Bank Math

PrepBank · পাতা ১৩১ / ১৬১ · ১৩,০০১–১৩,১০০ / ১৬,১২৪

১৩,০০১.

The simple interest on a certain sum at 6% p.a. is Tk. 360 in 1 year. What will be the additional interest earned in 1 year if the rate increases to 7% p.a. on the same sum?

ক
Tk. 60
খ
Tk. 80
গ
Tk. 70
ঘ
Tk. 100

ব্যাখ্যা

Question: The simple interest on a certain sum at 6% p.a. is Tk. 360 in 1 year. What will be the additional interest earned in 1 year if the rate increases to 7% p.a. on the same sum?

Solution:
Given,
Interest at 6% for 1 year:
Simple Interest, SI₁ = Tk. 360
Interest rate, R = 6%
Time, T = 1 year (initial)

We know,
SI₁ = PRT/100
⇒ 360 = (P × 6 × 1)/100
⇒ P = (360 × 100)/6
∴ P = Tk. 6000

So, the original sum (principal) is Tk. 6000.

Now,
Interest at 7% for 1 year:
SI₂ = PRT/100
⇒ SI₂ = (6000 × 7 × 1)/100
⇒ SI₂ = Tk. 420

Additional interest = SI₂ - SI_I
= 420 - 360
= Tk. 60

১৩,০০২.

The product of two numbers is 300, and the sum of their squares is 625. What is the sum of two numbers?

ক
33
খ
34
গ
35
ঘ
36

ব্যাখ্যা

Question: The product of two numbers is 300, and the sum of their squares is 625. What is the sum of two numbers?

Solution:
Let the numbers be x and y.
As per the question:
xy = 300
x² + y² = 625

So,
(x + y)² = x² + y² + 2xy
= 625 + 2 × 300
= 625 + 600
= 1225

∴ x + y = √1225 = 35

১৩,০০৩.

A wholesaler buys a laptop for Tk. 40,000 and sells it to a retailer at a profit of 20%. The retailer then sells it to a customer at a profit of 15%. How much does the customer pay to the retailer?

ক
Tk. 52,600
খ
Tk. 60,000
গ
Tk. 55,200
ঘ
Tk. 58,500

ব্যাখ্যা

Question: A wholesaler buys a laptop for Tk. 40,000 and sells it to a retailer at a profit of 20%. The retailer then sells it to a customer at a profit of 15%. How much does the customer pay to the retailer?

Solution:
পাইকারি বিক্রেতার ক্রয়মূল্য = 40,000 টাকা
20% লাভে পাইকারি বিক্রেতার বিক্রয়মূল্য (যা খুচরা বিক্রেতার ক্রয়মূল্য) = 40,000 + 40,000 এর 20%
= 40,000 + (40,000 × 20/100)
= 40,000 + 8,000 = 48,000 টাকা

∴ খুচরা বিক্রেতার ক্রয়মূল্য = 48,000 টাকা

আবার, খুচরা বিক্রেতা 15% লাভে এটি বিক্রি করেন।
∴ 15% লাভে খুচরা বিক্রেতার বিক্রয়মূল্য (যা ক্রেতার পরিশোধিত মূল্য) = 48,000 + 48,000 এর 15%
= 48,000 + (48,000 × 15/100)
= 48,000 + 7,200 = 55,200 টাকা

∴ ক্রেতা খুচরা বিক্রেতাকে 55,200 টাকা প্রদান করেন।

১৩,০০৪.

X and Y started a partnership business investing some amount in the ratio of 4 : 7. Z joined after 8 months with an amount equal to that of X. In what proportion should the profit at the end of one year be distributed among X, Y, and Z?

ক
12 : 21 : 5
খ
12 : 11 : 4
গ
10 : 21 : 4
ঘ
12 : 21 : 4
ঙ
None

ব্যাখ্যা

Question: X and Y started a partnership business investing some amount in the ratio of 4 : 7. Z joined after 8 months with an amount equal to that of X. In what proportion should the profit at the end of one year be distributed among X, Y, and Z?

Solution:
Let the initial investments of X and Y be 4b and 7b.

X : Y : Z = (4b × 12) : (7b × 12) : (4b × 4)
= 48 : 84 : 16
= 12 : 21 : 4

∴ Required proportion - 12 : 21 : 4

১৩,০০৫.

Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

ক
2 : 3 : 4
খ
6 : 7 : 8
গ
6 : 8 : 9
ঘ
2 : 4 : 3
ঙ
None of these

ব্যাখ্যা

Question: Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

Solution:
Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
⇒ (140/100) × 5x , (150/100) × 7x and (175/100) × 8x
⇒ 7x, 21x/2 and 14x.

The required ratio = 7x : 21x/2 : 14x
= 14x : 21x : 28x
= 2 : 3 : 4.

১৩,০০৬.

15 buckets of water fill a tank when the capacity of each bucket is 16 liters. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 12 liters?

ক
18
খ
20
গ
12
ঘ
25

ব্যাখ্যা

Question: 15 buckets of water fill a tank when the capacity of each bucket is 16 liters. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 12 liters?

Solution:
total capacity of the tank is = (15 × 16) = 240 liters.

total buckets of 12 liters = 240/12 = 20 buckets

১৩,০০৭.

How long will it take for two pipes to fill a tank together when they can fill it alone in 14 hours and 21 hours respectively?

ক
8.4 hours
খ
8 hours
গ
8.8 hours
ঘ
8.6 hours

ব্যাখ্যা

Question: How long will it take for two pipes to fill a tank together when they can fill it alone in 14 hours and 21 hours respectively?

Solution:
together in one hour they can fill = 1/14 + 1/21 = 5/42

so, the total time to fill the tank is = 42/5 hours = 8.4 hours

১৩,০০৮.

A sum of money becomes 4/3 of itself in 3 years at a certain rate of simple interest. What is the rate of interest per annum?

ক
ক) (50/9)%
খ
খ) (75/9)%
গ
গ) (100/9)%
ঘ
ঘ) (110/9)%

ব্যাখ্যা

Question: A sum of money becomes 4/3 of itself in 3 years at a certain rate of simple interest. What is the rate of interest per annum?

Solution:
আসল = 3y
সুদাসল = 3y × 4/3 = 4y
সুদ = 4y - 3y
= y

৩ বছরে,
y = 3yr × 3/100 [r = rate of simple interest]
or, r = 100/9

১৩,০০৯.

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

ক
ক) 56.25%
খ
খ) 25.56%
গ
গ) 50.25%
ঘ
ঘ) 54.25%

ব্যাখ্যা

Let the cost price of goods be 100 taka.
At 25% profit,
if cost price of goods is 100 taka, selling price of goods is (100 + 25) taka or 125 taka.

At a discount 20%,
80% of goods' price = 125 taka.
100% of goods' price shall be (125×100/80) taka or 156.25 taka.
profit percentage would be (156.25 - 100) taka or 56.25 taka.

১৩,০১০.

An iron rod that weights 30 kg is cut into two pieces so that one of these pieces weights 16 kg and 40 m long. If the weight of each piece is proportional to its length, how long is the other one is -

ক
30
খ
45
গ
35
ঘ
42

ব্যাখ্যা

Question: An iron rod that weights 30 kg is cut into two pieces so that one of these pieces weights 16 kg and 40 m long. If the weight of each piece is proportional to its length, how long is the other one is -

Solution:
Total weight = 30 kg,
1st piece weight = 16 kg and Length = 40 m

So, 2nd piece weight = (30 - 16) = 14 kg
Let the Length of the 2nd piece = x m

Now,
16 : 14 = 40 : x
⇒ 16/14 = 40/x
⇒ x = (40 × 14)/16
∴ x = 35

১৩,০১১.

The ratio of total surface area to lateral surface area of a cylinder whose radius is 25 cm and height 100 cm, is -

ক
5 : 3
খ
1 : 4
গ
5 : 4
ঘ
5 : 7

ব্যাখ্যা

Question: The ratio of total surface area to lateral surface area of a cylinder whose radius is 25 cm and height 100 cm, is -

Solution:
Total surface area : Lateral surface area
= (2πrh + 2πr²⁾ : 2πrh
= (h +r) : h
= (100 + 25) : 100
= 125 : 100
= 5 : 4

১৩,০১২.

