
বইয়ের বিক্রয় মূল্য, y = Tk. 1598

Formula:
If Tk. x be MP of the article and Tk. y be S.P of the article, then

ছাড় = (x - y)
ছাড় % = (Discount/MP) × 100

ছাড় = 1880 - 1598 = Tk. 282
∴ ছাড়ের শতাংশ = (282/1880) × 100 = 15%

১,৪৩৬.

A trader expects a gain of 15% on his cost price. If in a week his sale is of Tk. 580, then what is his profit?

ক
ক) 75.65
খ
খ) 73.26
গ
গ) 72.50
ঘ
ঘ) 70.78

ব্যাখ্যা

We are given selling price = Tk. 580 and expected profit of 15%
Therefore, we can easily solve this numerical, considering basic formulae of profit and loss.
Let cost price = x
Selling price = C.P. + Profit
S.P. = C.P. + (15% of C.P.) [We know that profit is gained on cost price]
580 = x + (0.15 x)
580 = 1.15 x

Therefore,
x = 504.347
Cost Price = Tk. 504.35
Now,
we have the cost price and hence,
Profit = S.P. – C.P. = 580 – 504.35
= Tk. 75.65
The trader gets a profit of Tk. 75.65

১,৪৩৭.

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

ক
ক) Tk. 56
খ
খ) Tk. 65
গ
গ) Tk. 72
ঘ
ঘ) Tk. 84

ব্যাখ্যা

C.P. = Tk. {(100/122.5) x 392}
= Tk. {(1000/1225) x 392}
= 320

Profit = Tk. (392 - 320)
= Tk. 72

১,৪৩৮.

A number increased by 37.5% gives 33. The number is -

ক
ক) 22
খ
খ) 24
গ
গ) 25
ঘ
ঘ) 27

ব্যাখ্যা

Let,
the number be x.
Then, (100 + 37.5)% of x
⇒ 137.5% of x = 33
⇒ 137.5 × (1/100) × x = 33
⇒ x = (33 × 100)/137.5
⇒ x = 24.

১,৪৩৯.

The profit percent gained if an object is sold at Tk. 464 is equals to the loss percent when the object is sold at Tk. 436. Find the cost price of this object?

ক
250
খ
400
গ
450
ঘ
500

ব্যাখ্যা

Question: The profit percent gained if an object is sold at Tk. 464 is equals to the loss percent when the object is sold at Tk. 436. Find the cost price of this object?

Solution:
Let cost price = x

Profit = selling price - cost price = 464 - x
Loss = cost price - selling price = x - 436

loss % = {(x - 436)/x} × 100
profit % = {(464 - x)/x} × 100

ATQ,
loss % = profit %
{(x - 436)/x} × 100 = {(464 - x)/x} × 100
⇒ (x - 436)/x = (464 - x)/x
⇒ x - 436 = 464 - x
⇒ 2x = 464 + 436
⇒ 2x = 900
∴ x = 450

১,৪৪০.

A dishonest dealer marks up the price of his goods by 20% and gives a discount of 10% to the customer. Besides, he also cheats both his supplier and his buyer by 100 grams while buying or selling 1 kilogram. Find the percentage profit earned by the shopkeeper?

ক
20%
খ
25%
গ
32%
ঘ
46.66%

ব্যাখ্যা

He buys 1100 grams instead of 1000 grams.
Suppose he bought 1100 grams for Tk. 1000.

He sells only 900 grams when he takes the money for 1 kg.
Now, according to the problem,
he sells at an 8% profit (20% markup, 10% discount).
Hence, his selling price is Tk. 1080 for 900 grams.

Now,
1100 grams for Tk. 1000
Hence, 1188 grams for Tk. 1080
Selling: 900 grams for Tk. 1080
Hence % profit = (288/900) × 100 = 32%

১,৪৪১.

A started a business with Tk. 2100 and is joined afterwards by B with Tk. 3600. After how many months did B join if the profits at the end of the year are divided equally?

ক
7 months
খ
3 months
গ
4 months
ঘ
5 months

ব্যাখ্যা

Question: A started a business with Tk. 2100 and is joined afterwards by B with Tk. 3600. After how many months did B join if the profits at the end of the year are divided equally?

Solution:
Suppose,
B joined after x months.

Then,
2100 × 12 = 3600 × (12 - x)
⇒ 252 = 432 - 36x
⇒ 36x = 180
∴ x = 5

∴ B joined after 5 months

১,৪৪২.

A pen was sold at 10% loss. If the selling price was Tk. 6 more, then the seller could have made a profit of 5%. What was the purchase price of the pen?

ক
ক) 45
খ
খ) 40
গ
গ) 30
ঘ
ঘ) 25

ব্যাখ্যা

মনে করি,
ক্রয়মূল্য = 100 টাকা
∴ 10% loss এ বিক্রয়মূল্য = 90 টাকা
এবং 5% profit এ বিক্রয়মূল্য = 105 টাকা
∴ বিক্রয়মূল্য (105 - 90) = 15 টাকা বেশি হলে,
5% profit হতো।
এখন ঐকিক নিয়ম ব্যবহার করে, বিক্রয়মূল্য 15 টাকা বেশি হলে ক্রয়মূল্য 100 টাকা
∴ বিক্রয়মূল্য 1 টাকা বেশি হলে ক্রয়মূল্য (100/15) টাকা
∴ বিক্রয়মূল্য 6 টাকা বেশি ক্রয়মূল্য (100/15) × 6
= 40 টাকা।

১,৪৪৩.

If 75% of a number is added to 75, then the result is the number itself. The number is -

ক
ক) 50
খ
খ) 60
গ
গ) 300
ঘ
ঘ) 400

ব্যাখ্যা

Let,
the number be x.
Then, 75% of x + 75 = x
⇒ x - 75x/100 = 75
⇒ x - 3x/4 = 75
⇒ x/4 = 75
⇒ x = 300

১,৪৪৪.

The monthly income of a person was Tk. 13500 and his monthly expenditure was Tk. 9000. Next year, his income increased by 14% and his expenditure by 7%. Find the percentage increase in his savings.

ক
28%
খ
25%
গ
24%
ঘ
30%

ব্যাখ্যা

Question: The monthly income of a person was Tk. 13500 and his monthly expenditure was Tk. 9000. Next year, his income increased by 14% and his expenditure by 7%. Find the percentage increase in his savings.

