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পরীক্ষা - ৯

বিষয়: গণিত - ৩
টপিক:
Percentage; Profit & Loss; Simple & Compound Interest

প্রশ্ন দেখুন অনুশীলন

পেট্রোবাংলা প্রিলি ও লিখিত সমন্বিত প্রস্তুতি [Archived]

পেট্রোবাংলা প্রিলি ও লিখিত সমন্বিত প্রস্তুতি [Archived] · তারিখ অনির্ধারিত · ২৯ প্রশ্ন

১.

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

২.

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

ক
Tk. 2200
খ
Tk. 1200
গ
Tk. 1280
ঘ
Tk. 3260
ঙ
None

ব্যাখ্যা

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

Solution:

Let the cost price of the table be x.

Selling price = x - 25% of x

⇒ 720 = x - (25x/100)

⇒ 720 = 75x/100

⇒ 75x = 72000

∴ x = 960

To gain 25%, the selling price should be = 960 + 25% of 960

= Tk. 1200

৩.

In a certain organization, 40% of employees are matriculated, 50% of the remaining are graduates and the remaining 180 are post-graduates. What is the number of graduate employees?

ক
120
খ
320
গ
180
ঘ
410
ঙ
None

ব্যাখ্যা

Question: In a certain organisation, 40% of employees are matriculated, 50% of the remaining are graduates and the remaining 180 are post-graduates. What is the number of graduate employees?

Solution:

Let the total number of employees be p

Then,

(100 - 50)% of (100 - 40)% of p = 180
⇒ 50% of 60% of p = 180
⇒ (50/100) × (60/100) of p = 180
⇒ 3p/10 = 180
⇒ p = (180 × 10)/3
⇒ p =600

∴ Number of graduate employees :

= 50% of 60% of p
= 50% of 60% of 600
= (50/100) × (60/100) × 600
= 180

৪.

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

ক
8%
খ
10%
গ
12%
ঘ
20%
ঙ
None

ব্যাখ্যা

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

Solution:

Let,

Cost price = Tk.100

Market price = 100 + 20% of 100

= 100 + (100 × 20/100)

= Tk. 120

Now,

Selling price = 120 - 10% of 120

= 120 - (120 × 10)/100

= Tk. 108

Profit = 108 - 100 = Tk. 8

∴ Profit % = (8 × 100)/100

= 8%

৫.

If the selling price of an article is 8/5 times its cost price, the profit percent on it is =?

ক
30%
খ
40%
গ
45%
ঘ
50%
ঙ
None

ব্যাখ্যা

Question: If the selling price of an article is 8/5 times its cost price, the profit percent on it is =?

Solution:
According to the question,
Selling price = (8/5) × Cost price
⇒ Selling price/Cost price = 8/5

So, gain = 8 - 5 = 3

∴ The profit percent = (3/5) × 100
= 60%

৬.

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%

৭.

How much time will it take for an amount of Tk. 1800 to yield Tk. 81 as interest at 9% per annum of simple interest?

ক
18 months
খ
12 months
গ
6 months
ঘ
4 months
ঙ
None

ব্যাখ্যা

Question: How much time will it take for an amount of Tk. 1800 to yield Tk. 81 as interest at 9% per annum of simple interest?

Solution:
I = Pnr
⇒ 81 = 1800 × n × (9/100)
⇒ n = (81 × 100)/(1800 × 9)
∴ n = 1/2 year = 6 months

৮.

If the price of the eraser is reduced by 25%, a person can buy 2 more erasers for a rupee. How many erasers are available for a rupee?

ক
6
খ
8
গ
10
ঘ
12
ঙ
None

ব্যাখ্যা

Question: If the price of the eraser is reduced by 25%, a person can buy 2 more erasers for a rupee. How many erasers are available for a rupee?

Solution:

Let 'p' be the erasers available for a rupee.

Reduced price = (75/100) × 1

= Tk. 3/4

Tk. 3/4 will fetch p erasers
Tk. 1 will fetch p × (4/3) erasers

Therefore,
4p/3 = p + 2
⇒ p = 6

৯.

5200 Taka is lent at compound interest of 10% per annum for 2 years. Find the amount after two years.

ক
Tk. 5280
খ
Tk. 6200
গ
Tk. 6292
ঘ
Tk. 7324
ঙ
None

ব্যাখ্যা

Question: 5200 Taka is lent at compound interest of 10% per annum for 2 years. Find the amount after two years.