In a certain language PENSION is coded as NEISNOP, how is COLLEGE coded in that code?

ক
EOELLGC
খ
EEOLLGC
গ
EOLELGC
ঘ
None of these

ব্যাখ্যা

Question: In a certain language PENSION is coded as NEISNOP, how is COLLEGE coded in that code?

Solution:
PENSION ⇔ NEISNOP
P ⇒ E ⇒ N ⇒ S ⇒ I ⇒ O ⇒ N
1 ⇒ 2 ⇒ 3 ⇒ 4 ⇒ 5 ⇒ 6 ⇒ 7
N ⇒ E ⇒ I ⇒ S ⇒ N⇒ O ⇒ P
Here,
Letters of 1st and 7th position inter-change their position.
Letters of 3rd and 5th position also inter-change their position.
And the letters of even number position remain same.

C ⇒ O ⇒ L ⇒ L ⇒ E ⇒ G ⇒ E
1 ⇒ 2 ⇒ 3 ⇒ 4 ⇒ 5 ⇒ 6 ⇒ 7
E ⇒ O ⇒ E ⇒ L ⇒ L ⇒ G ⇒ C

∴ COLLEGE ⇔ EOELLGC

১৩,০১৩.

Let N be the smallest positive integer that is divisible by both 12 and 15. How many distinct prime factors does N have?

ক
2
খ
3
গ
4
ঘ
5
ঙ
None of these

ব্যাখ্যা

Question: Let N be the smallest positive integer that is divisible by both 12 and 15. How many distinct prime factors does N have?

Solution:
এখানে, N হলো 12 এবং 15 দ্বারা বিভাজ্য ক্ষুদ্রতম সংখ্যা।

সুতরাং, N হবে 12 এবং 15 এর ল.সা.গু।

এখন, 12 = 2 × 2 × 3 = 2² ×3

এবং 15 = 3 × 5

LCM(12,15) = 2² × 3 × 5
= 60

অতএব, N = 60
60 এর মৌলিক উৎপাদক = 2² × 3 × 5

স্বতন্ত্র মৌলিক উৎপাদকগুলি হলো 2, 3 এবং 5।

∴ N এর স্বতন্ত্র মৌলিক উৎপাদকের সংখ্যা হলো 3টি।

১৩,০১৪.

If 9 examiners can examine a certain number of answer books in 12 days by working 5 hours a day; for how many hours a day would 4 examiners have to work in order to examine twice the number of answer books in 27 days?

ক
ক) 5 hours
খ
খ) 8 hours
গ
গ) 10 hours
ঘ
ঘ) 12 hours

ব্যাখ্যা

Question: If 9 examiners can examine a certain number of answer books in 12 days by working 5 hours a day; for how many hours a day would 4 examiners have to work in order to examine twice the number of answer books in 27 days?

Solution:
9 examiners need 12 days by working 5 hours
1 examiner needs 1 day by working 5 × 9 × 12 hours
4 examiners need 27 days by working (5 × 9 × 12)/(4 × 27) hours
= 5 hours

So, twice the work need twice time.
∴ So, the answer = (5 × 2) = 10 hours

১৩,০১৫.

In a market survey, 30% of respondents opted for product P and 50% opted for product Q. The remaining respondents were uncertain. If the difference between the number of respondents who opted for product Q and those who were uncertain is 420, how many respondents were surveyed?

ক
600
খ
900
গ
1200
ঘ
1400
ঙ
1700

ব্যাখ্যা

Question: In a market survey, 30% of respondents opted for product P and 50% opted for product Q. The remaining respondents were uncertain. If the difference between the number of respondents who opted for product Q and those who were uncertain is 420, how many respondents were surveyed?

Solution:
Here, product P opted for 30% respondents & product Q opted for 50% respondents.

Uncertain respondents = (100 - (30 + 50))% = 20%
The difference between those who opted for product Q and those who were uncertain = (50 - 20)% = 30%

Let total number of respondents = a
∴ a × 30% = 420
⇒ 30a/100 = 420
⇒ a = (420 × 100)/30
⇒ a = 1400

১৩,০১৬.

A pump can fill a tank with water in 2 hours. Because of a leak, it took 140 minutes to fill the tank. The leak can drain all the water of the tank in-

ক
7 hr
খ
10 hr
গ
12 hr
ঘ
14 hr

ব্যাখ্যা

Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 140 minutes to fill the tank. The leak can drain all the water of the tank in-

Solution:
একটি পাইপ চৌবাচ্চা পূর্ণ করতে পারে ২ ঘণ্টায় বা ১২০ মিনিটে
১ মিনিটে পূর্ণ করে ১/১২০ অংশ

একটি ছিদ্র থাকায় তা পূর্ণ করতে পারে ১৪০ মিনিটে
১ মিনিটে পূর্ণ হয় ১/১৪০ মিনিটে

ছিদ্র দিয়ে ১ মিনিটে খালি হয় = (১/১২০) - (১/১৪০)
= (৭ - ৬)/৮৪০
= ১/৮৪০ অংশ

সম্পূর্ণ অংশ খালি করতে সময় লাগে = ১/১/৮৪০ মিনিট
= ৮৪০ মিনিটে
= ৮৪০/৬০ ঘণ্টায়
= ১৪ ঘণ্টায়

১৩,০১৭.

55 men can finish a work in 42 days. How many additional men must be engaged to complete the work 9 days earlier?

ক
ক) 15
খ
খ) 16
গ
গ) 17
ঘ
ঘ) 18

ব্যাখ্যা

42 days এ কাজটি complete করতে লাগে 55 men
1 day এ কাজটি complete করতে লাগে 55 × 42 men
33 day এ কাজটি complete করতে লাগে (55 × 42)/33 men
= 70 men.
Additional men লাগবে 70 - 55 = 15 men.

১৩,০১৮.

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
ক) Tk. 1689
খ
খ) Tk. 2623
গ
গ) Tk. 1623
ঘ
ঘ) Tk. 3246

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.

১৩,০১৯.

36, 54, 18, 27, 9, 18.5, 4.5

ক
ক) 4.5
খ
খ) 18.5
গ
গ) 54
ঘ
ঘ) 18

ব্যাখ্যা

The terms are alternatively multiplied by 1.5 and divided by 3. However, 18.5 does not satisfy it.

১৩,০২০.

Machine A paints y units in 15 minutes and machine B paints 3y units in 30 minutes. In how many minutes will A and B, working together, paint 45y units?

ক
270 minutes
খ
240 minutes
গ
250 minutes
ঘ
280 minutes

ব্যাখ্যা

Question: Machine A paints y units in 15 minutes and machine B paints 3y units in 30 minutes. In how many minutes will A and B, working together, paint 45y units?

Solution:
Machine A paints per minute = y/15 units
Machine B paints per minute = 3y/30 = y/10 units

∴ A and B together paint per minute = y/15 + y/10
= (2y + 3y)/30
= 5y/30
= y/6 units

So, to paint y/6 units, it takes 1 minute.

Hence, to paint 45y units, time needed = (45y × 6)/y = 270 minutes.

১৩,০২১.

If a + b = √3 and a = √2 + b, what is the value of 4ab?

ক
1
খ
- 3
গ
- 1
ঘ
0

ব্যাখ্যা

Question: If a + b = √3 and a = √2 + b, what is the value of 4ab?

Solution:
given,
a + b = √3
a = √2 + b
∴ a - b = √2

4ab = (a + b)² - (a - b)²
= 3 - 2
= 1

১৩,০২২.

The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is-

ক
20
খ
38
গ
32
ঘ
26

ব্যাখ্যা

Question: The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is-

Solution:
Let the numbers are a, b and c.
Then,
a² + b² + c² = 138
and ab + bc + ca = 131.

Now,
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca) = 138 + (2 × 131) = 138 + 262 = 400
⇒ (a + b + c)² = 400
∴ a + b + c = 20.

১৩,০২৩.

A Boat takes a total 10 hours for traveling downstream from point A to point B and coming back point C which is somewhere between A and B. The speed of the Boat in still water is 9 km/hr and rate of stream is 3 km/hr, then what is the distance between A and B if the ratio of distance between A to C and distance between B to C is 2 : 1?