Solution:
Savings before increased income = Tk. (13500 - 9000)
= Tk. 4500

Increased income = 114% of 13500 = Tk. (114/100) × 13500
= Tk. 15390

Increased expenditure = 107% of 9000 = Tk. (107/100) × 9000
= Tk. 9630

Saving after Increased income = Tk. (15390 - 9630) = Tk. 5760

Increased Savings = Tk. (5760 - 4500)
= Tk. 1260

∴ Increase % in savings = (1260/4500) × 100 %
= 28%

১,৪৪৫.

If a student of the mathematics department sells all his books for Tk. 7,500, he loses 25%. To gain 10%, at what price should he sell the books?

ক
Tk. 11500
খ
Tk. 13000
গ
Tk. 11000
ঘ
Tk. 12000

ব্যাখ্যা

Question: If a student of the mathematics department sells all his books for Tk. 7,500, he loses 25%. To gain 10%, at what price should he sell the books?

Solution:
Let,
The cost price of the books x.
Selling price = x - 25% of x
⇒ 7500 = x - (25x/100)
⇒ 7500 = 75x/100
⇒ 75x = 750000
∴ x = 10000

To gain 10% = 10000 + 10% of 10000
= 10000 + 1000
= Tk. 11000

To gain 10%, he should sell the books for Tk. 11000.

১,৪৪৬.

The cost of a book was Tk.75. The cost was first increased by 20% and later on it was reduced by 20%. The present cost of the book is:

ক
Tk. 82
খ
Tk. 79
গ
Tk. 76
ঘ
Tk. 72
ঙ
None

ব্যাখ্যা

Question: The cost of a book was Tk.75. The cost was first increased by 20% and later on it was reduced by 20%. The present cost of the book is:

Solution:

Here, the initial Cost = Tk. 75

After 20% increase in the cost, it becomes,

(75 + 20% of 75) = Tk. 90

Now, the Cost is decreased by 20%, So the cost will become,

(90 - 20% of 90) = Tk. 72

Hence, the present cost is Rs. 72

১,৪৪৭.

If selling price is doubled, the profit fourples. Find the profit percent?

ক
25%
খ
33.33%
গ
50%
ঘ
100%

ব্যাখ্যা

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

Solution:
Let,
The cost price be Tk.100 and sell price be Tk .x,
Then
The profit is (x - 100)

Now The sell price is doubled, then the new sell price is 2x
New profit is (2x - 100)

ATQ,
4(x - 100) = 2x - 100
or, 4x - 400 = 2x - 100
or, 4x - 2x = 400 - 100
∴ x = 150

Then the Profit = (150 - 100) = 50
Hence the profit percentage is = (50 × 100)/100 %
= 50%

১,৪৪৮.

Pens that used to cost Tk. 150 for a package of 3 now cost Tk. 300 for a package of 5. What is the percent increase in the price of these pens?

ক
15%
খ
20%
গ
25%
ঘ
None

ব্যাখ্যা

Question: Pens that used to cost Tk. 150 for a package of 3 now cost Tk. 300 for a package of 5. What is the percent increase in the price of these pens?

Solution:
Original cost: Tk. 150 for a package of 3 pens.
Cost per pen originally: Original cost per pen = 150/3 = Tk. 50 per pen

New cost: Tk. 300 for a package of 5 pens.
Cost per pen now: New cost per pen=300/5 = Tk. 60 per pen

Increase in cost = 60 - 50 = Tk. 10 per pen

Percent increase = (10/50) × 100 = 20%

১,৪৪৯.

A shopkeeper marks an item at Tk 1500 and gives a 20% discount. If he still makes a 25% profit, what was the cost price?

ক
Tk. 900
খ
Tk. 960
গ
Tk. 870
ঘ
Tk. 800
ঙ
Tk. 1020

ব্যাখ্যা

Question: A shopkeeper marks an item at Tk 1500 and gives a 20% discount. If he still makes a 25% profit, what was the cost price?

Solution:
Selling price after 20% discount
= 1500 - 20% of 1500
= 1500 - {(20/100) × 1500}
= 1500 - 300
= 1200

Let the cost price = x
Profit = 25%

Now,
⇒ x + 25% of x = 1200
⇒ x + (25/100)x = 1200
⇒ x + (x/4) = 1200
⇒ 5x = 4800
⇒ x = 4800/5
∴ x = 960

So, the cost price of that item is Tk. 960

১,৪৫০.

২২৩৬ টাকা A, B ও C এর মধ্যে এমনভাবে ভাগ করে দেওয়া হলো যেন A, C থেকে ২৫% বেশি এবং C, B থেকে ২৫% কম পায়। তাহলে A কত টাকা পাবে?

ক
৮০০ টাকা
খ
৬২৮ টাকা
গ
৬৯০ টাকা
ঘ
৭৮০ টাকা
ঙ
কোনটিই নয়

ব্যাখ্যা

প্রশ্ন: ২২৩৬ টাকা A, B ও C এর মধ্যে এমনভাবে ভাগ করে দেওয়া হলো যেন A, C থেকে ২৫% বেশি এবং C, B থেকে ২৫% কম পায়। তাহলে A কত টাকা পাবে?

সমাধান:
মনে করি, A পায় = x টাকা
যেহেতু, A এর টাকা = C এর ১২৫% টাকা
∴ C পায় = {(x/১২৫) × ১০০} = ৪x/৫ টাকা

আবার, C পায় = B এর (১০০ - ২৫)%
⇒ ৪x/৫ = B এর ৭৫%
⇒ ৪x/৫ = B × (৭৫/১০০)
⇒ B = {(৪x/৫) × (১০০/৭৫)}
⇒ B = (৮০x/৭৫) = (১৬x/১৫) টাকা

প্রশ্নমতে,
x + (৪x/৫) + (১৬x/১৫) = ২২৩৬
⇒ (৯x/৫) + (১৬x/১৫) = ২২৩৬
⇒ (২৭x + ১৬x)/১৫ = ২২৩৬
⇒ ৪৩x/১৫ = ২২৩৬
⇒ x = (২২৩৬ × ১৫)/৪৩
∴ x = ৭৮০

সুতরাং, A পায় ৭৮০ টাকা।

১,৪৫১.