Solution:
Compound amount = P (1 + r)ⁿ
= 5200 [1 + (10/100)]²
= 5200 × (110/100) × (110/100)
= 52 × 11 × 11
= 6292

Hence, The amount after two years is Tk. 6292

১০.

What percentage of the whole week does Nazma spend in the office, if her office hours are 9 am to 5 pm from Monday to Friday?

ক
23.51%
খ
23.61%
গ
23.71%
ঘ
23.81%
ঙ
None

ব্যাখ্যা

Question: What percentage of the whole week does Nazma spend in the office, if her office hours are 9 am to 5 pm from Monday to Friday?

Solution:
Time spent by Nazma in a day = 5 pm - 9 am = 8 hrs

Time spend by Nazma in a week = 8 × 5 = 40 hrs

Percentage time spent in a week
= [40/(24 × 7)] × 100
= (40/168) × 100
= 23.81%

১১.

A sum of money lent out at simple interest amounts to Tk. 720 after 2 years and Tk. 1020 after a further period of 5 years. Find the principal?

ক
Tk. 400
খ
Tk. 450
গ
Tk. 500
ঘ
Tk. 550
ঙ
None

ব্যাখ্যা

Question: A sum of money lent out at simple interest amounts to Tk. 720 after 2 years and Tk. 1020 after a further period of 5 years. Find the principal?

Solution:
According to the question,
Principal + Simple interest for 2 years = Tk. 720 ------------- (1)
Principal + Simple interest for 7 years = Tk. 1020 ------------ (2)

Subtracting equation (1) from (2)
Principal + Simple interest for 7 years = Tk. 1020
Principal + Simple interest for 2 years = Tk. 720
--------------------------------------------------------
∴ Simple interest for 5 years = Tk. 300
⇒ Simple interest for 1 years = Tk. 300/5
⇒ Simple interest for 1 year = Tk. 60
⇒ Simple interest for 2 years = Tk. (60 × 2)
∴ Simple interest for 2 years = = Tk. 120

∴ Principal amount = (Amount after 2 years - 2 years Simple interest)
⇒ Principal amount = Tk. (720 - 120)
∴ Principal amount = Tk. 600

১২.

z% of z is the same as 10% of

ক
z³/10
খ
z²/10
গ
z⁵/10
ঘ
z^{- 2}/10
ঙ
None

ব্যাখ্যা

Question: z% of z is the same as 10% of

Solution:
Let z% of z = 10% of p
⇒ (z/100) × z = (10/100) × p
⇒ p = (z²/100) × 10
⇒ p = z²/10

১৩.

A sum of money at simple interest amounts to Tk. 721 in 3 years and to Tk. 854 in 4 years. The sum is-

ক
Tk. 522
খ
Tk. 426
গ
Tk. 336
ঘ
Tk. 322
ঙ
None

ব্যাখ্যা

Question: A sum of money at simple interest amounts to Tk. 721 in 3 years and to Tk. 854 in 4 years. The sum is-

Solution:
Simple interest for 1 year = Tk. (854 - 721)
= Tk. 133

∴ Simple interest for 3 years = Tk.(133 × 3)
= Tk. 399

∴ Sum = (721 - 399)
= Tk. 322

১৪.

In a college election between two candidates, one candidate got 55% of the total valid votes. 15% of the votes were invalid. If the total votes were 15200, what is the number of valid votes the other candidate got?

ক
5814
খ
6022
গ
7282
ঘ
7778
ঙ
None

ব্যাখ্যা

Question: In a college election between two candidates, one candidate got 55% of the total valid votes. 15% of the votes were invalid. If the total votes were 15200, what is the number of valid votes the other candidate got?

Solution:

Number of valid votes

= (100 - 15)% of 15200

= 85% of 15200

= (85/100) × 15200

= 12920

Valid votes polled by other candidates

= (100 - 55)% of 12920

= 45% of 12920

= (45/100) × 12920

= 5814

∴ The number of valid votes the other candidate got was 5814

১৫.

Rasel obtained an amount of Tk. 8376 as simple interest on a certain amount at 8 p.c.p.a. after 6 years. What is the amount invested by Rasel?

ক
16450 Tk.
খ
18470 Tk.
গ
17450 Tk.
ঘ
19472 Tk.
ঙ
None

ব্যাখ্যা

Question: Rasel obtained an amount of Tk. 8376 as simple interest on a certain amount at 8 p.c.p.a. after 6 years. What is the amount invested by Rasel?