ক
48 km
খ
56 km
গ
68 km
ঘ
72 km

ব্যাখ্যা

Question: A Boat takes a total 10 hours for traveling downstream from point A to point B and coming back point C which is somewhere between A and B. The speed of the Boat in still water is 9 km/hr and rate of stream is 3 km/hr, then what is the distance between A and B if the ratio of distance between A to C and distance between B to C is 2 : 1?

Solution:

Let, the distance between B to C = x
the distance between A to C = 2x
the distance between A to B = 3x

ATQ,
3x/12 + x/6 = 10
⇒ (3x + 2x)/12 = 10
⇒ 5x = 120
∴ x = 24

∴ The distance between A to B = 3 × 24 = 72 km

১৩,০২৪.

The radius and height of a cylinder are in the ratio 5 : 7 and its volume is 4400 cm³. Then its radius will be-

ক
ক) 4 cm
খ
খ) 7 cm
গ
গ) 10 cm
ঘ
ঘ) 13 cm

ব্যাখ্যা

Question: The radius and height of a cylinder are in the ratio 5 : 7 and its volume is 4400 cm³. Then its radius will be-

Solution:
Let the radius and height of the cylinder be 5x and 7x cm respectively.
Then, volume = πr²h
= (22/7) × (5x)² × 7x
= 550x³ATQ,
550x³ = 4400
x³ = 4400/550 = 8
x = ∛8 = 2

Hence, the radius = (5 × 2) = 10 cm

১৩,০২৫.

How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

ক
5
খ
10
গ
15
ঘ
20

ব্যাখ্যা

Question: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

Solution:
শেষ অঙ্কটি 5 হলে, সংখ্যাটি 5 দ্বারা নি:শেষে বিভাজ্য হবে।

১ম অঙ্কটি 2, 3, 6, 7, 9 এর যে কোন একটি হতে পারে।
১ম অঙ্কটি বাছাই করার উপায় = ⁵C₁ = 5

২য় অঙ্ক বাছাই করতে হবে অবশিষ্ট 4 টি অঙ্ক থেকে।
২য় অঙ্ক বাছাই করার উপায় = ⁴C₁
= 4

∴ মোট বাছাই করার উপায় = 5 × 4
= 20

১৩,০২৬.

How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

ক
10
খ
20
গ
15
ঘ
5

ব্যাখ্যা

Question: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

Solution:

শেষ অঙ্কটি 5 হলে, সংখ্যাটি 5 দ্বারা নি:শেষে বিভাজ্য হবে।

১ম অঙ্কটি 2, 3, 6, 7, 9 এর যে কোন একটি হতে পারে।

১ম অঙ্কটি বাছাই করার উপায় = ⁵C₁ = 5

২য় অঙ্ক বাছাই করতে হবে অবশিষ্ট 4 টি অঙ্ক থেকে।

২য় অঙ্ক বাছাই করার উপায় = ⁴C₁

= 4

∴ মোট বাছাই করার উপায় = 5 × 4

= 20

১৩,০২৭.

If a = 4, b = 6 and c = 3, then a(b - c)/b(a + b + c) =?

ক
2/15
খ
3/8
গ
1/11
ঘ
2/13

ব্যাখ্যা

Question: If a = 4, b = 6 and c = 3, then a(b - c)/b(a + b + c) =?

Solution:
Given that,
a = 4, b = 6 and c = 3

Now,
a(b - c)/b(a + b + c)
= 4(6 - 3)/6(4 + 6 + 3)
= 12/78
= 2/13

১৩,০২৮.

If 50% of (x - y) = 30% of (x + y), then what percent of x is y?

ক
25
খ
30
গ
35
ঘ
40

ব্যাখ্যা

Question: If 50% of (x - y) = 30% of (x + y), then what percent of x is y?

Solution:
50% of (x - y) = 30% of (x + y)
50(x - y)/100 = 30(x + y)/100
5(x - y) = 3(x + y)
5x - 5y = 3x + 3y
5x - 3x = 5y + 3y
2x = 8y
x/y = 8/2
x = 4y

Percent of x is y = (1/4) × 100%
= 25%

১৩,০২৯.

How long will it take for two pipes to fill a tank together when they can fill it alone in 10 hours and 15 hours respectively?

ক
4 hours
খ
3 hours
গ
6 hours
ঘ
5 hours

ব্যাখ্যা

Question: How long will it take for two pipes to fill a tank together when they can fill it alone in 10 hours and 15 hours, respectively?

Solution:
together in one hour they can fill = 1/10 + 1/15
= 5/30
= 1/6

so, the total time to fill the tank is = 6 hours

১৩,০৩০.

We rarely go out during exams, ______?

ক
don't we
খ
did we
গ
do we
ঘ
does we

ব্যাখ্যা

• Correct sentence: We rarely go out during exams, do we?

• Tag question করার নিয়ম:
- সাধারণত Tag question ব্যবহৃত হয় পূর্বে উল্লেখিত কোন উক্তি সত্য না মিথ্যা তা নিশ্চিত হওয়ার জন্য।
- Tag question এর subject সর্বদা মূল sentence এর subject এর pronoun হয়।
- Tag question গঠনে auxiliary verb ব্যবহৃত হয় এবং auxiliary verb এর সংক্ষিপ্ত রূপ হয়।
- Statement positive হলে tag question টা negative হবে। আবার statement negative হলে tag question positive হবে।

• hardly, rarely, scarcely, seldom ইত্যাদি কোনো sentence এ থাকলে, ওই sentence "negative' expression দেয়।
- এর ফলে প্রশ্ন প্রদও বাক্যটির tag 'affirmative' হয়েছে।
- Sentence টিতে subject We হওয়ার কারণে Auxiliary verb 'do' হয়েছে।
- অর্থাৎ, Tag question এর নিয়মানুযায়ী বাক্যটি Negative হওয়ায় Tag question Affirmative হয়েছে।

Source: Advanced Learner's Grammar and Composition by Chowdhury and Hossain.

১৩,০৩১.

Find the area of an isosceles triangle whose sides are 10 cm, 6 cm and 6 cm.

ক
√11 sq. cm.
খ
25√11 sq. cm.
গ
5 sq. cm.
ঘ
11 sq. cm.
ঙ
5√11 sq. cm.

ব্যাখ্যা

Question: Find the area of an isosceles triangle whose sides are 10 cm, 6 cm and 6 cm.

Solution:
Semi perimeter of triangle s = (10 + 6 + 6)/2 = 11.
Area of triangle = √{11 × (11 - 10) × (11 - 6) × (11 - 6)}
= √(11 × 5 × 5)
= 5√11 cm²

১৩,০৩২.

Two trains start from stations A and B and travel towards each other at a speed of 50 kmph and 60 kmph respectively. A the time of their meeting, the second train had travelled 120 km more then the first. The distance between A and B is :

ক
720 km
খ
1020 km
গ
1220 km
ঘ
1320 km

ব্যাখ্যা

Question: Two trains start from stations A and B and travel towards each other at a speed of 50 kmph and 60 kmph respectively. A the time of their meeting, the second train had travelled 120 km more then the first. The distance between A and B is :

Solution:
At the time of meeting, let the distance travelled by the first train be x km.
Then, discount covered by the second train = (x + 120) km

ATQ,
x/50 = (x + 120)/60
⇒ 60x = 50(x + 120)
⇒ 60x - 50x = 6000
⇒ 10x = 6000
∴ x = 600

So, distance between A and B = (x + x + 120) km
= (600 + 600 + 120) km
= 1320 km

১৩,০৩৩.

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 subjects.

ক
20%
খ
30%
গ
40%
ঘ
45%

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 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%

১৩,০৩৪.

The lengths of the two sides of a triangle are 9 cm and 10 cm respectively and the angle included between them is 30°. Find the area.

ক
45 cm²
খ
22.5 cm²
গ
50 cm²
ঘ
25.5 cm²

ব্যাখ্যা

Question: The lengths of the two sides of a triangle are 9 cm and 10 cm respectively and the angle included between them is 30°. Find the area.

Solution:
Given,
the sides of triangle are a = 9 cm. and b = 10 cm. respectively.
Their included angle θ = 30°

We know,
Area of the tringle = (1/2) × ab × sinθ
= (1/2) × 9 × 10 × sin30°
= (1/2) × 9 × 10 × (1/2)
= 22.5 cm²

১৩,০৩৫.

A person crosses a 600 meters long street in 5 minutes. What is his speed in kilometers per hour?

