Percentage and Profit & Loss

PrepBank · পাতা ১৭ / ১৭ · ১,৬০১–১,৬৮৮ / ১,৬৯৬

১,৬০১.

C scored 30% marks and failed by 15 marks. D scored 45% marks and obtained 30 marks more than the pass marks. What is the pass percentage?

ক
30%
খ
33%
গ
35%
ঘ
39%

ব্যাখ্যা

Question: C scored 30% marks and failed by 15 marks. D scored 45% marks and obtained 30 marks more than the pass marks. What is the pass percentage?

Solution:
Let the total marks be x.

Given,
C scored 30% marks and failed by 15 marks:
0.30x + 15 = Pass marks
D scored 45% marks and obtained 30 marks more than pass marks:
0.45x - 30 = Pass marks

Now,
0.30x + 15 = 0.45x - 30
⇒ 0.45x - 0.30x = 15 + 30
⇒ 0.15x = 45
⇒ x = 45/0.15
∴ x = 300

Pass marks = 0.30 × 300 + 15
= 90 + 15 = 105

∴ Pass percentage = (105/300) × 100% = 35%

১,৬০২.

The price of a product is reduced by 25%, but the daily sale of the article is increased by 30%. Find the net effect on the daily sale.

ক
2.5% increase
খ
1.5% decrease
গ
2% increase
ঘ
2.5% decrease

ব্যাখ্যা

Question: The price of a product is reduced by 25%, but the daily sale of the article is increased by 30%. Find the net effect on the daily sale.

Solution:
We can say that,
Total Sale = the price of one unit × no. of units sold

Let
the initial price of product = 100, sale =100 items.
Then, Total Sale = 100 × 100 = 10000

ATQ,
price reduces to 25%.
So, the new price = 100 - 25 = 75
Sale increase to 30%,
So, the new sale = 100 + 30 = 130
Now, the new total sale = 75 × 130 = 9750

Difference = 10000 - 9750 = 250
% net effect = (diff/original)× 100
= (250/10000) × 100 = 2.5
So, the net effect on daily sale = 2.5% decrease

১,৬০৩.

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

ক
Loss Tk. 2
খ
Loss Tk. 4
গ
Gains Tk. 1
ঘ
Gains Tk. 5

ব্যাখ্যা

Question: A man sells two articles at TK 99 each. He gains 10% on one and loses 10% on the other. Then on overall basis he -

Solution:
Total Selling Price =Tk. (2 × 99) = Tk.198

Now,
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

So, Loss = Tk. (200 - 198)
= Tk. 2

১,৬০৪.

By selling a bicycle for Tk. 2,850, a shopkeeper gains 14%. If the profit is reduced to 4%, then the selling price will be:

ক
ক) Tk. 2700
খ
খ) Tk. 2600
গ
গ) Tk. 2800
ঘ
ঘ) Tk. 2900

ব্যাখ্যা

Question: By selling a bicycle for Tk. 2,850, a shopkeeper gains 14%. If the profit is reduced to 4%, then the selling price will be:

Solution:
CP of bicycle = 100 × 2850/114
= Tk.2500
SP for the profit of 4% = 104 × 2500/100
= Tk. 2600

১,৬০৫.

In an examination, 35% of total students failed in Bangla, 45% failed in English and 20% failed in both. Find the percentage of those students who passed in both the subjects?

ক
60%
খ
50%
গ
40%
ঘ
35%

ব্যাখ্যা

Question: In an examination, 35% of total students failed in Bangla, 45% failed in English and 20% failed in both. Find the percentage of those students who passed in both the subjects?

Solution:
Failed students in Bangla = 35%
Failed students in English = 45%
Student failed in both subject Bangla and English = 20%

Student only fail in Bangla = (35 - 20)% = 15%
Student only fail in English = (45 - 20)% = 25%

Total fail students = (15 + 25 + 20)%
= 60%

Percentage of passed students in both subjects = (100 - 60)%
= 40%

১,৬০৬.

A tradesman gives 4% discount on the marked price and gives 1 article free for buying every 15 articles and thus gains 35%. The marked price is above the cost price by-

ক
30%
খ
40%
গ
45%
ঘ
50%
ঙ
None of these

ব্যাখ্যা

Question: A tradesman gives 4% discount on the marked price and gives 1 article free for buying every 15 articles and thus gains 35%. The marked price is above the cost price by-

Solution:
Let, the C.P. of each article be = Tk. 100

Then,
Cost Price of 16 articles = Tk. (100 × 16)
= Tk. 1600

Selling Price of 15 articles,
= Tk.{1600 × (135/100)}
= Tk. 2160

S.P. of each article = Tk.2160/15
= Tk. 144

If S.P. is Tk. 96, marked price = Tk. 100
If S.P. is Tk. 144, marked price = Tk.{(100/96) × 144}
= Tk. 150

∴ Marked price = 50% above C.P

১,৬০৭.

A student first reduced a number by 20 percent and then increased it again by 20 percent. If the difference between the two new numbers was 8, then what is the original number?

ক
ক) 40
খ
খ) 50
গ
গ) 75
ঘ
ঘ) 100

ব্যাখ্যা

Question: A student first reduced a number by 20 percent and then increased it again by 20 percent. If the difference between the two new numbers was 8, then what is the original number?

Solution:
ধরি, প্রকৃত সংখ্যাটি x

২০% কমালে, সংখ্যাটি = x - x এর ২০%
= x - ০.২x
= o.৮x

২০% বাড়ালে = ০.৮x + ০.৮x এর ২০%
= ০.৮x + ০.৮x × ০.২
= ০.৮x +০.১৬x
= ০.৯৬x

প্রশ্নমতে,
০.৯৬x - ০.৮x = ৮
⇒ ০.১৬x = ৮
⇒ x = ৮/০.১৬
= ৫০

অতএব, প্রকৃত সংখ্যাটি ৫০।

১,৬০৮.

A trader sells his goods at a discount of 20%. He still makes a profit of 25%. If he sells the goods at the marked price only, his profit will be:

ক
ক) 50.50%
খ
খ) 54.25%
গ
গ) 56.25%
ঘ
ঘ) 57.50%

ব্যাখ্যা

ধরি,
দ্রব্যটির বাজার মূল্য = 100 টাকা
∴ 20% ছাড়ে বিক্রয়মূল্য = (100 - 20) = 80 টাকা।
আবার, ধরি,
দ্রব্যটির উৎপাদন খরচ = x টাকা।
∴ x + x এর 25/100 = 80
⇒ x + x/4 = 80
⇒ 5x/4 = 80
⇒ x = 64

∴ Marked price (বাজার মূল্য) - এ পন্যটি বিক্রি করলে,
লাভ হয় - (100 - 64) = 36 টাকা।
∴ 64 টাকায় লাভ হয় = 36 টাকা
∴ 100 টাকায় লাভ হয় = (36 × 100)/64
= 56.25%

১,৬০৯.

The fourth proportional to 5, 6, and 15 is-

ক
53
খ
42
গ
18
ঘ
35

ব্যাখ্যা

Question: The fourth proportional to 5, 6, and 15 is-

Solution:
Let, The fourth proportional is x.

So, 5/6 = 15/x
⇒ 5x = 90
∴ x = 18

১,৬১০.

The price of an item was increased by 20% and then was reduced by 25% the next day. Which of these can be the new price of the item in Tk if all prices are integer?

ক
300
খ
325
গ
450
ঘ
475
ঙ
None

ব্যাখ্যা

Question: The price of an item was increased by 20% and then was reduced by 25% the next day. Which of these can be the new price of the item in Tk if all prices are integer?

Solution:
Let the original price be Tk. p (an integer).
After a 20% increase,
New price = p + p of 20% = p + (20p/100)
= p + (p/5)
= 6p/5

And then reduced by 25%,
Final price = (6p/5) - (6p/5) of 25%
= (6p/5) - (6p/20) = (6p/5) - (3p/10)
= (12p - 3p)/10
= 9p/10
For the final price to be an integer, 9p/10 must be integer and p must be divisible by 10.

Now, check the options,
ক) p = 300 × (10/9) = 333.33 (not integer)
খ) p = 325 × (10/9) = 361.11 (not integer)
গ) p = 450 × (10/9) = 500 (integer)
ঘ) p = 475 × (10/9) = 527.78 (not integer)

Only 450 works as a possible final integer price.
∴ The new price can be Tk 450.