An article is sold for Tk. 3600 at a profit of 25%. What would have been the actual profit or loss if it had been sold at Tk. 2700?

ক
profit 5.25%
খ
loss 5.25%
গ
profit 6.25%
ঘ
loss 6.25%
ঙ
None of these

ব্যাখ্যা

Question: An article is sold for Tk. 3600 at a profit of 25%. What would have been the actual profit or loss if it had been sold at Tk. 2700?

Solution:
The cost price = (3600 × 100)/125 = 2880
New selling price = Tk. 2700
∴ Loss = 2880 - 2700 = 180
∴ Loss percentage = (100 × 180)/2880 = 6.25%.

১,৪৫২.

A shopkeeper marks his umbrella at 25% above the cost price. During rainy season sale, he offers a discount of 12% on marked price. Find his profit percentage.

ক
12%
খ
13%
গ
10%
ঘ
11%

ব্যাখ্যা

Question: A shopkeeper marks his umbrella at 25% above the cost price. During rainy season sale, he offers a discount of 12% on marked price. Find his profit percentage.

Solution:
Let,
Cost Price (CP) = tk 100
Marked Price (MP) = CP + 25% of CP
= 100 + (100 × 25/100)
= 100 + 25
= tk 125
Selling Price (SP) = MP - 12% of MP
= 125 - (125 × 12/100)
= 125 - 15
= tk 110

Profit = SP - CP
= 110 - 100
= tk 10

Profit percentage = (Profit × 100)/CP
= (10 × 100)/100
= 10%

১,৪৫৩.

A retail appliance store priced a video recorder at 20 percent above the wholesale cost of Tk. 200. If a store employee applied the 10 percent employee discount to the retail price to buy the recorder, how much did the employee pay for the recorder?

ক
ক) Tk. 198
খ
খ) Tk. 216
গ
গ) Tk. 220
ঘ
ঘ) Tk. 230

ব্যাখ্যা

20% of 200 = 40
At 20 percent above the wholesale cost of Tk. 200
So, the total price = 200 + 40 = Tk. 240
At 10 percent employee discount to the retail price to buy the recorder
So, employee paid for the recorder = tk. (240 - 10% of 240) = 240 - 24 = Tk. 216

১,৪৫৪.

30% of a number when subtracted from 104, gives the number itself. Find the number.

ক
ক) 80
খ
খ) 70
গ
গ) 90
ঘ
ঘ) 200

ব্যাখ্যা

Question: 30% of a number when subtracted from 104, gives the number itself. Find the number.

Solution:
Let
The number be x
According to the question,
104 - (30x/100) = x
104 = x + (30x/100)
104 = 130x/100
104 = 13x/10
x = (104 × 10)/13
x = 80

১,৪৫৫.

If a man gains 10% by selling a watch for Taka 660, find the cost price.

ক
Taka 600
খ
Taka 620
গ
Taka 650
ঘ
Taka 670

ব্যাখ্যা

Question: If a man gains 10% by selling a watch for Taka 660, find the cost price.

Answer: Selling Price = 110% of Cost Price
→ Cost Price = 660 ÷ 1.1 = 600

Another Method,
With 10% gain,
Selling Price is 110 Taka when Cost Price is 100 Taka
Selling Price is 1 Taka when Cost Price is 100/110 Taka
Selling Price is 660 Taka when Cost Price is (100×660)/110 Taka = 600 Taka

১,৪৫৬.

An employee's annual salary was increased Tk. 25,000. If her new annual salary now equals Tk. 90,000, what was the percent increase?

ক
ক) 45%
খ
খ) 42%
গ
গ) 20%
ঘ
ঘ) None of these

ব্যাখ্যা

New annual salary = Tk. 90,000
Salary increase = Tk. 25,000.

Original salary
= Tk. (90,000 - 25,000).
= 65,000

Percentage Increase
= (25,000/ 65,000) × 100%
= 38.46%

১,৪৫৭.

If y% of x = 29, then x = ?

ক
ক) 2900/y
খ
খ) 29x/y
গ
গ) 29y/x
ঘ
ঘ) 29xy

ব্যাখ্যা

y% of x = 29
Or, y/100 × x = 29
So, x = 29×100/y = 2900/y

১,৪৫৮.

Man hardly believes a liar, ____ ?

ক
does he
খ
doesn't he
গ
are they
ঘ
aren't they

ব্যাখ্যা

• শূন্যস্থানে সঠিক উত্তর হবে - does he?
- Complete sentence: Man hardly believes a liar, does he?

• Tag question করার নিয়ম -
- সাধারণত Tag question ব্যবহৃত হয় পূর্বে উল্লেখিত কোন উক্তি সত্য না মিথ্যা তা নিশ্চিত হওয়ার জন্য।
- Statement positive হলে tag question টা negative হবে।
- আবার statement negative হলে tag question positive হবে।
- Subject ও Tense অনুসারে auxiliary verb দ্বারা tag question তৈরি হয়।

• Tag question এর নিয়মানুযায়ী বাক্যটি Negative হওয়ায় Tag question Negative হবে।
- Hardly = কদাচিৎ/ না বললেই চলে।
- Hardly, seldom, rarely ইত্যাদি থাকলে সাধারণত Present Indefinite Tense হয়।
- আর hardly নিজেই Negative অর্থ প্রকাশ করায়, এর সাথে কোন নাবোধক শব্দ বসে না।

• বাক্যটি Present indefinite tense হওয়ায় Tag question এর ক্ষেত্রে does he হবে।

১,৪৫৯.

5% merchandise of a trader was stolen another 5% was damaged during transportation. At what profit (in %) should he sell the rest of the goods so that he can make an overall profit of 20%?

ক
25%
খ
30%
গ
20%
ঘ
None of the above

ব্যাখ্যা

Question: 5% merchandise of a trader was stolen another 5% was damaged during transportation. At what profit (in %) should he sell the rest of the goods so that he can make an overall profit of 20%?