ক
ক) 3.6
খ
খ) 7.2
গ
গ) 8.4
ঘ
ঘ) 10

ব্যাখ্যা

Speed = 600 meters / 5 minutes
= (600 × 60)/(5 × 1000) km/hr
= 7.2 km/hr

১৩,০৩৬.

Today is Wednesday. After 86 days, what day of the week will it be?

ক
Friday
খ
Tuesday
গ
Wednesday
ঘ
Thursday

ব্যাখ্যা

Question: Today is Wednesday. After 86 days, what day of the week will it be?

Solution:
Each day of the week is repeated after 7 days.

So, after (7 × 12) = 84 days, it will be Wednesday.

After 85 days, it will be Thursday
After 86 days, it will be Friday.

∴ After 86 days, it will be Friday.

১৩,০৩৭.

If x : y = 5 : 2, then (8x + 9y) : (8x + 2y) is-

ক
20 : 22
খ
29 : 20
গ
29 : 22
ঘ
29 : 33

ব্যাখ্যা

Question: If x : y = 5 : 2, then (8x + 9y) : (8x + 2y) is-

Solution:
দেয়া আছে,
x : y = 5 : 2
⇒ x/y = 5/2
⇒ 2x = 5y
⇒ 8x = 20y [4 দিয়ে গুণ করে]
∴ 8x = 20y ........ (i)

এখন, (8x + 9y) : (8x + 2y)
= (20y + 9y) : (20y + 2y)
= 29y : 22y
= 29 : 22

১৩,০৩৮.

A shopkeeper incurs a loss by selling an article for Tk 720. If he had sold it for Tk 1080, he would have made a profit which is five times the initial loss. At what price should he sell the article to make 15% profit?

ক
Tk. 875
খ
Tk. 897
গ
Tk. 905
ঘ
Tk. 920

ব্যাখ্যা

Question: A shopkeeper incurs a loss by selling an article for Tk 720. If he had sold it for Tk 1080, he would have made a profit which is five times the initial loss. At what price should he sell the article to make 15% profit?

Solution:
ধরি, পণ্যের ক্রয়মূল্য = x টাকা
720 টাকায় বিক্রি করলে ক্ষতি = x - 720 টাকা
1080 টাকায় বিক্রি করলে লাভ = 1080 - x টাকা

প্রশ্নমতে,
1080 - x = 5(x - 720)
⇒ 1080 - x = 5x - 3600
⇒ 1080 + 3600 = 5x + x
⇒ 4680 = 6x
∴ x = 780 টাকা

এখন, 15% লাভে,
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য 115 টাকা
ক্রয়মূল্য 1 টাকা হলে বিক্রয়মূল্য (115/100) টাকা
∴ ক্রয়মূল্য 780 টাকা হলে বিক্রয়মূল্য (115 × 780)/100 টাকা
= 897 টাকা

১৩,০৩৯.

Ten years ago, the sum of ages of a father and his son was 34 years. If the ratio of present ages of the father and son is 7 : 2, find the present age of the son.

ক
12 years
খ
11 years
গ
10 years
ঘ
8 years

ব্যাখ্যা

Question: Ten years ago, the sum of ages of a father and his son was 34 years. If the ratio of present ages of the father and son is 7 : 2, find the present age of the son.

Solution:
Let the present age of the father is 7x and present age of son is 2x.

As per question, ten years ago;
(7x - 10) + (2x - 10) = 34
⇒ 7x - 10 + 2x - 10= 34
⇒ 9x = 34 + 20
⇒ 9x = 54
∴ x = 6

∴ Present age of son = 2 × 6= 12 years

১৩,০৪০.

28 is divided into two parts such that 6 times the first part added to 4 times the second part makes 152. The first part is-

ক
ক) 16
খ
খ) 18
গ
গ) 20
ঘ
ঘ) 22

ব্যাখ্যা

Let, first number be a and second number be b
Here, a+b = 28
ATQ, 6a+4b=152
⇒ 6a+4(28-a) = 152
⇒ 6a + 112 - 4a = 152
⇒ 2a = 152 - 112 = 40
⇒ a = 20

১৩,০৪১.

P, Q and R are in a cycle race of 4500 meters. P cycles twice as fast as Q. R cycles 1/3 as fast as Q. R completes the race in 45 minutes. Then where was Q from the finishing line when P finished the race?

ক
2250 m
খ
300 m
গ
1500 m
ঘ
3000 m

ব্যাখ্যা

Question: P, Q and R are in a cycle race of 4500 meters. P cycles twice as fast as Q. R cycles 1/3 as fast as Q. R completes the race in 45 minutes. Then where was Q from the finishing line when P finished the race?

Solution:
Given that,
Race = 4500 m
R finishes in 45 min
∴ speed of R = 4500/45 = 100 m/min

R’s speed = (1/3) Q’s speed
∴ Q’s speed = 300 m/min

And, P’s speed = 2 × Q’s speed = 600 m/min

∴ Time for P to finish 4500 m = 4500/600 = 7.5 min
In 7.5 min, Q covers = 300 × 7.5 = 2250 m

∴ Distance left for Q = 4500 - 2250 = 2250 m

So Q was 2250 meters from the finishing line when P finished.

১৩,০৪২.

What is the sum of first 17 terms of an AP, if the 1st term is - 20 and last term is 28?

ক
62
খ
64
গ
67
ঘ
68
ঙ
69

ব্যাখ্যা

First term of AP = a = -20 and last term = l = 28
Number of terms = n = 17
Sum of AP = n/2 × (a+l)=(17/2) × (−20+28) = 17×4 = 68

১৩,০৪৩.

Find the roots of 2x² - 18x = 180.

ক
ক) (15, - 6)
খ
খ) (15, 6)
গ
গ) (- 15, - 6)
ঘ
ঘ) (- 15, 6)

ব্যাখ্যা

Question: Find the roots of 2x² - 18x = 180.

Solution:
2x²- 18x = 180
2x² - 18x - 180 = 0
2x² - 30x + 12x - 180 = 0
2x(x - 15) + 12(x - 15) = 0
(x - 15)(2x + 12) = 0

either,
x - 15 =0
x = 15

or,
2x + 12
x = - 6

১৩,০৪৪.

A person can swim at a speed of 4 km/h in still water. If the speed of the current is 2 km/h, then the time taken to swim 12 km downstream and return to the starting point is -

ক
5 hours
খ
6 hours
গ
8 hours
ঘ
10 hours

ব্যাখ্যা

Question: A person can swim at a speed of 4 km/h in still water. If the speed of the current is 2 km/h, then the time taken to swim 12 km downstream and return to the starting point is -

Solution:
Speed of the swimmer in still water = 4 km/h
Speed of the current = 2 km/h
Distance one way = 12 km

Downstream Speed = 4 + 2 = 6 km/h
Upstream Speed = 4 - 2 = 2 km/h

Time taken downstream = 12/6 = 2 hours
Time taken upstream = 12/2 = 6 hours

Total time = 6 + 2 = 8 hours

১৩,০৪৫.

A 60-liter mixture contains milk and water in the ratio 5:1. How many liters of water must be added to the mixture so that the new ratio of milk to water becomes 2:1?

ক
12 liters
খ
15 liters
গ
18 liters
ঘ
20 liters

ব্যাখ্যা

Question: A 60-liter mixture contains milk and water in the ratio 5:1. How many liters of water must be added to the mixture so that the new ratio of milk to water becomes 2:1?

Solution:
Milk in the mixture = 60 × (5/6) = 50 liters
Water in the mixture = 60 - 50 = 10 liters

Let x liters of water be added.
Then the new ratio should be 2 : 1.

So,
50/(10 + x) = 2/1
⇒ 50 = 2(10 + x)
⇒ 50 = 20 + 2x
⇒ 2x = 30
⇒ x = 15

∴ 15 liters of water should be added.

১৩,০৪৬.

How many feet are equal to 1 nautical mile?

ক
ক) 5220
খ
খ) 7080
গ
গ) 6250
ঘ
ঘ) 6076

ব্যাখ্যা

1 nautical mile = 6076.12 feet

১৩,০৪৭.

Express the angle in degree included between hands of hour and minute of the clock at 4 : 30?