১,৬১১.

The price of sugar falls by 20%. By how much percent can a person increase consumption without increasing expenditure?

ক
18%
খ
20%
গ
22.5%
ঘ
25%

ব্যাখ্যা

Question: The price of sugar falls by 20%. By how much percent can a person increase consumption without increasing expenditure?

Solution:
Let,
Original price = 100 units
After 20% fall
New price = (100 - 20) = 80 units

With the same money,
Now we can buy = (100/80) × 100
= 1.25 × 100
= 125 units

Increase = 125 - 100
= 25 units

Percentage increase in consumption = (25/100) × 100%
= 0.25 × 100%
= 25%

∴ 25% consumption can be increased.

১,৬১২.

The cost of an article was Tk.150. The cost was first increased by 20% and later on it was reduced by 20%. The present cost of the article is:

ক
ক) Tk.180
খ
খ) Tk.136
গ
গ) Tk.172
ঘ
ঘ) Tk.144

ব্যাখ্যা

Question: The cost of an article was Tk.150. The cost was first increased by 20% and later on it was reduced by 20%. The present cost of the article is:

Solution:
Initial Cost = Tk. 150
After 20% increase in the cost, it becomes,
(150 + 20% of 150)
= 150 + 30
= Tk. 180
Now, Cost is decreased by 20%, So cost will become,
(180 - 20% of 180)
= 180 - 36
=Tk. 144
So, present cost is Tk.144

১,৬১৩.

If a number is reduced by 40% it becomes two-thirds of another number. What is the ratio of the first number to the second number?

ক
5 : 3
খ
10: 3
গ
5 : 9
ঘ
10 : 9

ব্যাখ্যা

Question: If a number is reduced by 40% it becomes two-thirds of another number. What is the ratio of the first number to the second number?

Solution:
Let the number be dx and y respectively.

ATQ,
60% of x = 2y/3
Or, 60x/100 = 2y/3
Or, 3x/5 = 2y/3
Or, x/y = (2/3) × (5/3)
Or, x/y = 10/9
x : y = 10 : 9

১,৬১৪.

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
Tk. 198
খ
Tk. 216
গ
Tk. 220
ঘ
Tk. 230
ঙ
Tk. 240

ব্যাখ্যা

Question: 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?

Solution:
Wholesale cost of video recorder = Tk. 200
Marked price of video recorder by retail is at 20% above Tk. 200 = (120/100) × 200 = 240

Employee 10% discount on retail price = 90% of 240 = (90/100) × 240 = 216
Therefore Employee paid Tk. 216

১,৬১৫.

A salesman receives daily wage of Tk. 350 and earns a commission of 15% on all sales he makes. How much taka worth of sales does he need to make in order to bring his total daily income of Tk. 1,100?

ক
ক) Tk. 7,000
খ
খ) Tk. 6,500
গ
গ) Tk. 5,000
ঘ
ঘ) Tk. 5,500

ব্যাখ্যা

Question: A salesman receives daily wage of Tk. 350 and earns a commission of 15% on all sales he makes. How much taka worth of sales does he need to make in order to bring his total daily income of Tk. 1,100?

Solution:
1100 টাকার মজুরি পেতে কমিশন লাগবে = 1100 - 350 = 750 টাকা

15 টাকা কমিশন হলে মোট বিক্রয় = 100 টাকা
1 টাকা কমিশন হলে মোট বিক্রয় = 100/15 টাকা
750 টাকা কমিশন হলে মোট বিক্রয় = (100 × 750)/15 টাকা
= 5000 টাকা

১,৬১৬.

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) 2%
খ
খ) 5%
গ
গ) 7%
ঘ
ঘ) 10%

ব্যাখ্যা

C.P. of 56 kg rice = (26 x 20 + 30 x 36)
=(520 + 1080)
=1600.
S.P. of 56 kg rice = (56 x 30)
= 1680.
Gain = 80x100% = 5%.

১,৬১৭.

60% of a number is added to 120, the result is the same number. Find the number?

ক
ক) 300
খ
খ) 200
গ
গ) 400
ঘ
ঘ) 500

ব্যাখ্যা

Let,
The number is X
According to the question,
(60/100) × X + 120 = X
⇒ 3X/5 + 120 = X
⇒ X - 3X/5 = 120
⇒ (5X - 3X)/5 = 120
⇒ 2X = 600
⇒ X = 300.

১,৬১৮.

On selling 17 balls at Tk. 720 there is a loss equal to the cost price of 5 balls. The cost price of a ball is-

ক
Tk. 50
খ
Tk. 55
গ
Tk. 60
ঘ
Tk. 70

ব্যাখ্যা

Question: On selling 17 balls at Tk. 720 there is a loss equal to the cost price of 5 balls. The cost price of a ball is-

Solution:
Let,
cost price of 1 ball is = Tk. x
cost price of 17 ball is = Tk. 17x

We know,
Cost price - Selling price = Loss
17x - 720 = 5x
⇒ 12x = 720
⇒ x = 720/12
∴ x = 60

∴ Cost price of 1 ball is Tk. 60

১,৬১৯.

A student erroneously multiplied a number by 4/5 instead of 5/4. What is the percentage error in the calculation?

ক
10%
খ
28%
গ
36%
ঘ
42%

ব্যাখ্যা

Question: A student erroneously multiplied a number by 4/5 instead of 5/4. What is the percentage error in the calculation?

Solution:
Let the number be 100.

Now,
(5/4) × 100 = 125
and (4/5) × 100 = 80
Difference = 125 - 80 = 45

∴ Percentage error = (45/125) × 100 = 36%

১,৬২০.

The cost price of 20 pens is the selling price of x number of pens. If the profit is 25%, then the value of x is -

ক
15
খ
16
গ
14
ঘ
13
ঙ
17

ব্যাখ্যা

X/20 = 100/125
X × 125 = 20 × 100
X = (20 × 100) / 125
X = 16

১,৬২১.

A football team has 40 games out of 60 played. It has 32 more games to play. How many of these must the team win to make it record 75% win for the seasons?

ক
20
খ
25
গ
29
ঘ
32
ঙ
None of these

ব্যাখ্যা

Total match = 60 + 32 = 92
75% of 92 = 69
Match needed to win = 69 - 40
= 29.

১,৬২২.

If the population of the village increases by 25% to 1,200, what was the previous population?

ক
ক) 1000
খ
খ) 980
গ
গ) 960
ঘ
ঘ) 940

ব্যাখ্যা

Question: If the population of the village increases by 25% to 1,200, what was the previous population?

Solution:
জনসংখ্যা ২৫% বৃদ্ধিতে
পূর্বের জনসংখ্যা ১০০ জন হলে বর্তমান জনসংখ্যা = (১০০ + ২৫) জন = ১২৫ জন

বর্তমান জনসংখ্যা ১২৫ জন হলে পূর্বের জনসংখ্যা ১০০ জন
বর্তমান জনসংখ্যা ১ জন হলে পূর্বের জনসংখ্যা ১০০/১২৫ জন
বর্তমান জনসংখ্যা ১,২০০ জন হলে পূর্বের জনসংখ্যা (১০০ × ১,২০০)/১২৫ জন
= ৯৬০ জন

১,৬২৩.

After two successive discounts, a tie with a list price of Tk. 120 is available at Tk. 90. If the second discount is 9%, what is the first discount?

ক
ক) 15.23%
খ
খ) 13.26%
গ
গ) 17.58%
ঘ
ঘ) 18.53%

ব্যাখ্যা

Let first discount = x
91% discount of (100 – x) % of 120 = 90
⇒ (91/100) × {(100 – x)/100} × 120 = 90
⇒ (100 - x) = (90 × 100 × 100)/(120 × 91) = 82.42
⇒ x = (100 – 82.42) = 17.58
Therefore, first discount = 17.58%

১,৬২৪.

Due to a reduction in books price by 10%, the number of books sold increased by 30%. What was the percentage increase in revenue?

ক
12%
খ
15%
গ
17%
ঘ
20%

ব্যাখ্যা

Question: Due to a reduction in books price by 10%, the number of books sold increased by 30%. What was the percentage increase in revenue?

Solution:
ধরি,
বইয়ের মূল্য = 100 টাকা
10% কমে বইয়ের মূল্য = 90 টাকা
30% বৃদ্ধিতে বিক্রয়মূল্য = 90 × (130/100) = 117 টাকা

∴ শতকরা রেভিনিউ = (117 - 100)/100 × 100%
= 17%

১,৬২৫.