Solution:
ধরি,
১০০ টাকার পণ্য ছিল।
তাহলে, বিক্রয়যোগ্য পণ্য = ১০০ - ৫ - ৫ = ৯০ টাকার
এখন,
২০% লাভ করতে হলে ৯০ টাকার পণ্য বিক্রয় করতে হবে ১২০ টাকা।
অর্থাৎ লাভ করতে হবে = ১২০ - ৯০ = ৩০ টাকা

৯০ টাকায় লাভ করতে হবে = ৩০ টাকা
১ টাকায় লাভ করতে হবে = ৩০/৯০ টাকা
∴ ১০০ টাকায় লাভ করতে হবে = (৩০ × ১০০)/৯০ টাকা
= ৩৩.৩৩ টাকা বা ৩৩.৩৩%

১,৪৬০.

If the population of a village went from 2105 to 1705, then the percent decrease in population is closest to

ক
ক) 19
খ
খ) 21
গ
গ) 22
ঘ
ঘ) 23

ব্যাখ্যা

Question: If the population of a village went from 2105 to 1705, then the percent decrease in population is closest to-

Solution:
শতকরা জনসংখ্যা হ্রাস পাবে = (২১০৫ - ১৭০৫) × ১০০%/২১০৫
= ৪০০ × ১০০%/২১০৫
= ১৯%

১,৪৬১.

A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for Tk 22500. What is the reduced price per kg of tea?

ক
81 tk
খ
90 Tk
গ
93 Tk
ঘ
97 Tk
ঙ
None

ব্যাখ্যা

Question: A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for Tk 22500. What is the reduced price per kg of tea?

Solution:
Let 10% of 22500 = 2250
Now,
25 kg = 2250
⇒ 1kg = 2250/25
∴ 1kg = 90

১,৪৬২.

125 gallons of a mixture contains 20% water. What amount of additional water should be added such that water content be raised to 25%?

ক
ক) 15/2 gallons
খ
খ) 13/2gallons
গ
গ) 9/2 gallons
ঘ
ঘ) 8(1/3) gallons

ব্যাখ্যা

In the original 125 gallons of mixture, 20% is water.
Hence, no. of gallons of other materials in the mixture: 125 x 80% = 100 gallons
In the new mixture, water makes up 25%, thus 75% is other materials.
As no. of gallons of others is unchanged, 100 gallons = 75% in the new mixture volume.
The total volume of the new mixture is : 100 / 75% = 100/ 0.75 = 133.33 gallons.
∴ Required additional amount of water = 133.3 – 125 = 8.33 = 8(1/3) gallons

১,৪৬৩.

A merchant has 1000 kg of sugar, part of which he sells at 8% and the remaining at 18% profit. He gains 14% on the whole. Find the quantity of sugar that he sold at 18% profit.

ক
400kg
খ
560kg
গ
600kg
ঘ
640kg

ব্যাখ্যা

Question: A merchant has 1000 kg of sugar, part of which he sells at 8% and the remaining at 18% profit. He gains 14% on the whole. Find the quantity of sugar that he sold at 18% profit.

Solution:
Let the cost price of 1kg of sugar be Tk.100.

The selling price of 1kg sugar sold at 8% profit
⇒ 100 × 108/100 = Tk.108

The selling price of 1kg sugar sold at 18% profit
⇒ 100 × 118/100 = Tk.118

The average selling price of 1kg of sugar
⇒ 100 × 114/100 = Tk.114

Using the rule of the allegation,

The ratio of sugar sold at 8% and 18% profit
⇒ (118 - 114) : (114 - 108)
⇒ 4 : 6 = 2 : 3

∴ Quantity sold at 18% profit = 3/5 × 1000 = 600 kg

১,৪৬৪.

A shopkeeper expects a gain of 25% on his cost price. If in a week, his sale was Tk. 1600, what was his profit?

ক
Tk. 250
খ
Tk. 280
গ
Tk. 320
ঘ
Tk. 350

ব্যাখ্যা

Question: A shopkeeper expects a gain of 25% on his cost price. If in a week, his sale was Tk. 1600, what was his profit?

Solution:
Let
the cost price be x

∴ The selling price = {x + (25% of x)}

ATQ,
x + (25% of x) = 1600
⇒ x + (25x/100) = 1600
⇒ x + (x/4) = 1600
⇒ (4x + x)/4 = 1600
⇒ 5x = 1600 × 4
⇒ x = (1600 × 4)/5
∴ x = 1280

∴ Profit = (1600 - 1280) = Tk. 320

১,৪৬৫.

What percent of 500 is 1.5?

ক
0.3%
খ
3%
গ
0.5%
ঘ
30%

ব্যাখ্যা

Question: What percent of 500 is 1.5?

Solution:
ধরি,
500 এর x% = 1.5
⇒ 500 এর (x/100) = 1.5
⇒ 5x = 1.5
⇒ x = 1.5/5
⇒ x = 0.3

সুতরাং, 500 এর 0.3% হলো 1.5

১,৪৬৬.

The price of an article was increased by p% . Later the new price was decreased by p%. If the latest price was TK. 1, The original price was:

ক
ক) 1
খ
খ) (1 - p²)/100
গ
গ) 10000/(1000-p²)
ঘ
ঘ) √{(1 - p²)/100}
ঙ
ঙ) None of above

ব্যাখ্যা

At p% profit, selling price = 100 + p
at p% loss, new selling price = (100 + p) - (100 + p) × p/100
= (100 + p) - {(100p + p²)/100}
= 10000 + 100p - 100p - p²
= (10000 - p²)/100

so, (10000 - p²)/100 is equal to 1
1 is equal to 1/(10000 - p²)/100
100 is equal to 1 × (100/ 10000 - p²) × 100
= 10000/(10000 - p²)

অপশন গ) (10000/10000-p^2) হওয়ার কথা ছিলো। সেক্ষেত্রে উত্তর ঠিক হয়।
লাইভ পরীক্ষার প্রশ্নে অপশন ভুল থাকায় উত্তর হিসাবে ঙ) None of above কে ধরা হয়েছে।

১,৪৬৭.

Rony and Jony invest in a business in the ratio 7 : 5. If 4% of the total profit goes to charity and Rony's share is Tk. 224, what is the total profit?

ক
ক) Tk. 200
খ
খ) Tk. 300
গ
গ) Tk. 400
ঘ
ঘ) Tk. 500

ব্যাখ্যা

Question: Rony and Jony invest in a business in the ratio 7 : 5. If 4% of the total profit goes to charity and Rony's share is Tk. 224, what is the total profit?