ক
ক) 40°
খ
খ) 45°
গ
গ) 50°
ঘ
ঘ) 55°

ব্যাখ্যা

Question: Express the angle in degree included between hands of hour and minute of the clock at 4 : 30?

Solution:
আমরা জানি,
মধ্যবর্তী কোণ, θ = Ι(11M - 60H)/2Ι°
= Ι(11 × 30) - (60 × 4)/2Ι°
= Ι(330 - 240)/2Ι°
= 45°

১৩,০৪৮.

If (2x - 1)² = 100, then which one of the following could equal x?

ক
- 11/2
খ
11/2
গ
9/2
ঘ
13/2

ব্যাখ্যা

Question: If (2x - 1)² = 100, then which one of the following could equal x?

Solution:
(2x - 1)² = 100
⇒ 2x - 1 = √100
⇒ 2x - 1 = ± 10
Take the positive value
⇒ 2x = 11
∴ x = 11/2

Take the Negative value
⇒ 2x = - 10 + 1
∴ x = - 9/2

১৩,০৪৯.

The average monthly salary of 40 employees in a company is Tk. 9000. If three employees with monthly salaries of Tk. 12,500, Tk. 15,000, and Tk. 14,300 leave the company, what will be the new average monthly salary of the remaining employees?

ক
Tk. 6,250
খ
Tk. 7,680
গ
Tk. 8,600
ঘ
Tk. 8,750

ব্যাখ্যা

Question: The average monthly salary of 40 employees in a company is Tk. 9000. If three employees with monthly salaries of Tk. 12,500, Tk. 15,000, and Tk. 14,300 leave the company, what will be the new average monthly salary of the remaining employees?

Solution:
Here,
The average monthly salary of 40 employees = Tk. 9000
∴ Total monthly salary of 40 employees = 9000 × 40 = Tk. 3,60,000

three employees with monthly salaries of Tk. 12,500, Tk. 15,000, and Tk. 14,300 leave the company
∴ Total monthly salary of 3 employees = (12,500 + 15,000 + 14,300) = Tk. 41,800

Remaining total salary = (3,60,000 - 41,800) = Tk. 3,18,200

Remaining number of employees = (40 - 3) = 37 employees

∴ New average = 3,18,200/37
= Tk. 8,600

Therefore, the new average monthly salary of the remaining employees = Tk. 8,600

১৩,০৫০.

ক
ক) 1/2
খ
খ) 2/3
গ
গ) 4/5
ঘ
ঘ) 3/8

ব্যাখ্যা

Question:

Solution:

১৩,০৫১.

If the curved surface area of a sphere is same as the curved surface area of a hemisphere, find the radius of the hemisphere.

ক
Same as that of the sphere.
খ
√2 times that of the sphere.
গ
√3 times that of the sphere.
ঘ
2 times that of the sphere.

ব্যাখ্যা

Question: If the curved surface area of a sphere is same as the curved surface area of a hemisphere, find the radius of the hemisphere.

Solution:
Let,
R as the radius of the sphere.
r as the radius of the hemisphere.

Curved surface area of a sphere = Curved surface area of a hemisphere
4πR² = 2πr²
⇒ 2R² = r²
⇒ r = √2R

∴ The radius of the hemisphere = √2 times that of the sphere.

১৩,০৫২.

If a man sells a chair for Tk. 600 and he would loss 20%, then at what price should he sell it to gain 20%?

ক
Tk. 800
খ
Tk. 850
গ
Tk. 1050
ঘ
Tk. 900

ব্যাখ্যা

Question: If a man sells a chair for Tk. 600 and he would loss 20%, then at what price should he sell it to gain 20%?

Solution:
Let
the cost price of the chair be x.

Selling price = x - 20% of x
⇒ 600 = x - (20x/100)
⇒ 600 = x - (x/5)
⇒ 600 = 4x/5
⇒ 4x = 3000
∴ x = 750

To gain 20%, the selling price should be = 750 + 20% of 750
= 750 + {(20/100) of 750}
= 750 + 150
= Tk. 900

১৩,০৫৩.

How many integers from 1 to 1000 are divisible by 16 but not by 30?

ক
50
খ
56
গ
58
ঘ
62

ব্যাখ্যা

প্রশ্ন: How many integers from 1 to 1000 are divisible by 16 but not by 30?

সমাধান:
৩০ ও ১৬ এর ল.সা.গু = ২৪০

১০০০ ÷ ২৪০ = ভাগফল ৪, ভাগশেষ ৪০
৩০ ও ১৬ উভয় সংখ্যা দ্বারা ১ থেকে ১০০০ এর মধ্যে বিভাজ্য পূর্ণসংখ্যা ৪টি

১০০০ ÷ ১৬ = ভাগফল ৬২, ভাগশেষ ৮
১৬ দ্বারা ১ থেকে ১০০০ এর মধ্যে বিভাজ্য পূর্ণসংখ্যা ৬২টি

১ থেকে ১০০০ এর মধ্যে ১৬ দ্বারা বিভাজ্য কিন্তু ৩০ দ্বারা বিভাজ্য নয় এমন সংখ্যা ৬২ - ৪ টি
= ৫৮টি

১৩,০৫৪.

A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Tk. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

ক
Tk. 400
খ
Tk. 500
গ
Tk. 600
ঘ
Tk. 800

ব্যাখ্যা

Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Tk. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

Solution:
C's 1 day's work = 1/3 - (1/6 + 1/8)
= (1/3) - (7/24)
= 1/24

A's wages: B's wages: C's wages = 1/6 : 1/8 : 1/24
= 4 : 3 : 1.

C's share (for 3 days) = Tk. 3 × 1/24 × 3200 = Tk. 400.

১৩,০৫৫.

Find the average of all the numbers between 10 and 50 which are divisible by 4.

ক
27
খ
30
গ
34
ঘ
32

ব্যাখ্যা

Question: Find the average of all the numbers between 10 and 50 which are divisible by 4.

Solution:
Numbers between 10 and 50 divisible by 4 are = 12, 16, 20, 24, 28, 32, 36, 40, 44, 48.

Required average = (12 + 16 + 20 + 24 + 28 + 32 + 36 + 40 + 44 + 48)/10
= 300/10
= 30

১৩,০৫৬.

The average age of Arif, Tania, Joya, and Rafi is 22 years. The average age of Arif, Tania, and Joya is 20 years and the average age of Tania, Joya, and Rafi is 24 years. Find the average age of Tania and Joya.

ক
20 years
খ
22 years
গ
25 years
ঘ
23.5 years

ব্যাখ্যা

Question: The average age of Arif, Tania, Joya, and Rafi is 22 years. The average age of Arif, Tania, and Joya is 20 years and the average age of Tania, Joya, and Rafi is 24 years. Find the average age of Tania and Joya.

Solution:
Given,
Arif + Tania + Joya + Rafi = 22 × 4 = 88 years ……(1)
Arif + Tania + Joya = 20 × 3 = 60 years ……(2)
Tania + Joya + Rafi = 24 × 3 = 72 years ……(3)

From (1) - (2)⇒
Rafi’s age = 88 − 60 = 28 years

From (3)⇒
Tania + Joya = 72 - 28 = 44 years

∴ Average age of Tania and Joya = 44/2 = 22 years

১৩,০৫৭.

Aisha is five times as old as Rohan. 8 years ago, Aisha was thirteen times as old as Rohan. What will be the sum of their ages after 4 years?

ক
72
খ
80
গ
88
ঘ
64

ব্যাখ্যা

Question: Aisha is five times as old as Rohan. 8 years ago, Aisha was thirteen times as old as Rohan. What will be the sum of their ages after 4 years?

Solution:
Let,
The present age of Rohan is x years.
∴ The present age of Aisha is 5x years.

ATC,
5x - 8 = 13(x - 8)
⇒ 5x - 8 = 13x - 104
⇒ - 8x = - 96
⇒ x = 12

So, Rohan's current age = 12 years.
Aisha's current age = 5 × 12 = 60 years.

Rohan's age after 4 years = 12 + 4 = 16 years
Aisha's age after 4 years = 60 + 4 = 64 years

∴ Sum of their ages After 4 years = 16 + 64 = 80 years.

১৩,০৫৮.

What is the slope of the line: 5x - 3y + 2 = 0?