Solution:
Here,
Simple interest, I = Tk. 8376
Rate of interest, r = 8%
Time, n = 6 years

We know,
I = Pn(r/100)
Or, P = 100I/nr
= (8376 × 100)/(6 × 8)
∴ P = 17450 Tk.

১৬.

The ratio of the cost price and selling price is 5 : 4, the loss percent is =?

ক
20%
খ
15%
গ
17.33%
ঘ
25%
ঙ
None

ব্যাখ্যা

Question: The ratio of the cost price and selling price is 5 : 4, the loss percent is =?

Solution:

Let the cost price be Tk. 5x

The selling price is Tk. 4x

Hence, the loss percent = [(5x - 4x)/5x] × 100%

= (1/5) × 100%

= 20%

১৭.

30% of a number when subtracted from 91, gives the number itself. Find the number.

ক
50
খ
55
গ
60
ঘ
65
ঙ
None

ব্যাখ্যা

Question: 30% of a number when subtracted from 91, gives the number itself. Find the number.

Solution:

Let the number be p

According to the question,

91 - 30p/100 = p
⇒ 9100 - 30p = 100p
⇒ 9100 = 130p
∴ p = 70

Hence, the number = 70

১৮.

The compound interest on Tk. 2800 for 18 months at 10% per annum is-

ক
Tk. 425.25
খ
Tk. 538
গ
Tk. 434
ঘ
Tk. 336
ঙ
None

ব্যাখ্যা

Question: The compound interest on Tk. 2800 for 18 months at 10% per annum is-

Solution:
Interest after 1 year or 12 months = 2800 × 1 × (10/100)
= 280
New principal = 2800 + 280
= 3080

6 months = 1/2 year

Now,
I = Pnr
= 3080 × (1/2) × (10/100)
= 154

∴ Total interest = 280 + 154 = Tk. 434

১৯.

A merchant buys an article for Tk. 27 and sells it at a profit of 10 percent of the selling price. The selling price of the article is -

ক
Tk. 30
খ
Tk. 35
গ
Tk. 40
ঘ
Tk. 32
ঙ
None

ব্যাখ্যা

Question: A merchant buys an article for Tk. 27 and sells it at a profit of 10 percent of the selling price. The selling price of the article is -

Solution:
Let, the selling price of the article be Tk. p

Cost price = Tk. 27
Profit = 10% of p

Again,
Profit = Selling price - Cost price
⇒ 10% of p = p - 27
⇒ p - 10% of p = 27
⇒ 90% of p = 27
⇒ 9p/10 = 27
⇒ p = 27 × (10/9)
⇒ p = 30

Hence, The selling price of the article is Tk. 30

২০.

The marked price of a DVD is Tk. 250. It is sold for Tk. 225. The rate of discount is = ?

ক
20%
খ
25%
গ
10%
ঘ
30%
ঙ
None

ব্যাখ্যা

Question: The marked price of a DVD is Tk. 250. It is sold for Tk. 225. The rate of discount is = ?

Solution:
Here,

Marked Price = Tk. 250

Selling Price = Tk. 225

Difference = 250 - 225 = Tk. 25

∴ Discount = (25/250) × 100
= 10%

২১.

A is 6 times greater than B then by what percent is B smaller than A?

ক
83.33%
খ
85%
গ
89.33%
ঘ
72%
ঙ
None

ব্যাখ্যা

Question: A is 6 times greater than B then by what percent is B smaller than A?

Solution:

Let B = 10

Then, A = 10 + 60 = 70

∴ A - B = 70 - 10 = 60

B is 60 less than A.

∴ B, % less than A = (60/70) × 100 = 85.71%

২২.

Interest obtained on a sum of Tk. 5000 for 3 years is Tk. 1500. Find the rate percent.

ক
20%
খ
15%
গ
10%
ঘ
25%
ঙ
None

ব্যাখ্যা

Question: Interest obtained on a sum of Tk. 5000 for 3 years is Tk. 1500. Find the rate percent.

Solution:
Here,
p = Tk. 5000
n = 3 years
I = Tk. 1500

Now,
I = pn(r/100)
⇒ 1500 = 5000 × 3 × (r/100)
⇒ r = 10%

২৩.

A shopkeeper marks his goods 30% above his cost price but allows a discount of 10% at the time of sale. His gain is =?