Solution:
Let,
The total profit be Tk. 100.
Sum of their ratios = 7 + 5 = 12
After paying 4% to charity,
Rony's share = 96 × (7/12) = Tk. 56

If Rony's share is Tk. 56, total profit = Tk. 100.
If Rony's share is Tk. 1, total profit = Tk. 100/56
∴ If Rony's share is Tk. 224, total profit = Tk. (100 × 224)/56
= Tk. 400

১,৪৬৮.

At what percentage profit must an article be sold such that selling it at two-thirds of that price results in a 20% loss?

ক
20%
খ
20.50%
গ
17.50%
ঘ
35%
ঙ
15%

ব্যাখ্যা

Question: At what percentage profit must an article be sold such that selling it at two-thirds of that price results in a 20% loss?

Solution:
Let,
Cost Price be x .
Selling Price be y.

Selling at 2/3 of y, causes 20% loss,
So, 2y/3 = x - 20% of x
⇒ 2y/3 = x - (20x/100)
⇒ 2y/3 = x{(1 - (20/100)}
⇒ 2y/3 = x × (80/100)
∴ y = 6x/5

Profit = Selling Price - Cost Price
= (6x/5) - x
= (6x - 5x)/5
= x/5

∴ Profit Percentage = (Profit/Cost Price) × 100%
= {(x/5)/x} × 100%
= 20%

১,৪৬৯.

60% of 500 is what percent of 400?

ক
80%
খ
75%
গ
70%
ঘ
65%

ব্যাখ্যা

Question: 60% of 500 is what percent of 400?

Solution:
Let
60% of 500 be x percent of 400.

That means,
60% of 500 = x% of 400.
⇒ 60 × 500/100 = 400x/100
⇒ 300 = 4x
⇒ 4x = 300
⇒ x = 75

১,৪৭০.

A man spends 45% of his salary on rent, 25% on food, and saves the rest. If his salary is Tk. 60000. how much does he save?

ক
Tk. 21500
খ
Tk. 18000
গ
Tk. 15300
ঘ
Tk. 12000

ব্যাখ্যা

Question: A man spends 45% of his salary on rent, 25% on food, and saves the rest. If his salary is Tk. 60000. how much does he save?

Solution:
Given that,
Total salary = Tk. 60000

Now,
Spends on rent = 45% of 60000
= (45/100) × 60000
= Tk. 27000

And spends on food = 25% of 60000
= (25/100) × 60000
= Tk. 15000

∴ Total expenditure = rent + food
= 27000 + 15000
= Tk. 42000

∴ Savings = Total salary - Total expenditure
= 60000 - 42000
= Tk. 18000

He saves Tk. 18000

Shortcut method:
Percentage saved = 100% - (45% + 25%)
= 100% - 70%
= 30%

∴ Savings = 30% of 60000
= 0.30 × 60,000
= Tk. 18000

১,৪৭১.

In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 15000, the number of valid votes that the other candidate got, was-

ক
5000
খ
5400
গ
5800
ঘ
6200

ব্যাখ্যা

Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 15000, the number of valid votes that the other candidate got, was-

Solution:

Total number of votes = 15000

Given that 20% of Percentage votes were invalid

⇒ Valid votes = 80%

∴ Total valid votes = 15000 × (80/100) = 12000

1st candidate got 55% of the total valid votes.

Hence the 2nd candidate should have got 45% of the total valid votes

∴ Valid votes that 2nd candidate got = total valid votes × (45/100)
= 12000 × (45/100) = 5400

১,৪৭২.

Alloy A contains 40% gold and 60% silver. Alloy B contains 35% gold and 40% silver and 25% copper. Alloys A and B are mixed in the ratio of 1:4 .What is the ratio of gold and silver in the newly formed alloy?

ক
11:9
খ
9:11
গ
3:6
ঘ
6:3
ঙ
None of the above

ব্যাখ্যা

A:: - G:S = 40:60
B:: - G:S:C = 35:40:25
New,
G:S= (1×40 + 4×35) : (40×4 + 1×60)
= 180:220
= 18:22
= 9:11

১,৪৭৩.

A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Tk. 1000 more than D, what is B's share?

ক
Tk. 500
খ
Tk. 1500
গ
Tk. 2000
ঘ
None of these

ব্যাখ্যা

Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Tk. 1000 more than D, what is B's share?

Solution:
let, they get 5x, 2x, 4x, 3x

4x - 3x = 1000
⇒ x = 1000

∴ B's share is = 2x
= 2 × 1000
= 2000 taka

১,৪৭৪.

A man buys a cycle for Tk. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?

ক
Tk. 1220
খ
Tk. 1808
গ
Tk. 1190
ঘ
Tk. 1197

ব্যাখ্যা

At 15% loss, selling price = 85% of Tk. 1400
= Tk. 85 x 1400/100 = Tk. 1190
--------------------------------
Alternative way:
Selling price = 1400 - 15% of Tk. 1400 = 1400 - 210 = Tk. 1190

১,৪৭৫.

A cloth merchant sold half of his cloth at 20% profit, half of the remaining at 20% loss and the rest was sold at the cost price. Calculate the overall profit% or loss%?

ক
8% profit
খ
6.5% loss
গ
5% profit
ঘ
9% loss

ব্যাখ্যা

Question: A cloth merchant sold half of his cloth at 20% profit, half of the remaining at 20% loss and the rest was sold at the cost price. Calculate the overall profit% or loss%?

Solution:
Let the CP of the whole cloth be x
CP of 1/2 cloth = x/2

CP of half of the remaining = x/4

SP of first half of cloth = (120 × x/2) ÷ 100

SP of the half of the remaining cloth = (80 × x/4) ÷ 100

SP of the remaining half = x/4

Total SP = (120 × x/2)/100 + (80 × x/4)/100 + x/4
= 3x/5 + x/5 + x/4
= (12x + 4x + 5x)/20
= 21x/20

Gain = 21x/20 - x = x/20

Gain % = (x/20)/x × 100% = 5%

১,৪৭৬.