A vendor purchased 200 books for Taka 150 each and sold them for Taka 200 each. Calculate the total profit.

ক
Taka 9,000
খ
Taka 10,000
গ
Taka 11,000
ঘ
Taka 5,000

ব্যাখ্যা

Question: A vendor purchased 200 books for Taka 150 each and sold them for Taka 200 each. Calculate the total profit.

Solution:
Cost Price of 200 books = 200 × Taka 150 = Taka 30,000
Selling Price of 200 books = 200 × Taka 200 = Taka 40,000
∴ Total Profit = Selling Price - Cost Price
= Taka 40,000 - Taka 30,000
= Taka 10,000

১,৬২৬.

In a college election between two candidates, one candidate got 55% of the total valid votes. 10% of the votes were invalid. If the total number of votes were 16200, what is the number of valid votes the other candidate got?

ক
ক) 5325
খ
খ) 5719
গ
গ) 6327
ঘ
ঘ) 6561

ব্যাখ্যা

Question: In a college election between two candidates, one candidate got 55% of the total valid votes. 10% of the votes were invalid. If the total number of votes were 16200, what is the number of valid votes the other candidate got?

Solution:
Number of valid votes
= (100 - 10)% of 16200
= 90% of 16200
= (90/100) × 16200
= 14580

Valid votes polled by other candidate
= (100 - 55)% of 14580
= 45% of 14580
= (45/100) × 14580
= 6561

∴ The number of valid votes the other candidate got is 6561

১,৬২৭.

A man bought some eggs of which 10% are rotten. He gives 80% of the remainder to his neighbor. Now he is left out with 36 eggs. How many eggs he bought?

ক
ক) 40
খ
খ) 100
গ
গ) 200
ঘ
ঘ) 72

ব্যাখ্যা

Question: A man bought some eggs of which 10% are rotten. He gives 80% of the remainder to his neighbor. Now he is left out with 16 eggs. How many eggs he bought?

Solution:
Let he bought 100 eggs.
Eggs after removing rotten one = 90.
Eggs given to neighbour = 80% of 90 = 72 eggs.
Now he left with eggs = 90 - 72 = 18 eggs.

Now,
Comparing,
18 = 36
1 = 36/18
100 = 200.
So, he bought 200 eggs.

১,৬২৮.

Rifat bought 4 apples at taka 8 and sold 4 apples at taka 6. What will be the rate of loss?

ক
ক) 15%
খ
খ) 25%
গ
গ) 20%
ঘ
ঘ) 30%

ব্যাখ্যা

4টি আপেলের ক্রয়মূল্য 8 টাকা
1টি আপেলের ক্রয়মূল্য 8/4 টাকা
= 2 টাকা

4টি আপেলের বিক্রয়মূল্য 6 টাকা
1টি আপেলের বিক্রয়মূল্য 6/4 টাকা
=1.5 টাকা
ক্ষতি = (2 - 1.5)টাকা = 0.5 টাকা

শতকরা ক্ষতি = {(.5/2) × 100}%
= 25%

১,৬২৯.

After the increase of price of oil by 40%, a family decided to reduce its oil consumption so that the expenditure for oil goes up by 26% only. If the total consumption of oil before the price rise was 10 kg per month, then what is the current consumption oil per month (in kg)?

ক
8
খ
8.50
গ
9
ঘ
None of these

ব্যাখ্যা

Question: After the increase of price of oil by 40%, a family decided to reduce its oil consumption so that the expenditure for oil goes up by 26% only. If the total consumption of oil before the price rise was 10 kg per month, then what is the current consumption oil per month (in kg)?

Solution:
40% বৃদ্ধিতে,

বর্তমানমূল্য 140 টাকা হলে পূর্বমূল্য 100 টাকা

বর্তমানমূল্য 1 টাকা হলে পূর্বমূল্য 100/140 টাকা

বর্তমান মূল্য 126 টাকা হলে পূর্ব মূল্য (100 × 126)/140
= 90 টাকা

এখন,
পূর্বে 100 টাকায় পাওয়া যেত 10 কেজি তেল

পূর্বে 1 টাকায় পাওয়া যেত 10/100 কেজি তেল

পূর্বে 90 টাকায় পাওয়া যেত (10 × 90)/100 = 9 কেজি তেল

অর্থাৎ, বর্তমান ব্যবহার 9 কেজি।

১,৬৩০.

You have saved 1250 Taka by purchasing a laptop with 5% discount on it. what is the quoted price of the laptop in Taka?

ক
ক) Tk 30,000
খ
খ) Tk 35,000
গ
গ) Tk 25,000
ঘ
ঘ) None of the above

ব্যাখ্যা

প্রশ্ন: You have saved 1250 Taka by purchasing a laptop with 5% discount on it. what is the quoted price of the laptop in Taka?

সমাধান :

5% ছাড়ে
5 টাকা ছাড় পাওয়া যায় যখন তালিকামূল্য 100 টাকা
1 টাকা ছাড় পাওয়া যায় যখন তালিকামূল্য 100/5 টাকা
1250 টাকা ছাড় পাওয়া যায় যখন তালিকামূল্য (100 × 1250)/5 টাকা
= 25,000 টাকা

১,৬৩১.

By selling a property for Tk. 45000 a person incurs a loss of 10%. Find the selling price to gain the profit of 15%?

ক
55000
খ
60000
গ
57500
ঘ
58000

ব্যাখ্যা

Question: By selling a property for Tk. 45000 a person incurs a loss of 10%. Find the selling price to gain the profit of 15%?

Solution:
CP = SP × 100/(100 - L%)
SP = CP × (100 + P%)/100
Here SP → Selling Price, CP → Cost Price, L% → Loss%, P% → Profit%

Calculation:
CP = 45000 × 100/(100 - 10)
⇒ CP = 45000 × (10/9)
= 50000

New Selling price = CP × (100 + 15)/100
⇒ New Selling price = 50000 × (115/100)
= 57500

∴ He should sell the land for Tk. 57500 to gain 15%

১,৬৩২.

A sells an article to B at a profit of 10% B sells the article back to A at a loss of 10%. In this transaction -

ক
A neither losses nor gains
খ
A makes a profit of 11%
গ
A makes a profit of 20%
ঘ
B loses 20%

ব্যাখ্যা

Let CP was 100 for A originally
A sells article to B at 10% profit,
CP for B = 100 + 10% of 100 = 110
Now, B sells it A again with loss 10%
Now, CP for A this time = 110 - 10% of 110 = 99
A makes Profit = 110 - 99 = 11

%profit for A = (11 × 100)/100 = 11%

১,৬৩৩.

Rita bought a television set with a 20% discount on the labelled price. She made a profit of Tk. 800 by selling it for Tk. 16800. The labelled price of the set was -

ক
ক) Tk. 10,000
খ
খ) Tk. 20,000
গ
গ) Tk. 20,800
ঘ
ঘ) Tk. 24,000

ব্যাখ্যা

Let the labeled price of TV = Tk. R
∴ SP of the TV = [R x (100 - 20)] / 100
= Tk. 4R/5
But 16,800 - 800 = 4R/5
∴ x = (16,000 x 5)/4
= Tk. 20,000

১,৬৩৪.

A merchant mixes two types of sugar costing Tk. 250/kg and Tk. 350/kg in the ratio 3:2. If he sells the mixture at Tk. 360/kg, what is his profit percentage?

ক
5%
খ
24%
গ
20%
ঘ
15%

ব্যাখ্যা

Question: A merchant mixes two types of sugar costing Tk. 250/kg and Tk. 350/kg in the ratio 3:2. If he sells the mixture at Tk. 360/kg, what is his profit percentage?

Solution:
Cost of first variety = 250 Taka/kg
Cost of second variety = 350 Taka/kg
Ratio = 3:2

Cost price of mixture = {(3×250) +(2×350)}/(3+2)
= 1450/5
= 290 Taka/kg

Profit = Selling price - Cost price
= 360 - 290
= 70 Taka/kg

Profit percentage = (70/290) × 100%
= 24.13% ≈ 24%

১,৬৩৫.

A merchant buys two articles for Taka 1400. He sells one of them at a profit of 20% and the others at a loss of 8%. He makes no profit or loss in the end. What is the selling price of the article that he sold at a loss?