ক
2/3
খ
5
গ
- 5
ঘ
5/3

ব্যাখ্যা

5x - 3y + 2 = 0
or, 5x + 2 = 3y
or, y = (5x + 2)/3
or, y = 5x/3 + 2/3
The coefficient of x is 5/3

∴ Required slope of the given line = 5/3

১৩,০৫৯.

How many degrees are between the hands of a clock at 10:05?

ক
92.5°
খ
82.5°
গ
72.5°
ঘ
87.5°

ব্যাখ্যা

Required degrees = । (11M - 60H)/2 ।°
= । (11 × 5 - 60 × 10)/2 ।°
= । - 545/2 ।°
= । - 272.5 ।°
= 272.5°
Now, 360° - 272.5° = 87.5°

১৩,০৬০.

Jamil can run 1 km in 4 minutes. He has a car that has a top speed of 75 km/hour. Jamil's speed is what percentage of his car's top speed?

ক
ক) 10%
খ
খ) 20%
গ
গ) 25%
ঘ
ঘ) 30%

ব্যাখ্যা

Question: Jamil can run 1 km in 4 minutes. He has a car that has a top speed of 75 km/hour. Jamil's speed is what percentage of his car's top speed?

Solution:
4 মিনিট= 4/60 ঘণ্টা
= 1/15 ঘণ্টা

জামিলের গতিবেগ = 1/(1/15) কি.মি./ঘণ্টা
= 15 কি.মি./ঘণ্টা

গাড়ির গতিবেগ = 75 কি.মি./ঘণ্টা

জামিলের গতিবেগ তার গাড়ির গতিবেগের = {(15/75) × 100}%
= 20%

১৩,০৬১.

With an average speed of 50 km/hr, a train reaches its destination in time. If it goes with an average speed of 40 km/hr, it is late by 24 min. The total journey is:

ক
60 km
খ
75 km
গ
80 km
ঘ
85 km

ব্যাখ্যা

Question: With an average speed of 50 km/hr, a train reaches its destination in time. If it goes with an average speed of 40 km/hr, it is late by 24 min. The total journey is:

Solution:
Difference between timings = 24 min = 24/60 hr = 2/5 hr.
Let the length of the journey be x km.

Then,
(x/40) - (x/50) = 2/5
Or, (5x - 4x)/200 = 2/5
Or, x/200 = 2/5
Or, x = (25 × 200)
∴ x = 80 km.

∴ The total journey is 80 km.

১৩,০৬২.

What is the average of the first five multiples of 12?

ক
24
খ
32
গ
36
ঘ
48

ব্যাখ্যা

Average = 12 × (1 + 2 + 3 + 4 + 5) × (1/2)
= 12 × 15 × (1/2)
= 12 × 3
= 36.

∴ The first five multiples of 12 is 36.

১৩,০৬৩.

If the ratio of two numbers is 3 : 4, and their Least Common Multiple (LCM) is 180, what are the two numbers?

ক
18, 24
খ
27, 36
গ
45, 60
ঘ
36, 48

ব্যাখ্যা

Question: If the ratio of two numbers is 3 : 4, and their Least Common Multiple (LCM) is 180, what are the two numbers?

Solution:
ধরি,
সংখ্যা দুটি = 3x এবং 4x
∴ সংখ্যা দুটির লসাগু (LCM) = 12x

প্রশ্নমতে,
12x = 180
⇒ x = 180/12
∴ x = 15

∴ সংখ্যা দুটি = 3 × 15 = 45 এবং 4 × 15 = 60

১৩,০৬৪.

What is the value of a, if 3x² + ax + a + 3 divisible by x + 2?

ক
ক) 15
খ
খ) - 15
গ
গ) - 9
ঘ
ঘ) 9

ব্যাখ্যা

ধরি, f(x) = 3x² + ax + a +3
যেহেতু, x + 2 দ্বারা বিভাজ্য সেহেতু,
f(-2) = 0 হবে
⇒ 3(-2)² + a(-2) + a + 3 = 0
⇒ 12 - 2a + a + 3 = 0
⇒ - a + 15 = 0
⇒ a = 15

১৩,০৬৫.

A train 200 m long passed a pole in 20 seconds. How long will it take to pass a platform 610 m long?

ক
64 sec
খ
81 sec
গ
73 sec
ঘ
89 sec

ব্যাখ্যা

Question: A train 200 m long passed a pole in 20 seconds. How long will it take to pass a platform 610 m long?

Solution:
Speed = 200/20 = 10 m/s
∴ Required time = (200 + 610)/10
= 81 sec

১৩,০৬৬.

The sum of the present ages of a mother and daughter is 50 years. Five years ago, the mother was seven times as old as the daughter. How much older is the mother than the daughter?

ক
28
খ
40
গ
30
ঘ
50

ব্যাখ্যা

Question: The sum of the present ages of a mother and daughter is 50 years. Five years ago, the mother was seven times as old as the daughter. How much older is the mother than the daughter?

Solution:
Let mother’s age = M, daughter’s age = D.
Given:
⟹ M+D=50 --------------------------(1)
Five years ago:
⟹ M−5=7(D−5)
⟹ M−5=7D−35
⟹ M=7D−30 ---------------------(2)

Substitute Equation 2 into Equation 1:
(7D−30)+D=50
⟹ 8D=80
⟹ D=10 (Daughter's age)

Then,
M=50−10=40. (Mother's age)
Age difference: 40−10=30
Answer: 30

১৩,০৬৭.

From a pack of 52 cards, two cards are drawn at random. What is the probability of getting two queens?

ক
1/21
খ
5/221
গ
1/221
ঘ
1/52

ব্যাখ্যা

Question: From a pack of 52 cards, two cards are drawn at random. What is the probability of getting two queens?

Solution:
Total queen 4
Total possibilities = ⁵²C₂
getting two queens = ⁴C₂

∴ probability = ⁴C₂/⁵²C₂
= 6/1326
= 1/221

১৩,০৬৮.

A table fan is quoted for Tk. 1500. Saadman pays Tk. 1173 for it. If he gets a series of two discounts and the rate of the first discount is 15%, then the rate of the second discount is?

ক
4%
খ
6.67%
গ
8%
ঘ
12%

ব্যাখ্যা

Question: A table fan is quoted for Tk. 1500. Saadman pays Tk. 1173 for it. If he gets a series of two discounts and the rate of the first discount is 15%, then the rate of the second discount is?

Solution:
After first discount = 1500 - 1500 × 15%
= 1500 - 1500 × 15/100
= 1500 -225
= 1275 taka

let second discount is x%

1275 - 1275 × x/100 = 1173
⇒ 1275x/100 = 1275 - 1173 = 102
⇒ x = 102 × 100/1275
= 8

১৩,০৬৯.

If sin A + sin²A = 1, then the value of the expression (cos²A + cos⁴A) is –

ক
ক) 1
খ
খ) 1/2
গ
গ) 2
ঘ
ঘ) 3

ব্যাখ্যা

Given, sin A + sin²A = 1
⇒ sinA = 1 - sin²A
⇒ sinA = cos²A
⇒ sin²A = cos⁴A
⇒ 1 - cos²A = cos⁴A
∴ cos²A + cos⁴A = 1

১৩,০৭০.

If cosA sinA = 1,then (cosA + sinA)² =?

ক
1
খ
2
গ
3
ঘ
4

ব্যাখ্যা

Question: If cosA sinA = 1,then (cosA + sinA)² =?

Solution:
(cosA + sinA)²
= cos²A + 2 cosA sinA + sin²A
= 1 + 2.1 [sin²A + cos²A = 1]
= 1 + 2
= 3

১৩,০৭১.

There are 6 orange, 2 pink, 4 yellow and 3 green towels in a carton. What is the probability of picking up 2 orange towels randomly.

ক
ক) 1/7
খ
খ) 2/15
গ
গ) 2/7
ঘ
ঘ) 6/15

ব্যাখ্যা

We know,
Probability = what we want/Total
Or = add; AND = multiply

We want 2 orange towels
That means to choose one AND then choose other from the remaining towels
There are 6 orange towels
Total 15 towels

So probability for two orange towels = 6/15 × 5/14
= 1/7 [Here we reduce the denominator i.e. the total number of towels because once we remove a towel from the box we do not put it back in the box.
So while removing the 2^nd towel, there are only 15 - 1 = 14 towels in the box.]