If a man were to sell his chair for Tk. 720, he would lose 25%. To gain 25% he should sell it for:

ক
ক) Tk. 1200
খ
খ) Tk. 1000
গ
গ) Tk. 1300
ঘ
ঘ) Tk. 960

ব্যাখ্যা

Question: If a man were to sell his chair for Tk. 720, he would lose 25%. To gain 25% he should sell it for:

Solution:
Let the Cost price of the Chair is x.
Selling price = x - 25% of x
⇒ 720 = x - (25x/100)
⇒ 720 = 75x/100
⇒ 75x = 72000
∴ x = 960

To gain 25% = 960 + 25% of 960
= Tk. 1200

১,৪৭৭.

If the price of a commodity is decreased by 25% and its consumption is increased by 25%, what will be the increase or decrease in expenditure on the commodity?

ক
4% increase
খ
8.25% decrease
গ
6.25% decrease
ঘ
8% increase
ঙ
10% increase

ব্যাখ্যা

Question: If the price of a commodity is decreased by 25% and its consumption is increased by 25%, what will be the increase or decrease in expenditure on the commodity?

Solution:
Let,
The initial expenditure on the commodity be Tk. 100.
Now, the price decreases by 25%,
∴ Current Price = (100 - 25% of 100) = Tk. 75

Same time due to decrements in price 25% consumption has been increased.
So, Current expenses on commodity = (75 + 25% of 75) = Tk. 93.75

Here,
The initial expenditure was Tk. 100 which became Tk. 93.75 at the end, it means there is 6.25% decrements in the expenditure of the commodity.

So the expenditure decreases by 6.25%

১,৪৭৮.

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

ক
11%
খ
15.5%
গ
8.25%
ঘ
9%

ব্যাখ্যা

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

Solution:
Given that,
AB = 5 cm (fixed)
Initially, AC = 3 cm
So, CB = AB - AC = 5 - 3 = 2 cm

Now,
Increase in AC = 6%
∴ Increase in AC = (106/100) × 3 = 3.18cm
And,
Decrease in CB = 5 - 3.18 = 1.82 cm
∴ Decrease = 2 - 1.82 = 0.18 cm

So Percentage of decrease = (0.18/2) × 100%
= (18/2)%
= 9%

Thus, the length of CB is decreased by 9%.

১,৪৭৯.

Chocolates are bought at 10 for Tk 20 and sold at 12 for Tk 30. The gain percent is-

ক
25%
খ
30%
গ
35%
ঘ
23%

ব্যাখ্যা

Question: Chocolates are bought at 10 for Tk 20 and sold at 12 for Tk 30. The gain percent is-

Solution:
Cost per chocolate = 20/10 Tk.
= 2 Tk.

Sell per chocolate = 30/12 Tk.
= 2.5 Tk.

So, gain percentage = {(2.5 - 2)/2} × 100
= 25 Tk. or 25%

১,৪৮০.

A worker union contract specifies a 6% salary increase plus a Tk. 450 bonus for each worker. For a worker, this is equivalent to 8% salary increase. What was this worker's salary before the new contract?

ক
21,500
খ
22,000
গ
22,500
ঘ
23,500

ব্যাখ্যা

Question: A worker union contract specifies a 6% salary increase plus a Tk. 450 bonus for each worker. For a worker, this is equivalent to 8% salary increase. What was this worker's salary before the new contract?

Solution:
ধরি,
পূর্বে কর্মীর বেতন ছিলো = x টাকা

6% বৃদ্ধিতে বেতন = x + x এর 6%
= x + x এর 6/100
= (100x + 6x)/100
= 106x/100

8% বৃদ্ধিতে বেতন = x + x এর 8%
= x + x এর 8/100
= (100x + 8x)/100
= 108x/100

প্রশ্নমতে
(106x/100) + 450 = 108x/100
⇒ 450 = (108x/100) - (106x/100)
⇒ 450 = 2x/100
⇒ 450 = x/50
⇒ x = 50 × 450
∴ x = 22,500

১,৪৮১.

A dealer allows his customer a discount of 25% and still gains 25%. If the cost price of a ratio is Tk. 1440. Its Marked price is -

ক
ক) 2500
খ
খ) 2440
গ
গ) 2400
ঘ
ঘ) 2300

ব্যাখ্যা

Let
Marked price = X
Cost Price(C.P.) = 1440
Sale price(S.P.) = 1440 + 25% of 1440
= Tk. 1800

S.P. = M.P. - 25% of M.P.
S.P. = X - 25% of X
S.P. = X - 0.25X
1800 = 0.75X
X = 1800/.25
= 2400
M.P. = Tk. 2400

১,৪৮২.

By selling a bicycle for Tk. 2850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be?

ক
Tk. 2780
খ
Tk. 2650
গ
Tk. 2500
ঘ
Tk. 2700
ঙ
None of these

ব্যাখ্যা

Question: By selling a bicycle for Tk. 2850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be?

Solution:
Let Cost Price was x.
⇒ x + 14% of x = 2850
⇒ x + (14x/100) = 2850
⇒ (100x + 14x)/100 = 2850
⇒ 114x/100 = 2850
⇒ x = (2850 × 100)/114
∴ x = 2500.
So, Cost Price = Tk. 2500.

Now, Selling Price When profit remains at 8%,
= 2500 + 8% of 2500
= 2500 + (8/100) × 2500
= 2500 + 200
= Tk. 2700

১,৪৮৩.

A sum of 5000 will give a return of 625 tk at 6.25% simple interest in the period of -

ক
1 years.
খ
4 years.
গ
3 years.
ঘ
2 years.

ব্যাখ্যা

Question: A sum of 5000 will give a return of 625 tk at 6.25% simple interest in the period of -

Solution:
here,
P = 5000
I = 625
r = 6.25%
n = ?

we know that,
I = Pnr
n = I/Pr
= 625/(5000 × 6.25%)
= 2 years.

১,৪৮৪.

A trader mixes 26 kg of rice at Tk. 20 per kg with 30 kg of rice of other variety at Tk. 36 per kg and sells the mixture at Tk. 30 per kg. His profit percent is:

ক
ক) 3%
খ
খ) 4%
গ
গ) 5%
ঘ
ঘ) 7%

ব্যাখ্যা

C.P. of 56 kg rice = Tk. (26 x 20 + 30 x 36)
= Tk. (520 + 1080)
= Tk. 1600.

S.P. of 56 kg rice = Tk. (56 x 30)
= Tk. 1680.