ক
ক) 1000
খ
খ) 960
গ
গ) 880
ঘ
ঘ) 920

ব্যাখ্যা

মনে করি,
loss এ sell করা article এর cost price x
profit এ sell করা article এর cost (1400 - x)
এখন, overall কোন profit বা loss নেই,
অর্থ্যাৎ,
দুই article এর profit এবং loss equal.
8x/100 = 20/100(1400 - x)
⇒ 8x = 28000 - 20x
⇒ 28x = 28000
⇒ x = 28000/28
⇒ x = 1000.
অর্থ্যাৎ, Selling price of the article sold at 8% loss = 920 Tk.

১,৬৩৬.

If the list price of a shirt is Tk. 800, and a Tk. 160 discount is offered on the shirt, then what is the discount percentage?

ক
10%
খ
15%
গ
20%
ঘ
25%

ব্যাখ্যা

Question: If the list price of a shirt is Tk. 800, and a Tk. 160 discount is offered on the shirt, then what is the discount percentage?

Solution:
Discount % = (Discount/marked Price) × 100
Marked Price = Tk. 800
Discount = Tk. 160

Discount (%) = (160/800) ×100%
= 20%

∴ Therefore, the discount percentage is calculated as 20%.

১,৬৩৭.

Harun sells a book to Kabil at a profit of 15%, Kabil sells that book to Rasel for Tk.1012 and makes a profit of 10%. At what cost did Harun purchase the book?

ক
ক) Tk.800
খ
খ) Tk.920
গ
গ) Tk.850
ঘ
ঘ) Tk.782

ব্যাখ্যা

প্রশ্ন: Harun sells a book to Kabil at a profit of 15%, Kabil sells that book to Rasel for Tk.1012 and makes a profit of 10%. At what cost did Harun purchase the book?

সমাধান:
১০% লাভে,
কাবিলের বিক্রয়মূল্য ১১০ টাকা হলে ক্রয়মূল্য ১০০ টাকা
∴ কাবিলের বিক্রয়মূল্য ১০১২ টাকা হলে ক্রয়মূল্য (১০০ × ১০১২)/১১০ টাকা
= ৯২০ টাকা

১৫% লাভে,
হারুনের বিক্রয়মূল্য ১১৫ টাকা হলে ক্রয়মূল্য ১০০ টাকা
∴ হারুনের বিক্রয়মূল্য ৯২০ টাকা হলে ক্রয়মূল্য (১০০ × ৯২০)/১১৫ টাকা
= ৮০০ টাকা

১,৬৩৮.

A dealer sells a radio at a gain of 10%. If he had bought it at 10% less and sold it for Tk. 132 less, he would have still gained 10%. The cost price of the radio is:

ক
ক) 1188
খ
খ) 1200
গ
গ) 1320
ঘ
ঘ) 1400
ঙ
ঙ) 1500

ব্যাখ্যা

Cost Price = 100
Selling price = 100 + 10 = 110
New cost price after 10% less = 100 - 10 = 90
New selling price = 90 × (110/100) = 99
difference between two selling price = 110 - 99 = 11%
11% price is equal to Tk. 132
1% price is equal to Tk. 132/11%
100% price is equal to Tk. (132/11%) × 100
= 1200

১,৬৩৯.

Mr. Chowdhury's salary is Tk. 25000 and he gets 10% commission of his salary. If his salary increased by 10%, by what percent his commission will increase?

ক
10%
খ
20%
গ
17%
ঘ
25%

ব্যাখ্যা

Question: Mr. Chowdhury's salary is Tk. 25000 and he gets 10% commission of his salary. If his salary increased by 10%, by what percent his commission will increase?

Solution:
পূর্বের কমিশন:
= 25000 এর 10% টাকা
= 25000 এর 10/100
= 2500 টাকা

১০% বৃদ্ধিতে
বর্তমান বেতন = 25000 + 25000 এর 10%
= 25000 + 25000 এর 10/100
= 25000 + 2500
= 27500 টাকা

নতুন কমিশন = 27500 এর 10%
27500 এর 10/100
= 2750 টাকা

কমিশন বৃদ্ধি পায় = 2750 - 2500 = 250 টাকা

শতকরা কমিশন বৃদ্ধি পায় = {(250/2500) × 100}%
= 10%

১,৬৪০.

বার্ষিক ১০% সুদে ৫০০ টাকার ২ বছরের চক্রবৃদ্ধি মুনাফা কত?

ক
১০২ টাকা
খ
১০৫ টাকা
গ
১০৬ টাকা
ঘ
২০০ টাকা
ঙ
কোনটিই নয়

ব্যাখ্যা

প্রশ্ন: বার্ষিক ১০% সুদে ৫০০ টাকার ২ বছরের চক্রবৃদ্ধি মুনাফা কত?

সমাধান:
আমরা জানি,
সরল মুনাফা, I = Pnr
= ৫০০ × ২ × (১০/১০০)
= ১০০

আবার,
চক্রবৃদ্ধি মুনাফা = p(1 + r)ⁿ - p
= ৫০০{১ + (১০/১০০)}^২ - ৫০০
= ৫০০{১ + (১/১০)}^২ - ৫০০
= ৫০০(১১/১০)^২ - ৫০০
= ৫০০{(১২১/১০০) - ১}
= ৫০০{(১২১ - ১০০)/১০০}
= (৫০০ × ২১)/১০০
= ১০৫

∴ চক্রবৃদ্ধি মুনাফা = ১০৫ টাকা

১,৬৪১.

If the price of Onion is increased by 50% by what fraction must its consumption be reduced so as to keep the same expenditure on its consumption?

ক
1/2
খ
1/3
গ
1/4
ঘ
2/3

ব্যাখ্যা

Question: If the price of Onion is increased by 50% by what fraction must its consumption be reduced so as to keep the same expenditure on its consumption?

Solution:
let, x kg onion costs 100 taka

increased by 50%, x kg costs = 100 + 100 × .5 = 150 taka

in 100 taka, new amount = 100x/150 = 2x/3 kg

fraction must its consumption be reduced = {x - (2x/3)}/x
= 1/3

১,৬৪২.

If the cost price of 12 pens is equal to the selling price of 8 pens, the gain percent is?

ক
12%
খ
30%
গ
50%
ঘ
60%
ঙ
70%

ব্যাখ্যা

Friends, we know we will need gain amount to get gain percent, right.
So, lets get gain first.
Let the cost price of 1 pen is Tk 1
Cost of 8 pens = Tk 8
Selling price of 8 pens = 12
Gain = 12 - 8 = 4
Gain% = (gain/cost × 100)%
= (4/8 × 100)%
= 50%

১,৬৪৩.

If the average of a number, its 75% and its 25% is 240, then the number is-

ক
ক) 390
খ
খ) 360
গ
গ) 320
ঘ
ঘ) 300

ব্যাখ্যা

Let the number be x
⇒ (x + 75% of x + 25% of x)/3 = 240
⇒ {x + (75x/100) + (25x/100)}/3 = 240
⇒ {x + (3x/4) + ( x/4)}/3 = 240
⇒ (4x + 3x +x)/4 = 720
⇒ 8x/4 = 720
⇒ 2x = 720
⇒ x = 720/2
⇒ x = 360

১,৬৪৪.

A cloth merchant on selling 33 meters of cloth obtains a profit equal to the selling price of 11 meters of cloth the profit is =?

ক
50%
খ
40%
গ
11%
ঘ
None of these

ব্যাখ্যা

Question: A cloth merchant on selling 33 meters of cloth obtains a profit equal to the selling price of 11 meters of cloth the profit is = ?

Solution:
Profit = selling price of 11 m of cloth = 1/3 selling price of 33 m of cloth

Let selling price of 33 meters of cloth = 3x
∴ profit = 1/3 (3x) = x

So, cost price = selling price - profit = 3x - x = 2x

% Profit = (x/2x) × 100% = 50%

১,৬৪৫.

In an examination, 80% of the candidates passed algebra and 85% passed mechanics. If 73% of the candidates passed both subjects, what percentage of candidates failed in both algebra and mechanics?

ক
8%
খ
15%
গ
27%
ঘ
35%
ঙ
None of these

ব্যাখ্যা

Question: In an examination, 80% of the candidates passed algebra and 85% passed mechanics. If 73% of the candidates passed both subjects, what percentage of candidates failed in both algebra and mechanics?