১৩,০৭২.

In a class of 35 students, Rajib is placed seventh from the bottom whereas Karim is placed ninth from the top. Dipa is placed exactly in between the two. What is the difference in the positions of Rajib and Dipa?

ক
9
খ
10
গ
11
ঘ
13

ব্যাখ্যা

Question: In a class of 35 students, Rajib is placed seventh from the bottom whereas Karim is placed ninth from the top. Dipa is placed exactly in between the two. What is the difference in the positions of Rajib and Dipa?

Solution:
Total students = 35
Rajib is 7th from bottom, Karim is 9th from top and Dipa is exactly between Karim and Rajib

We know,
n position from bottom = (Total + 1 - n) position from top

Rajib's position = 7th from bottom = (35 + 1 - 7)th from top = 29th from top
Karim's position = 9th from top

Dipa is placed exactly in between Rajan and Karan.
Total students between Karim and Rajib = 35 - (9 + 7) = 35 - 16 = 19
Thus, Dipa's position from Karim = (19 + 1)/2 = 20/2 = 10
Dipa's position from top = 9 + 10 = 19,

Hence, differences in the positions of Rajib and Dipa = 29 - 19 = 10 i.e total 10 seats.

১৩,০৭৩.

A pipe can fill a tank in 6 hours and another pipe can empty the tank in 12 hours. If both the pipes are opened at the same time,the tank can be filled in-

ক
10 hours
খ
12 hours
গ
14 hours
ঘ
16 hours

ব্যাখ্যা

Question: A pipe can fill a tank in 6 hours and another pipe can empty the tank in 12 hours. If both the pipes are opened at the same time,the tank can be filled in-

Solution:
1st pipe can fill in 1 hour 1/6 of the tank
2nd pipe can empty in 1 hour 1/12 of the tank

∴ Both pipe can fill in 1 hour (1/6 - 1/12) of the tank
= (2 - 1)/12 of the tank
= 1/12 of the tank

∴ the tank can be filled in 12 hours

১৩,০৭৪.

If (x - 2) is a factor of - 6x³ - 5x + g, then the value of g is -

ক
45
খ
48
গ
52
ঘ
58

ব্যাখ্যা

x - 2 = 0
⇒ x = 2
The function, f(x) = - 6x³ - 5x + g
⇒ f(2) = - 6 × 2³ - 5 × 2 + g
⇒ f(2) = - 48 - 10 + g
⇒ f(2) = - 58 + g
(x - 2) is a factor of - 6x³ - 5x + g, so f(2) = 0
Therefore, - 58 + g = 0
⇒ g = 58

১৩,০৭৫.

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

ক
Tk. 6800
খ
Tk. 5800
গ
Tk. 800
ঘ
Tk. 680

ব্যাখ্যা

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

Answer:
Given,
Cost Price (CP) = 8000 Taka
Loss = 1200 Taka
Using Formula
Selling Price (SP) = Cost Price - Loss
⇒ Selling Price (SP) = Tk. 8000 - Tk. 1200
⇒ Selling Price (SP) = Tk. 6800

Therefore, the selling price of the bicycle is Tk. 6800.

১৩,০৭৬.

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%

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%

১৩,০৭৭.

If a/3 = b/4 = c/7, the value of (a + b + c)/c is-

ক
ক) 7
খ
খ) 1/7
গ
গ) 1/2
ঘ
ঘ) 2

ব্যাখ্যা

Question: If a/3 = b/4 = c/7, the value of (a + b + c)/c is-

Solution:
Let
a/3 = b/4 = c/7 = x
a = 3x, b = 4x, c = 7x.

Now
(a + b + c)/c = (3x + 4x + 7x)/7x
= 14x/7x
= 2

১৩,০৭৮.

If A = x% of y and B = y% of x, then which of the following is true?

ক
A is smaller than B
খ
If x is smaller than y, then A is greater than B.
গ
A is greater than B
ঘ
None of these

ব্যাখ্যা

Question: If A = x% of y and B = y% of x, then which of the following is true?

Solution:
Given that,
A = x% of y
= (x/100) × y
= (xy)/100

And,
B = y% of x
= (y/100) × x
= (yx)/100
= (xy)/100

So, A = (xy)/100 and B = (xy)/100
⇒ A = B

১৩,০৭৯.

Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:

ক
15
খ
29
গ
36
ঘ
12
ঙ
None of the above

ব্যাখ্যা

Question: Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:

Solution:
Let the three odd integers be x, x + 2 and x + 4.

Then,
3x = 2(x + 4) + 3
⇒ 3x = 2x + 8 + 3
∴ x = 11

Third integer = x + 4 = 11 + 4 = 15

১৩,০৮০.

In a 500-meter race, B starts 50 meters ahead of A, yet A defeats B by a margin of 25 meters. What distance did B cover when A reached the finish line?

ক
400 meters
খ
425 meters
গ
450 meters
ঘ
475 meters

ব্যাখ্যা

Question: In a 500-meter race, B starts 50 meters ahead of A, yet A defeats B by a margin of 25 meters. What distance did B cover when A reached the finish line?

Solution:
500 মিটার রেসে B 50 মিটার এগিয়ে থেকে দৌড় শুরু করায় B কে দূরত্ব অতিক্রম করতে হবে = (500 - 50) মিটার = 450 মিটার
A এর অতিক্রান্ত দূরত্ব = 500 মিটার

কিন্তু A, B-কে 25 মিটার দূরত্বে পরাজিত করে।
∴ A যখন শেষপ্রান্ত স্পর্শ করে তখন B এর অতিক্রান্ত দূরত্ব = (450 - 25) মিটার = 425 মিটার

১৩,০৮১.

ক
0.9
খ
0.3
গ
0.03
ঘ
0.008

ব্যাখ্যা

Question:

Solution:

১৩,০৮২.

P and Q can complete a work in 15 days and 10 days respectively. They started the work together and then Q left after 2 days. P alone completed the remaining work. The work was finished in --- days.

ক
ক) 16 days
খ
খ) 24 days
গ
গ) 20 days
ঘ
ঘ) 12 days

ব্যাখ্যা

Work done by P in 1 day = 1/15
Work done by Q in 1 day = 1/10

Work done by P and Q in 1 day = 1/15 + 1/10 = 1/6
Work done by P and Q in 2 days = 2 × (1/6) = 1/3

Remaining work = 1 - 1/3 = 2/3

Time taken by P to complete the remaining work 2/3 = (2/3) / (1/15) = 10 days

Total time taken = 2 + 10 = 12 days.

১৩,০৮৩.

A clock seen through a mirror, shows quarter past five. What is the correct time shown by the clock?

ক
5 : 45
খ
7 : 25
গ
4 : 25
ঘ
None of these

ব্যাখ্যা

Question: A clock seen through a mirror, shows quarter past five. What is the correct time shown by the clock?

Solution:
Quarter past five = 5 : 15

আমরা জানি,
প্রকৃত সময় = 11 : 60 - আয়নার দেখা সময়
= 11 : 60 - 5 : 15
= 6 : 45

১৩,০৮৪.

A number is multiplied by 5 and then 7 is added. The result is 52. What is the number?

ক
7
খ
13
গ
6
ঘ
9

ব্যাখ্যা

Question: A number is multiplied by 5 and then 7 is added. The result is 52. What is the number?

Solution:
Let the number be = x

According to the question,
5x + 7 = 52
⇒ 5x = 52 - 7
⇒ 5x = 45
⇒ x = 45/5
⇒ x = 9

১৩,০৮৫.

The number of students in 3 classes is in the ratio 2 : 3 : 4. If 12 students are increased in each class this ratio changes to 8 : 11 : 14. The total number of students in the three classes in the beginning was?

ক
162
খ
148
গ
208
ঘ
320
ঙ
410

ব্যাখ্যা

Question: The number of students in 3 classes is in the ratio 2 : 3 : 4. If 12 students are increased in each class this ratio changes to 8 : 11 : 14. The total number of students in the three classes in the beginning was-

Solution:
Let the number of students in the classes be 2x, 3x and 4x respectively;
∴ Total students = 2x + 3x + 4x = 9x

ATQ,
⇒ (2x + 12)/(3x + 12) = 8/11
⇒ 24x + 96 = 22x + 132
⇒ 24x - 22x = 132 - 96
⇒ 2x = 36
∴ x = 18

Hence, Original number of students,
9x = 9 × 18 = 162

১৩,০৮৬.