Gain ={(80/1600) × 100}%
= 5%

১,৪৮৫.

A restaurant makes 20% profit after selling a set menu at a discount of 20%. What is the percentage increase of the marked price?

ক
ক) 30%
খ
খ) 20%
গ
গ) 40%
ঘ
ঘ) 50%

ব্যাখ্যা

Let the Market Price of the product is MP.
Let the Original Cost Price of the product is CP.
Selling Price (Discounted Price) = 100% of MP - 20% of MP = 80% of MP ......... (1)
Profit made by selling at discounted price = 20% of CP ........... (2)
Apply the formula:
Profit = Selling Price - Original Cost Price
⇒ 20% of CP = 80% of MP - 100% CP
⇒ MP = (120×CP)/80 = 3/2 × CP
Now if product is sold without any discount, then,
Profit = Selling Price (without discount) - Original Cost Price
= Market Price - Original Cost Price
= MP - CP
= 3/2 CP - CP
= 1/2 CP
= 50% of CP

১,৪৮৬.

The price of a car depreciates in the first year by 25%, in the second year by 20% , in third year by 15% and so on. The final price of the car after 3 years, if the present cost of the car is Tk.10,00,000-

ক
ক) 7,80,000
খ
খ) 1,70,000
গ
গ) 6,90,000
ঘ
ঘ) 5,10,000

ব্যাখ্যা

1000000 × 0.75 × 0.80 × 0.85= 5,10,000

১,৪৮৭.

Questions (21-30 ) : Read the following questions carefully and choose the right answer.
21. Alam sold two vehicles for Tk 46000 each. If he gained 10% on the first and lost 10% on another, then what is his percentage profit or loss in this transaction?

ক
ক) 2% loss
খ
খ) 1% profit
গ
গ) 1% loss
ঘ
ঘ) None of these

ব্যাখ্যা

Question: Alam sold two vehicles for Tk 46000 each. If he gained 10% on the first and lost 10% on another, then what is his percentage profit or loss in this transaction?

Solution:
Let the profit be x% and loss be y%.
Net profit or loss% = {x + (- y) + x ×(- y)}/100 [Negative sign denotes that their is a loss]
Their is 10% loss and 10% profit then
∴ Net profit or loss% = {10 + (- 10) + 10 ×(- 10)}/100
= (10 - 10 - 100)/100
= - 1
∴ The net loss is 1%

১,৪৮৮.

A football team lost 40% of the matches it played. If it won 75 matches, then find the number of matches it played.

ক
ক) 125
খ
খ) 115
গ
গ) 110
ঘ
ঘ) 120

ব্যাখ্যা

ম্যাচ হারে % = 40%
ম্যাচ জয় করে = 75 matches
ম্যাচ জয়ের হার = 100% - lost% = 100 - 40 = 60%

ধরি, ম্যাচ খেলার সংখ্যা 'x'

প্রশ্নমতে,
60% of x = 75
⇒ 60/100 × (x) = 75
⇒ x = (75/60) × 100
⇒ x = 5/4 × 100
⇒ x = 5 × 25 = 125

∴ ফুটবল দলটি ম্যাচ খেলে ১২৫টি।

১,৪৮৯.

A shopkeeper marks the price of an article at Tk. 80. What will be the selling price, if he allows two successive discounts of 5% each?

ক
Tk. 72.20
খ
Tk. 72
গ
Tk. 72.22
ঘ
Tk. 72.25

ব্যাখ্যা

At 5% discount for the first time = 80 × 95/100 = Tk. 76
At 5% discount for second time = 76 × 95/100 = Tk. 72.20

১,৪৯০.

In an examination, 25% candidates failed in English and 35% students failed in Math. If 15% candidates failed in both, what is the percentage of candidates who passed in both the subjects?

ক
45%
খ
55%
গ
50%
ঘ
58%

ব্যাখ্যা

Question: In an examination, 25% candidates failed in English and 35% students failed in Math. If 15% candidates failed in both, what is the percentage of candidates who passed in both the subjects?

Solution:
Failed in both English and Math = 15%
Only failed in English = (25 - 15)% = 10%
Only failed in Math = (35 - 15)% = 20%

∴ Candidates who failed one or both subjects = 15% + 10% + 20%
= 45%

∴ Candidates who passed in both the subject = (100 - 45)% = 55%

১,৪৯১.

In January, the value of a stock increased by 50%; and in February, it decreased by 20%. In March, it increased by 25%; and in April, it decreased by 10%. If a person invested Tk. 200 in the stock on January 1 and sold it at the end of April, what was the percentage change in the price of the stock?

ক
0%
খ
15%
গ
25.5%
ঘ
35%

ব্যাখ্যা

Question: In January, the value of a stock increased by 50%; and in February, it decreased by 20%. In March, it increased by 25%; and in April, it decreased by 10%. If a person invested Tk. 200 in the stock on January 1 and sold it at the end of April, what was the percentage change in the price of the stock?

Solution:
At the end of January,
The value of the stock is = Tk. 200 + 50% of (Tk. 200)
= Tk. 200 + Tk. 100 = Tk. 300.

At the end of February,
The value of the stock is = Tk. 300 - 20% of (Tk. 300)
= Tk. 300 - Tk. 60 = Tk. 240.

At the end of March,
The value of the stock is = Tk. 240 + 25% of (Tk. 240)
= Tk. 240 + Tk. 60 = Tk. 300.

At the end of April,
The value of the stock is = Tk. 300 - 10% of (Tk. 300)
= Tk. 300 - Tk. 30 = Tk. 270.

Now, the percentage change in price is,
= (Change in price/Original price) × 100%
= (270 - 200)/200 × 100%
= (70/200) × 100%
= 35%

১,৪৯২.

3 horses cost is equal to 5 cows cost. If 4 horses and 6 cows total cost is Tk. 19000, then what is the cost of each horse?

ক
ক) Tk. 2500
খ
খ) Tk. 1500
গ
গ) Tk. 2000
ঘ
ঘ) Tk. 5000

ব্যাখ্যা

Question: 3 horses cost is equal to 5 cows cost. If 4 horses and 6 cows total cost is Tk. 19000, then what is the cost of each horse?