Solution:
Students passed in algebra = 80%
Students passed in mechanics = 85%
Students passed in both subjects = 73%
Then, number of students passed in at least one subject
= (80 + 85) - 73
= 92%.

Thus, students failed in both subjects = 100 - 92 = 8%.

১,৬৪৬.

A makes an article for Tk.120 and sells it to B at a profit of 25% . B sells it to C who sells it for Tk.198 making a profit of 10%. What profit percent did B make?

ক
ক) 10%
খ
খ) 20%
গ
গ) 15%
ঘ
ঘ) 18%

ব্যাখ্যা

Question: A makes an article for Tk.120 and sells it to B at a profit of 25% . B sells it to C who sells it for Tk.198 making a profit of 10%. What profit percent did B make?

Solution:
২৫% লাভে A এর বিক্রয়মূল্য = (১০০ + ২৫) = ১২৫ টাকা
ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য ১২৫ টাকা
ক্রয়মূল্য ১২০ টাকা হলে বিক্রয়মূল্য (১২৫ × ১২০)/১০০ টাকা
= ১৫০ টাকা।

B এর ক্রয়মূল্য ১৫০ টাকা
১০% লাভে বিক্রয়মূল্য = (১০০ + ১০) = ১১০ টাকা

C এর বিক্রয়মূল্য ১১০ টাকা হলে ক্রয়মূল্য ১০০ টাকা
C এর বিক্রয়মূল্য ১৯৮ টাকা হলে ক্রয়মূল্য (১০০ × ১৯৮)/১১০ টাকা
= ১৮০ টাকা

B এর বিক্রয়মূল্য ১৮০ টাকা।
∴ লাভ = (১৮০ - ১৫০) টাকা = ৩০ টাকা

১৫০ টাকায় লাভ হয় ৩০ টাকা
১০০ টাকায় লাভ হয় (৩০ × ১০০)/১৫০ টাকা
= ২০%

১,৬৪৭.

A merchant mixes two varieties of tea costing Taka 250/kg and Taka 350/kg in the ratio 3:2. If he sells the mixture at Taka 360/kg, his profit percentage is -

ক
20%
খ
25%
গ
30%
ঘ
15%

ব্যাখ্যা

Question: A merchant mixes two varieties of tea costing Taka 250/kg and Taka 350/kg in the ratio 3:2. If he sells the mixture at Taka 360/kg, his profit percentage is -

Solution:
Cost of first variety = 250 Taka/kg
Cost of second variety = 350 Taka/kg
Ratio = 3:2

Cost price of mixture = {(3×250) +(2×350)}/(3+2)
= 1450/5
= 290 Taka/kg

Profit = Selling price - Cost price
= 360 - 290
= 70 Taka/kg

Profit percentage = (70/290) × 100%
= 24.13%
= 25%

১,৬৪৮.

7.2 is 60 percent of 30 percent of a certain number. What is the number?

ক
24
খ
36
গ
40
ঘ
120

ব্যাখ্যা

Question: 7.2 is 60 percent of 30 percent of a certain number. What is the number?

Solution:
ধরি, সংখ্যাটি x

প্রশ্নমতে,
60% of 30% of x = 7.2
⇒ 60% of 30x/100 = 7.2
⇒ 60% of 3x/10 = 7.2
⇒ (60 × 3x)/(100 × 10) = 7.2
⇒ (6 × 3x)/(10 × 10) = 7.2
⇒ 18x/100 = 7.2
⇒ 18x = 7.2 × 100
⇒ 18x = 720
∴ x = 40

১,৬৪৯.

A tradesman marks his goods 10% above his cost price. If he allows his customers 10% discount on the marked price. How much profit or loss does he make, if any?

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

ব্যাখ্যা

Question: A tradesman marks his goods 10% above his cost price. If he allows his customers 10% discount on the marked price. How much profit or loss does he make, if any?

Solution:
Let cost price of goods = Tk. 100
Market price of goods
=110% of 100
=(110/100)×100
=Tk. 110

After discount selling price of goods
= 90% of 110
= (90/100) × 110
=Tk. 99

Loss = 100 - 99 = Tk. 1

Loss % = (1/100) × 100 = 1%

১,৬৫০.

A manufacturer sells three products i.e. A, B and C. Product A costs 200 and sells for 250. Product B costs 150 and sells for 180. Product C costs 100 and sells for 110. On which product, he has maximum percentage of profit?

ক
ক) B only
খ
খ) A and B both
গ
গ) A only
ঘ
ঘ) C only

ব্যাখ্যা

Product A’s percentage of profit = {(250 - 200)/200} × 100 = 25%
Product B’s percentage of profit = {(180 - 150)/150} × 100 = 20%
Product C’s percentage of profit = {(110 - 100)/100} × 100 = 10%

So, only product A has the highest profit margin.

১,৬৫১.

A machine making cost is Tk 25,000, sold with two successive discounts of 25% and 20%. An additional discount of 10% is offered for cash payment. What is the total loss in the selling price of the machine at cash payment?

ক
10856 Tk
খ
11500 Tk
গ
12420 Tk
ঘ
None of the above

ব্যাখ্যা

Question: A machine making cost is Tk 25,000, sold with two successive discounts of 25% and 20%. An additional discount of 10% is offered for cash payment. What is the total loss in the selling price of the machine at cash payment?

Solution:
Making price = 25000 Tk
Selling Price after first Discount of 25% = 25000 - 25% of 25000
= 25000 - {(25/100) × 25000}
= 18750 Tk

The selling price after the second Discount of 20% = 18750 - 20% of 18750
= 18750 - {(20/100) × 18750
= 15000 Tk

∴ The final selling price at cash = 15000 - 10% of 15000
= 15000 - {(10/100) × 15000}
= 13500 Tk

Total loss = (25000 - 13500) = 11500 Tk

১,৬৫২.

A fruit seller sells apples at the rate of Tk. 9 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5%?

ক
Tk. 12
খ
Tk. 11.81
গ
Tk. 11
ঘ
Tk. 11.32

ব্যাখ্যা

Selling price = 9
Loss = 20%
Cost price = (9 × 100)/80
= 45/4
To make a profit of 5% selling price
= (45/4) × (105/100)
= (9 × 21)/(4 × 4)
= 11.81

১,৬৫৩.

If the price of a commodity is increased by 25% and its consumption is decreased by 20%, what will be the increase or decrease in expenditure on the commodity?

ক
4% decrease
খ
4% increase
গ
5% decrease
ঘ
No increase or decrease

ব্যাখ্যা

Question: If the price of a commodity is increased by 25% and its consumption is decreased by 20%, what will be the increase or decrease in expenditure on the commodity?

Solution:
Let the initial expenditure on the commodity be Tk. 100.

Price increases by 25%:
New Price = 100+ (25% of 100) = 100+ 25 = Tk. 125

Consumption decreases by 20%:
New Consumption = 125 (20% of 125) 125 - 25 = Tk. 100

So, the final expenditure remains Tk. 100, meaning there is no change in the expenditure on the commodity.

১,৬৫৪.

The price of an article is raised by 30% and then two successive discounts of 10% each are allowed. Ultimately, the price of the article is:

ক
Tk. 105.3
খ
Tk. 100
গ
Tk. 104
ঘ
Tk. 109.7

ব্যাখ্যা

Question: The price of an article is raised by 30% and then two successive discounts of 10% each are allowed. Ultimately, the price of the article is:

Solution:
let, the price be 100 taka

after 30% raise = 100 + 30 = 130 taka

after first 10% discount = 130 - 13 = 117 taka

after second 10% discount = 117 - 117 × 0.1
= 117 - 11.7
= 105.3

১,৬৫৫.

If the cost price of 20 books is the same as selling price of 25 books, then the loss percentage is-

ক
10%
খ
25%
গ
20%
ঘ
50%

ব্যাখ্যা

Question: If the cost price of 20 books is the same as selling price of 25 books, then the loss percentage is-

Solution:
Let, the cost price of 1 book be x
So, the cost price of 20 books is = 20x

Let, the selling price of 1 book be y
So, the selling price of 25 books is = 25y

Given that the cost price of 20 books is equal to the selling price of 25 books.
⇒ 20x = 25y
⇒ y = (20/25)x = 4x/5

∴ Loss = cost price - selling price = x - y = x - (4x/5)
∴ Loss = x/5

∴ The loss percentage is = {(x/5)/x} × 100
= (1/5) × 100
= 20%

১,৬৫৬.