ক
27.31%
খ
25%
গ
20%
ঘ
17%
ঙ
None

ব্যাখ্যা

Question: A shopkeeper marks his goods 30% above his cost price but allows a discount of 10% at the time of sale. His gain is =?

Solution:

Let the cost price be Tk.100

Then the markup price which is 30% above the cost price,

Mark price = (100 + 30% of 100) = Tk. 130

The shopkeeper gives a discount of 10% on mark up price, then the

Selling Price = (130 - 10% of 130) = Tk. 117

Gain = 117 - 100 = Tk. 17

∴ His gain in percentage is = (17 × 100)/100
= 17%

২৪.

A line of length 1.5 metres was measured as 1.55 metres by mistake. What will be the value of the error percent?

ক
7%
খ
5.33%
গ
4%
ঘ
3.33%
ঙ
None

ব্যাখ্যা

Question: A line of length 1.5 metres was measured as 1.55 metres by mistake. What will be the value of the error percent?

Solution:
Percentage error = 1.55 - 1.50 = 0.05

∴ Percentage error % = (0.05/1.50) × 100
= (5/150) × 100
= 10/3
= 3.33%

২৫.

A house worth Tk. 150000 is sold by X at a 5% profit to Y, Y sells the house back to X at a 2% loss. Then find profit and loss in the entire transaction = ?

ক
X gains Tk. 4250
খ
X loses Tk. 2750
গ
X loses Tk. 3740
ঘ
X gains Tk. 3150
ঙ
None

ব্যাখ্যা

Question: A house worth Tk. 150000 is sold by X at a 5% profit to Y, Y sells the house back to X at a 2% loss. Then find profit and loss in the entire transaction = ?

Solution:
Here,

Money spent by X = Tk. 150000

Money received by X = 105% of Tk. 150000 = Tk. 157500

Cost Price to X = 98% of Tk. 157500 = Tk. 154350

∴ X gains = Tk. (157500 - 154350) = Tk. 3150

২৬.

2100 Taka is lent at compound interest of 5% per annum for 2 years. Find the amount after two years.

ক
Tk. 2315.25
খ
Tk. 2325.25
গ
Tk. 2425
ঘ
Tk. 2575
ঙ
None

ব্যাখ্যা

Question: 2100 Taka is lent at compound interest of 5% per annum for 2 years. Find the amount after two years.

Solution:
Here,
p = Tk. 2100
r% = 5%
n = 2 years

C = p[1 + (r/100)]ⁿ
= 2100 [1 + (5/100)]2
= 2100 × [105/100]²
= (2100 × 11025)/10000
= 2315.25

Hence, the amount after two years is Tk. 2315.25

২৭.

By how much percent is four-fifths of 70 lesser than five-sevenths of 112?

ক
12%
খ
24%
গ
36%
ঘ
40%
ঙ
None

ব্যাখ্যা

Question: By how much percent is four-fifths of 70 lesser than five-sevenths of 112?

Solution:

Here,
four-fifth of 70

= 4/5 × 70

= 56

Again,

five-seventh of 112

= 5/7 × 112

= 80

% lesser

= [(80 - 56)/80] × 100%

= (24/80) × 100%

= 30%

২৮.

Tk. 1200 is lent out at 5% per annum simple interest for 3 years. Find the amount after 3 years.

ক
Tk. 1320
খ
Tk. 1380
গ
Tk. 1360
ঘ
Tk. 1390
ঙ
None

ব্যাখ্যা

Question: Tk 1200 is lent out at 5% per annum simple interest for 3 years. Find the amount after 3 years.

Solution:
Here,
p = Tk. 1200
r% = 5%
n = 3 years

Now,
A = p[1 + (nr/100)]
= 1200[1 + (3 × 5)/100]
= 12000 × (115/100)
= 1380

Hence, the amount after 3 years is Tk. 1380

২৯.

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

ক
25%
খ
30%
গ
15%
ঘ
10%
ঙ
None

ব্যাখ্যা

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

Solution:

Let the initial expenses on salt was Tk. 100.

Now, the price of salt has risen 25%.

So, to buy the same amount of salt, they need to spend,

= (100 + 25% of 100) = Tk. 125.

But, They want to keep expenses on salt, so they have to cut Tk. 25 in the expenses to keep it to Tk. 100.

Now, % decrease in Consumption,
(25/125) × 100 = 20%