Solution:
Let,
cost of one horse = Tk. x
cost of one cow = Tk. y

ATQ,
3x = 5y
x = 5y/3 ............ (1)

Again,
4x + 6y = 19000
⇒ 4 × (5y/3) + 6y = 19000
⇒ (20y + 18y)/3 = 19000
⇒ 38y = 19000 × 3
⇒ 38y = 57000
⇒ y = 57000/38
∴ y = 1500

From (1) we get,
x = (5 × 1500)/3
∴ x = 2500

∴ Cost of one horse = Tk. 2500

১,৪৯৩.

If 25% of 1200 + 35% of 600 = x% of 4000, find the value of x.

ক
14.65
খ
10.50
গ
12.75
ঘ
11.50

ব্যাখ্যা

Question: If 25% of 1200 + 35% of 600 = x% of 4000, find the value of x.

Solution:
25% of 1200 + 35% of 600 = x% of 4000
⇒ (25/100) × 1200 + (35/100) × 600 = (x/100) × 4000
⇒ 300 + 210 = 40x
⇒ 40x = 510
⇒ x = 510/40
∴ x = 12.75

১,৪৯৪.

Rahim buys a Tk. 50 share of a company that pays 12% profit. He buys the share at such a price that he earns 20% on his investment. At what price did Rahim buy the share?

ক
Tk. 36
খ
Tk. 35
গ
Tk. 32
ঘ
Tk. 30

ব্যাখ্যা

Question: Rahim buys a Tk. 50 share of a company that pays 12% profit. He buys the share at such a price that he earns 20% on his investment. At what price did Rahim buy the share?

Solution:
Here
profit given by the company on 1 share = 12% of 50
= Tk. 6

Let
Rahim buys one share for x Tk

ATQ,
20% of x = 6
20x/100 = 6
⇒ 20x = 600
⇒ x = 600/20
∴ x = 30

Rahim bought the share at Tk. 30

১,৪৯৫.

If a shopkeeper buys eggs at Tk. 42 per sext (six eggs) and sells them at Tk. 56 per two quads (eight eggs), what percentage profit does he make?

ক
5%
খ
1%
গ
7%
ঘ
None

ব্যাখ্যা

Question: If a shopkeeper buys eggs at Tk. 42 per sext (six eggs) and sells them at Tk. 56 per two quads (eight eggs), what percentage profit does he make?

Solution:
Cost price of 6 eggs = Tk. 42
Cost price of 1 egg = 42/6
= 7 Tk.

Cost price of 8 eggs = 8 × 7
= 56
Selling price of 8 eggs = Tk. 56

∴ Profit = 56 − 56
= 0

∴ As the selling and cost prices are the same, there is no profit.

১,৪৯৬.

In an office, 40% of the staff is female. 70% of the female staff and 50% of the male staff are married. The percentage of the unmarried staff in the office is

ক
52
খ
50
গ
45
ঘ
42

ব্যাখ্যা

Question: In an office, 40% of the staff is female. 70% of the female staff and 50% of the male staff are married. The percentage of the unmarried staff in the office is

Solution:
Let, total staff 100

female = 40
male = 100 - 40
= 60

married staff = 40 × 0.7 + 60 × 0.5
= 28 + 30
= 58

∴ unmarried staff = 100 - 58
= 42

১,৪৯৭.

There is a dishonest shopkeeper whose claim is that he sells a certain product at a cost of Tk 23/kg, which actually costs him Tk 25/kg. The shopkeeper says that he is taking the loss to let his customers get a better deal. When examined thoroughly, a policeman finds that the shopkeeper is actually using an 800 gms weight in place of a 1 kg weight. How much does he gain or lose?

ক
23.3% profit
খ
15% loss
গ
23.3% loss
ঘ
15% profit

ব্যাখ্যা

Question: There is a dishonest shopkeeper whose claim is that he sells a certain product at a cost of Tk 23/kg, which actually costs him Tk 25/kg. The shopkeeper says that he is taking the loss to let his customers get a better deal. When examined thoroughly, a policeman finds that the shopkeeper is actually using an 800 gms weight in place of a 1 kg weight. How much does he gain or lose?

Solution:
selling price of 0.8 kg = 23 taka

selling price of 1 kg = 23/0.8 taka
= 115/4 taka
= 28.75 taka

percentage profit = {(28.75 - 25)/25} × 100%
= (3.75/25) × 100%
= 15%

১,৪৯৮.

Parimal purchased 10 calculators and 16 watches for Tk. 56100 and sold them so as to earn an overall profit of 20%. At what total price should he sell 15 calculators and 24 watches together so as to earn the same percentage profit?

ক
Tk. 100980
খ
Tk. 116176
গ
Tk. 121176
ঘ
Tk. 100660

ব্যাখ্যা

Question: Parimal purchased 10 calculators and 16 watches for Tk. 56100 and sold them so as to earn an overall profit of 20%. At what total price should he sell 15 calculators and 24 watches together so as to earn the same percentage profit?

Solution:
Calculators = 10
Watches = 16
Total Item = 10 + 16 = 26
Total Cost price = Tk. 56,100
Average price of Each item = 56100/26
= Tk. 2157.69

Second Time total item = 15 + 24 = 39
So, Total cost price of 39 items = 2157.69 × 39 = 84,150
thus, the selling price of 39 items with 20% profit,
= 84,150 + 20% of 84,150
= Tk 84,150 + 16,830
= Tk. 100,980

১,৪৯৯.

If 25 is 25 percent of 40 percent of a certain number, what is the number?

ক
250
খ
50
গ
350
ঘ
280

ব্যাখ্যা

Question: If 25 is 25 percent of 40 percent of a certain number, what is the number?

Solution:
Let, The number be x then
25 = 25% of 40% of x
or, 25 = (25/100) × (40/100) × x
or, x = (25 × 100 × 100)/(25 × 40)
or, x = 250

So the number is 250.

১,৫০০.

If 75% of the students in a school are boys and the number of girls is 420, the number of boys is:

ক
1170
খ
1680
গ
1555
ঘ
1260

ব্যাখ্যা

Question: If 75% of the students in a school are boys and the number of girls is 420, the number of boys is:

Solution:
75% of the students in a school are boys
girls = 25%

25% of total students = 420
⇒ total students = 420/0.25
= 1680

∴ the number of boys is = 1680 - 420
= 1260