A person subscribing to Sky Cable for a year packs Tk. 1785. If the monthly subscription is Tk. 175, how much discount does a yearly subscriber get?

ক
10%
খ
13.33%
গ
25%
ঘ
15%
ঙ
None

ব্যাখ্যা

Question: A person subscribing to Sky Cable for a year packs Tk. 1785. If the monthly subscription is Tk. 175, how much discount does a yearly subscriber get?

Solution:
Here, the yearly subscription rate = Tk. 1785

The charge for 12 months is the rate of Tk. 175 per month

= 12 × 175 = Tk. 2100

Discount = 2100 - 1785 = Tk. 315

% discount = (315/2100) × 100 = 15%

১,৬৫৭.

The profit earned after selling an article for Tk. 1754 is the same as loss incurred after selling the article for Tk. 1492. What is the cost price of the article?

ক
Tk. 2623
খ
Tk. 1646
গ
Tk. 1423
ঘ
Tk. 1623

ব্যাখ্যা

Question: The profit earned after selling an article for Tk. 1754 is the same as loss incurred after selling the article for Tk. 1492. What is the cost price of the article?

Solution:
Let,
The cost price of the article be Tk. x.

ATQ,
x - 1492 = 1754 - x
⇒ 2x = 1754 + 1492
⇒ 2x = 3246
⇒ x = 3246/2
∴ x = 1623

∴ The cost price of the article is Tk. 1623.

১,৬৫৮.

Topu's income is Tk.2,000 more than that of Jamal. Their total salary is Tk.x. What is Jamal's salary?

ক
ক) x - 1000
খ
খ) x/2 - 1000
গ
গ) x/2 - 2000
ঘ
ঘ) None

ব্যাখ্যা

ধরি, জামালের আয় = y টাকা
সুতরাং তপুর আয় = y + 2000 টাকা
প্রশ্নমতে,
y + (y + 2000) = x
বা, 2y + 2000 = x
বা, 2y = x - 2000
বা, y = x/2 - 1000.

১,৬৫৯.

Suppose a shopkeeper has bought 1 kg of apples for Tk. 100. And sold it for Tk. 120 per kg. How much is the profit gained by him?

ক
Tk. 20
খ
Tk. 10
গ
Tk. 25
ঘ
Data inadequate

ব্যাখ্যা

Question: Suppose a shopkeeper has bought 1 kg of apples for Tk. 100. And sold it for Tk. 120 per kg. How much is the profit gained by him?

Solution:

Cost Price for apples is Tk. 100

Selling Price for apples is Tk. 120

Then profit gained by shopkeeper is = SP - CP = 120 - 100 = Tk. 20

১,৬৬০.

A fruit seller sells 20 pomegranates for Tk. 900 and incurs a loss equal to the cost of 5 pomegranates. What is the cost price of one pomegranate?

ক
Tk. 40
খ
Tk. 60
গ
Tk. 50
ঘ
Tk. 65

ব্যাখ্যা

Question: A fruit seller sells 20 pomegranates for Tk. 900 and incurs a loss equal to the cost of 5 pomegranates. What is the cost price of one pomegranate?

Solution:

Selling price of 20 pomegranates for Tk. 900

Let,
cost price of 1 pomegranate is = Tk. x
∴ cost price of 20 pomegranates is = Tk. 20x
∴ cost price of 5 pomegranates is = Tk. 5x

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

∴ The cost price of 1 pomegranate is Tk. 60

১,৬৬১.

By selling an article, Rakesh earned a profit to one-fourth of the price he bought it. If he sold it for Tk. 375, what was the cost price?

ক
ক) Tk. 320
খ
খ) Tk. 300
গ
গ) Tk. 280
ঘ
ঘ) Tk. 250

ব্যাখ্যা

Question: By selling an article, Rakesh earned a profit to one-fourth of the price he bought it. If he sold it for Tk. 375, what was the cost price?

Solution:
Selling Price of article = Tk.375
Let the cost price be = a
Selling Price = a + a/4
= (4a + a)/4
= 5a/4

Now
5a/4 = 375
a = (4 × 375)/5
a = Tk .300

১,৬৬২.

There is a ratio of 5 : 4 between two numbers. If 40% of the first number is 12, then what would be 50% of the second number is?

ক
24
খ
12
গ
18
ঘ
6

ব্যাখ্যা

Question: There is a ratio of 5 : 4 between two numbers. If 40% of the first number is 12, then what would be 50% of the second number is?

Solution:
Let the numbers be 5x and 4x respectively

According to the question,
⇒ 5x × (40/100) = 12
⇒ 2x = 12
∴ x = 6

Now,
50% of the second number is,
= 4x of 50%
= 4 × 6 × (50/100)
= 12

So 50% of the second number is 12.

১,৬৬৩.

The price of rice falls by 15%. By what percentage a person can increase the consumption of rice so that his overall budget does not change?

ক
ক) 10.74%
খ
খ) 17.64%
গ
গ) 20.46%
ঘ
ঘ) 21.90%

ব্যাখ্যা

If the price of goods decreases by R%, then the increase in consumption so as not to decrease the expenditure can be calculated using the formula:
[{R/(100 - R)} × 100]%
Using this trick,
The price of rice falls by 15%, therefore substituting this value
we get,
[{15/(100 - 15)} × 100]%
= 17.64%
Therefore, the person can increase his consumption by 17.64%.

১,৬৬৪.

Arjun purchased 30 kg of wheat at the rate of Tk. 11.50 per kg and 20 kg of wheat at the rate of Tk 14.25 per kg. he mixed the two and sold the mixture. Approximately what price per kg should he sell the mixture to make 30% profit?

ক
Tk. 16.38
খ
Tk. 15.5
গ
Tk. 12.96
ঘ
Tk. 10.35

ব্যাখ্যা

Question: Arjun purchased 30 kg of wheat at the rate of Tk. 11.50 per kg and 20 kg of wheat at the rate of Tk 14.25 per kg. he mixed the two and sold the mixture. Approximately what price per kg should he sell the mixture to make 30% profit?

Solution:
Total cost = 30 × 11.5 + 20 × 14.25
= 345 + 285
= 630

Selling price = 630 + 630 × 30%
= 630 + 189
= 819

Then, price per kg = 819/50
= 16.38 taka

১,৬৬৫.

If a man sells 1/4th of his goods sold at a profit of 10% and the remaining goods at a loss of 20%, what is his percentage profit or loss?

ক
12.5%
খ
15%
গ
12%
ঘ
25%

ব্যাখ্যা

Question: If a man sells 1/4th of his goods sold at a profit of 10% and the remaining goods at a loss of 20%, what is his percentage profit or loss?

সমাধান:
ধরি
মোট পণ্য = ১০০ টি
১০০টি পণ্যের মোট ক্রয়মূল্য = ১০০ টাকা

১০% লাভে,
২৫টি পণ্যের বিক্রয়মূল্য = (২৫ × ১১০)/১০০ = ২৭.৫ টাকা

২০% ক্ষতিতে
৭৫টি পণ্যের বিক্রয়মূল্য = (৭৫ × ৮০)/১০০ = ৬০ টাকা

∴ মোট বিক্রয়মূল্য = (২৭.৫ + ৬০) টাকা = ৮৭.৫ টাকা

∴ ক্ষতি = ১০০ - ৮৭.৫ = ১২.৫
∴ শতকরা ক্ষতি = {(১২.৫/১০০) × ১০০}% = ১২.৫%

১,৬৬৬.

একটি পরীক্ষায় বালিকাদের পাশ নম্বর এবং বালকদের পাশ নম্বর যথাক্রমে ৩৫% এবং ৪০%। একজন বালক ৪৮৩ নম্বর পেয়েও ১১৭ নম্বরের জন্য ফেল করলো। বালিকাদের পাশ নম্বর কত?

ক
৫১৫
খ
৫২৫
গ
৫৩০
ঘ
৫৩৫
ঙ
৫৪০

ব্যাখ্যা

প্রশ্ন: একটি পরীক্ষায় বালিকাদের পাশ নম্বর এবং বালকদের পাশ নম্বর যথাক্রমে ৩৫% এবং ৪০%। একজন বালক ৪৮৩ নম্বর পেয়েও ১১৭ নম্বরের জন্য ফেল করলো। বালিকাদের পাশ নম্বর কত?

সমাধান:
ধরি,
মোট নম্বর = ক
তাহলে, বালিকাদের পাশ নম্বর = ৩৫ক/১০০ = ৭ক/২০
বালকের পাশ নম্বর = ৪৮৩ + ১১৭ = ৬০০

প্রশ্নমতে,
৪০ক/১০০ = ৬০০
⇒ ৪০ক = ৬০০০০
∴ ক = ১৫০০

∴ বালিকাদের পাশ নম্বর = (৭ × ১৫০০)/২০ = ৫২৫

১,৬৬৭.

Bob invested in a stock that increased in value by 17% to 25.74. What was the actual increase in the stock’s value?

ক
ক) 3.74
খ
খ) 3.47
গ
গ) 4.25
ঘ
ঘ) 4.47

ব্যাখ্যা

17% বৃদ্ধিতে বর্তমান মূল্য = 117 টাকা
বর্তমান মূল্য 117 টাকা হলে পূর্ব মূল্য = 100 টাকা
∴ বর্তমান মূল্য 25.74 টাকা হলে পূর্ব মূল্য = (100 × 25.74)/100 টাকা
= 22 টাকা
∴ প্রকৃত মূল্য বৃদ্ধি = 25.74 - 22 = 3.74

১,৬৬৮.

স্কীম A থেকে স্কীম B তে তিনগুণ বিনিয়োগ করা হলো। বার্ষিক ৮% সরল সুদে ৪ বছরের জন্য A তে এবং বার্ষিক ১৩% হারে ২ বছরের জন্য B তে বিনিয়োগ করা হলো। দুইটি স্কীম থাকে বার্ষিক সুদ আয় ১৩২০ টাকা। স্কীম A তে কত টাকা বিনয়োগ করা হলো?

ক
৯৮৮ টাকা
খ
১০৪০ টাকা
গ
১২০০ টাকা
ঘ
৮০০ টাকা
ঙ
কোনোটিই নয়

ব্যাখ্যা

প্রশ্ন: স্কীম A থেকে স্কীম B তে তিনগুণ বিনিয়োগ করা হলো। বার্ষিক ৮% সরল সুদে ৪ বছরের জন্য A তে এবং বার্ষিক ১৩% হারে ২ বছরের জন্য B তে বিনিয়োগ করা হলো। দুইটি স্কীম থাকে বার্ষিক সুদ আয় ১৩২০ টাকা। স্কীম A তে কত টাকা বিনয়োগ করা হলো?

সমাধান:
ধরি,
A তে বিনিয়োগের পরিমাণ = ক টাকা
B তে বিনিয়োগের পরিমাণ = ৩ক টাকা

প্রশ্নমতে,
{(ক × ৪ × ৮)/১০০} + {(৩ক × ২ × ১৩)/১০০} = ১৩২০
⇒ (৩২ক/১০০) + (৭৮ক/১০০) = ১৩২০
⇒ (৩২ক + ৭৮ক)/১০০ = ১৩২০
⇒ (১১০ক/১০০) = ১৩২০
⇒ ক = (১৩২০ × ১০০)/১১০
∴ ক = ১২০০

১,৬৬৯.

কমলার দাম ৮% কমে যাওয়ায় ৫০০ টাকায় পূর্বাপেক্ষা ১ হালি কমলা বেশি পাওয়া যায়। এক ডজন কমলার বর্তমান মূল্য কত?

ক
১৪০ টাকা
খ
১৩০ টাকা
গ
১২০ টাকা
ঘ
১৫০ টাকা
ঙ
কোনটিই নয়

ব্যাখ্যা

প্রশ্ন: কমলার দাম ৮% কমে যাওয়ায় ৫০০ টাকায় পূর্বাপেক্ষা ১ হালি কমলা বেশি পাওয়া যায়। এক ডজন কমলার বর্তমান মূল্য কত?

সমাধান:
কমলার দাম ৮% কমে যাওয়ায়,
১০০ টাকায় কমে = ৮ টাকা
১ টাকায় কমে = ৮/১০০ টাকা
৫০০ টাকায় কমে = (৮ × ৫০০)/১০০ টাকা
= ৪০ টাকা

শর্তমতে, ৪০ টাকায় পাওয়া যায় ১ হালি বা ৪টি কমলা।
∴ ১ টি কমলার দাম = ৪০/৪ = ১০ টাকা
∴ ১২টি কমলার দাম = ১২ × ১০ = ১২০ টাকা

১,৬৭০.

Nasim has saved 135 Taka by purchasing a blanket with 15% discount on it. what is the quoted price of the blanket in Taka?

ক
Tk. 300
খ
Tk. 400
গ
Tk. 700
ঘ
Tk. 900

ব্যাখ্যা

Question: Nasim has saved 135 Taka by purchasing a blanket with 15% discount on it. what is the quoted price of the blanket in Taka?

Solution:
15% ছাড়ে,
15 টাকা ছাড় পাওয়া যায় যখন তালিকামূল্য 100 টাকা
1 টাকা ছাড় পাওয়া যায় যখন তালিকামূল্য 100/15 টাকা
∴ 135 টাকা ছাড় পাওয়া যায় যখন তালিকামূল্য (100 × 135)/15 টাকা
= 900 টাকা

১,৬৭১.

A book is sold for Tk. 575 the amount of profit is equal to the amount of loss if it is sold for Tk. 385, the cost price for this book is-

ক
ক) Tk. 450
খ
খ) Tk. 480
গ
গ) Tk. 490
ঘ
ঘ) Tk. 520

ব্যাখ্যা

Given,
Selling price of book = Tk. 575
Let cost price of book be Tk. a.
⇒ Profit = 575 - a

Given,
Selling price of book = Tk. 385
⇒ Loss = a - 385

Then,
⇒ 575 - a = a - 385
⇒ 2a = 960
⇒ a = 480

∴ cost price of a book is Tk. 480

১,৬৭২.

Simple interest obtained on a sum of Tk. 8000 for 4 years is Tk. 3200. Find the rate percent.

ক
8%
খ
10%
গ
12%
ঘ
6%

ব্যাখ্যা

Question: Simple interest obtained on a sum of Tk. 8000 for 4 years is Tk. 3200. Find the rate percent.

Solution:
Here,
p = Tk. 8000
n = 4 years
I = Tk. 3200

Now,
I = pn(r/100)
⇒ 3200 = 8000 × 4 × (r/100)
⇒ 3200 = 32000 × (r/100)
⇒ r = 10%

১,৬৭৩.

If 3x/4 = 1, then x is greater than 3/4 approximately by what percent?

ক
58
খ
62
গ
78
ঘ
80
ঙ
None

ব্যাখ্যা

Question: If 3x/4 = 1, then x is greater than 3/4 approximately by what percent?

Solution:
Given that,
3x/4 = 1
⇒ 3x = 4
∴ x = 4/3

∴ Difference = x - (3/4) = (4/3) - (3/4)
= (16 - 9)/12
= 7/12

∴ Percentage increase = (Difference/Original) × 100%
= {(7/12)/(3/4)} × 100%
= (7/9) × 100%
= 77.78%
= 78%

∴ Rounded to the nearest whole number 78%. (Correct answer গ)

১,৬৭৪.

A manufacturer marked an article at Tk.50 and sold it allowing 20% discount. If his profit was 25%, then the cost price of the article was-

ক
ক) Tk.40
খ
খ) Tk.35
গ
গ) Tk.32
ঘ
ঘ) Tk. 30
ঙ
ঙ) Tk. 36

ব্যাখ্যা

Selling price = 50 - (50 × 20%)
= 50 - 10
= 40
Cost Price = (100/100+25) × 40
= (100/125) × 40
= 32

১,৬৭৫.

By selling a pen for Tk 15, a man losses one-sixteenth of what it costs him. What is the cost price of the pen?

ক
ক) 16 Tk
খ
খ) 18 Tk
গ
গ) 21 Tk
ঘ
ঘ) 20 Tk

ব্যাখ্যা

Question: By selling a pen for Tk 15, a man losses one-sixteenth of what it costs him. What is the cost price of the pen?

Solution:
Let the cost price of the pen be Tk x

Then,
x - 15 = x/16
⇒ x - x/16 = 15
⇒ 15x/16 = 15
⇒ x/16 = 1
⇒ x = 16

১,৬৭৬.

Kamal went to a shop and bought things worth Tk 25, out of which 30 paisa went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?

ক
ক) Tk 15
খ
খ) Tk 15.70
গ
গ) Tk 19.70
ঘ
ঘ) Tk 20
ঙ
ঙ) None of these

ব্যাখ্যা

25 টাকার মধ্যে 30 পয়সা ট্যাক্স হলে পণ্যের প্রকৃত মূল্য (25 - 0.3) = 24.7 টাকা। X টাকার পণ্য যদি ট্যাক্স ফ্রি হয় তবে বাকি জিনিসের উপর প্রশ্নানুসারে 6% হারে ট্যাক্স আরোপ হয়।
∴ (24.7 - x)×.06 = .3
⇒ 1.482 - 0.06x = .3
⇒0.06x = 1.482 - .3 = 1.182
⇒ x = 1.182/0.06 = 19.70

১,৬৭৭.

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

ক
ক) 44
খ
খ) 45
গ
গ) 66
ঘ
ঘ) 77

ব্যাখ্যা

Total marks obtained by the student
= 55% of 800 = (55/100)×800 = 440

∴ Marks scored in English
= 15% of 440 = (15/100)×440 = 66

১,৬৭৮.

A man sells two books at Tk. 120 each and by doing so he gains 25% on one book and loses 25% on the other. His loss on the whole in Tk. is = ?

ক
Tk. 12
খ
Tk. 16
গ
Tk. 18
ঘ
Tk. 20

ব্যাখ্যা

Question: A man sells two books at Tk. 120 each and by doing so he gains 25% on one book and loses 25% on the other. His loss on the whole in Tk. is = ?

Solution:
Sells price of two books = (120 × 2) = Tk. 240
Cost price of first book = (100/125) × 120
= Tk. 96

Cost price of second book = (100/75) × 120
= Tk. 160

∴ Loss = (160 + 96) - 240
= 256 - 240
= Tk. 16

১,৬৭৯.

If A's income is 80% of B's income, then B's income is more than A's income by -

ক
ক) 12.5%
খ
খ) 15%
গ
গ) 20%
ঘ
ঘ) 25%
ঙ
ঙ) 30%

ব্যাখ্যা

When A’s income is Tk 80 B’s Income is Tk 100
when A’s income is Tk 1 B’s Income is Tk 100/80
when A’s income is Tk 100 B’s Income is Tk (100/80) × 100 = 125%

So, A’s income is 125 - 100 = 25% more

Short-cut,
A’s income is 20% less than B’s
r = 20%
(r/100 - r) × 100
(20/100) × 100
= 25%

১,৬৮০.

A fruit seller sells mangoes at the rate of Tk. 9 per kg and thereby loses 20%. At what price per kg, he should have sold, them to make a profit of 5%?

ক
ক) Tk. 11.81
খ
খ) Tk. 12.81
গ
গ) Tk. 12.25
ঘ
ঘ) Tk. 12.31

ব্যাখ্যা

Let the new S.P. be Tk. x
Then,80:9=105:x
⇒x=(9×105/ 80)=11.81

১,৬৮১.

Abir is paid an hourly wage totalling Tk 500 for 50 hours of work in a week. If his hourly wage increases by 20% and he decides to work 20% fewer hours each week, how much will Abir be paid in a week?

ক
375 Tk
খ
480 Tk
গ
550 Tk
ঘ
620 Tk
ঙ
725 Tk

ব্যাখ্যা

Question: Abir is paid an hourly wage totalling Tk 500 for 50 hours of work in a week. If his hourly wage increases by 20% and he decides to work 20% fewer hours each week, how much will Abir be paid in a week ?

Solution:
Here,
Hourly wage = 500/50 = 10

The hourly wage increases by 20%;
Then, the present hourly wage = 10 + (10 × 20%)
= 10 + [10 × (20/100)]
= (10 + 2) Tk
= 12 Tk/hour

The work hour decreases by 20%;
Then, the present work hour = 50 - (50 × 20%)
= 50 - [50 × (20/100)]
= (50 - 10) hour
= 40 hour

∴ Present weekly income = 12 × 40 = 480 Tk.

১,৬৮২.

At what rate percent per annum will a sum of money double in 4 years?

ক
ক) 15%
খ
খ) 20%
গ
গ) 25%
ঘ
ঘ) 18%

ব্যাখ্যা

Question: At what rate percent per annum will a sum of money double in 4 years?

Solution:
ধরি, সুদের হার x%

আসল x টাকা
সুদাসল = 2x টাকা
সুদ = 2x - x টাকা
= x টাকা

x = x × r × 4/100
∴ r = 25%

১,৬৮৩.

By selling a property for Tk. 45000 a person incurs a loss of 10%. Find the selling price to gain the profit of 15%?

ক
55000
খ
60000
গ
57500
ঘ
58000

ব্যাখ্যা

১,৬৮৪.

Ashik buys a field of agricultural land for Tk. 3,60,000. He sells one-third at a loss of 20% and two-fifths at a gain of 25%. At what price must he sell the remaining field so as to make an overall profit of 10%?

ক
125000 tk
খ
120000 tk
গ
140000 tk
ঘ
145000 tk
ঙ
None

ব্যাখ্যা

Question: Ashik buys a field of agricultural land for Tk. 3,60,000. He sells one-third at a loss of 20% and two-fifths at a gain of 25%. At what price must he sell the remaining field so as to make an overall profit of 10%?

Solution:
Selling price of total agricultural field at a profit at 10% = 3,60,000 + 10% of 3,60,000
= 3,60,000 + 36000
= 396000

Selling price of 1/3 agricultural field at a loss of 20% = (3,60,000/3) × (80/100)
= 120000 × (80/100)
= 96000

Selling price of 2/5 agricultural field at a profit of 25% = {(2 × 3,60,000)/5} × (125/100)
= 144000 × (125/100)
= 180000

Sell price of the remaining field = {396000 - (96000 + 180000)}
= 120000 tk

১,৬৮৫.

A trader buys a chair for Tk. 500 and sells it for Tk. 612 at a credit of 6 months. Reckoning money worth 4% per annum, his gain percent is-

ক
ক) 12%
খ
খ) 15%
গ
গ) 18%
ঘ
ঘ) 20%

ব্যাখ্যা

Question: A trader buys a chair for Tk. 500 and sells it for Tk. 612 at a credit of 6 months. Reckoning money worth 4% per annum, his gain percent is-

Solution:
Money worth in 12 months = 4%
So, money worth in 6 months = (4 × 6)/12 = 2%

So, for 500 Tk. money worth = 2% of 500 = Tk. 10

Total cost of the chair = 500 + 10 = Tk. 510
Total profit = 612 - 510 = Tk. 102

∴ Profit = (102 × 100)/510 = 20%

১,৬৮৬.

In a class 11% students got A grade. If the number of students in the class is 400, how many students got A grade?

ক
ক) 32
খ
খ) 36
গ
গ) 44
ঘ
ঘ) 48

ব্যাখ্যা

100 জনে A গ্রেড পেয়েছে 11 জন
1 জনে A গ্রেড পেয়েছে 11/100জন
400 জনে A গ্রেড পেয়েছে (11 × 400)/100 জন
= 44 জন

১,৬৮৭.

The present worth of Tk. 10816 due to in 2 years at 4% per annum compound interest is

ক
ক) Tk. 10,000
খ
খ) Tk. 12,000
গ
গ) Tk. 15,000
ঘ
ঘ) Tk. 18,000

ব্যাখ্যা

A = P(1 + r)ⁿ
⇒ 10816 = P(1 + 4/100)²
Therefore, present worth,
P = 10816/(1 + 4/100)²
= 10816/(1.04)²
= 10816/1.0816
= Tk. 10,000

১,৬৮৮.

A person buys a TV worth BDT 3,90,000 with a down payment of 40,000 including Tk. 5000 as first month's installment. How many more installments does he have to pay if his installments had to double after each successive payment?

ক
ক) 6
খ
খ) 7
গ
গ) 8
ঘ
ঘ) 10

ব্যাখ্যা

After down payment and first installment, remaining amount = 3,90,000 - 40,000 - 5,000 = 3,45,000
As the installments will be doubled each month, next installments are 10000, 20000, 40000, 80000, 160000, 320000
As the amounts won't be repaid by 5th installments fully, it will take 6th installments to complete the payment.