1740 is divided among A, B, and C such that 0.5 of A = 0.6 of B = 0.75 of C. Then C will get

ক
348 tk
খ
464 tk
গ
528 tk
ঘ
696 tk

ব্যাখ্যা

Question: 1740 is divided among A, B, and C such that 0.5 of A = 0.6 of B = 0.75 of C. Then C will get

Solution:
A × 0.5 = B × 0.6 = C × 0.75
⇒ (A × 5)/10 = (B × 6)/10 = (C × 75)/100
⇒ A/2 = B/(5/3) = C/(4/3)
⇒ A : B : C = 2 : (5/3) : (4/3)
⇒ A : B : C = 6 : 5 : 4

∴ C’s share = (4/15) × 1740 = 464 tk

১৩,০৮৭.

An outgoing pipe pours water at 10 liters per hour. A cistern of capacity 200 liters was 4/5th full. How much time will the outgoing pipe take to empty the cistern?

ক
12 hours
খ
14 hours
গ
24 hours
ঘ
16 hours

ব্যাখ্যা

Question: An outgoing pipe pours water at 10 liters per hour. A cistern of capacity 200 liters was 4/5th full. How much time will the outgoing pipe take to empty the cistern?

Solution:
total water = 4/5th of 200 liters
= 160 liters.

time = 160/10 = 16 hours

১৩,০৮৮.

Find the value of cosec(π/3)

ক
√3
খ
2/√3
গ
1
ঘ
√3/2

ব্যাখ্যা

Question: Find the value of cosec(π/3)

Solution:
cosec(π/3)
= cosec(π/3)
= 1/sin(π/3)
= 1/sin60°
= 1/(√3/2)
= 2/√3

১৩,০৮৯.

What will come at the place of question mark? 6, 11, 21, 36, 56, ?

ক
76
খ
81
গ
86
ঘ
91

ব্যাখ্যা

Question: What will come at the place of question mark?
6, 11, 21, 36, 56, ?

Solution:
11 - 6 = 5
21 - 11 = 10
36 - 21 = 15
56 - 36 = 20

প্রতিবার পার্থক্য 5 করে বৃদ্ধি পাচ্ছে।

∴ পরবর্তী পার্থক্য হবে = 20 + 5 = 25

∴ পরবর্তী সংখ্যা = 56 + 25 = 81

Shortcut: 6 (+5)→ 11 (+10)→ 21 (+15)→ 36 (+20)→ 56 (+25) → 81.

১৩,০৯০.

A and B working together can finish a work in 12 days, B and C working together can finish the work in 16 days. If A works for 5 days, B works for 7 days, and C completes the remaining work in 13 days, C alone can complete the work in how many days?

ক
22 days
খ
24 days
গ
26 days
ঘ
28 days

ব্যাখ্যা

Question: A and B working together can finish a work in 12 days, B and C working together can finish the work in 16 days. If A works for 5 days, B works for 7 days, and C completes the remaining work in 13 days, C alone can complete the work in how many days?

Solution:
ATQ,
A+B = 12 days
B+C = 16 days

Note: Assume the total work = LCM of the given days
Take the LCM of days = LCM of (12 and 16) = 48
Let the total work = 48

Note: One day work = (total work/ days)
Now,
(A+B)'s one day work = 48/12 = 4 unit
(B+C)'s one day work = 48/16 = 3 unit

As per the question:
A works for 5 days
B works for 7 days or (5 + 2) days, that means B works 5 days with A and remaining 2 days with C.
C works 13 days or (2 + 11) days, that means C works 2 days with B and remaining 11 days alone.

That means total work done by (A + B) in 5 days
A + B = 5 days × 4 unit = 20 units
And, total work done by (B + C) = 2 days × 3 unit = 6 units
So, A + B + C finish the 26 units of work.

Remaining work = 48 - 26 = 22 unit work
And C completes the remaining work in 11 days.
i.e., C's one day's works = 22/11 = 2 units.

C alone can finish total work in [total work/ C's one day work] = [48/2] = 24 days.

১৩,০৯১.

The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is-

ক
28
খ
32
গ
40
ঘ
64

ব্যাখ্যা

Question: The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is-

Solution:
Let the numbers be 2x and 3x.
Then, their L.C.M. = 6x.
So,
6x = 48
∴ x = 8.

The numbers are 16 and 24.

Hence, required sum = (16 + 24) = 40.

১৩,০৯২.

A man and a boy recieved Tk. 600 as wages for 6 days for the work they did together. The man's efficiency in the work was three times that of the boy. What is the daily wages of the boy?

ক
ক) Tk. 20
খ
খ) Tk. 25
গ
গ) Tk. 30
ঘ
ঘ) Tk. 35

ব্যাখ্যা

Question: A man and a boy recieved Tk. 600 as wages for 6 days for the work they did together. The man's efficiency in the work was three times that of the boy. What is the daily wages of the boy?

Solution:
Ratio of 1 day's work of man and boy = 3 : 1
Total wages of the boy = 600 × ( 1/4) = 150
Daily wages of the boy = 150/6 = Tk. 25

১৩,০৯৩.

By selling a bicycle for Tk. 2,850 a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be

ক
Tk. 2,500
খ
Tk. 2,600
গ
Tk. 2,700
ঘ
Tk. 2,900

ব্যাখ্যা

Question: By selling a bicycle for Tk. 2,850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be

Solution:
Let Cost Price was x
ATQ,
x + 14% of x = 2850
⇒ x + 14x/100 = 2850
⇒ x + 0.14x = 2850
⇒ 1.14x = 2850
⇒ x = 2850/1.14
∴ x = 2500

So, Cost Price = 2500
Now, Selling Price When profit remains at 8%,
= 2500 + 8% of 2500
= 2500 + 200
= Tk. 2700

১৩,০৯৪.

ক
30°
খ
60°
গ
45°
ঘ
90°

ব্যাখ্যা

Question:

Solution:

১৩,০৯৫.

If xy(x + y) = 1 then = ?

ক
ক) 1
খ
খ) 3
গ
গ) - 3
ঘ
ঘ) - 5

ব্যাখ্যা

Question: If xy(x + y) = 1 then = ?

Solution:
Given,
xy(x + y) = 1
⇒ x + y = 1/xy

Now,
x³+ y³ - 1/x³y³
= x³ + y³ - (x + y)³
= x³ + y³ - {x³ + y³ + 3xy (x + y)}
= x³ + y³ - x³ - y³ - 3xy (x + y)
= - 3 . 1
= - 3

১৩,০৯৬.

If Rahim walks at 14 km/hr instead of 10 km/hr for a certain time, he would have walked 30 km more. if Rahim walks at a speed of 10 km/hr, the distance travelled by him within that time is-

ক
66 km
খ
72 km
গ
75 km
ঘ
84 km

ব্যাখ্যা

Question: If Rahim walks at 14 km/hr instead of 10 km/hr for a certain time, he would have walked 30 km more. if Rahim walks at a speed of 10 km/hr, the distance travelled by him within that time is-

Solution:
Let,
the actual distance travelled be = a km.

Then,
a/10 = (a + 30)/14
⇒ 14a = 10a + 300
⇒ 14a - 10a = 300
⇒ 4a = 300
⇒ a = 300/4
∴ a = 75 km

১৩,০৯৭.

A boat's speed with the current is 17 km/hr and the speed of the current is 3.5 km/hr. What is the boat's speed against the current?

ক
12 km/hr
খ
10 km/hr
গ
13.5 km/hr
ঘ
14.5 km/hr

ব্যাখ্যা

Question: A boat's speed with the current is 17 km/hr and the speed of the current is 3.5 km/hr. What is the boat's speed against the current?

Solution:
নৌকার স্রোতের সাথে গতিবেগ = 17 কিমি/ঘন্টা
স্রোতের গতিবেগ = 3.5 কিমি/ঘন্টা

স্থির পানিতে নৌকার গতিবেগ = স্রোতের সাথে গতিবেগ - স্রোতের গতিবেগ
= (17 - 3.5) কিমি/ঘন্টা
= 13.5 কিমি/ঘন্টা

স্রোতের বিপরীতে নৌকার গতিবেগ = স্থির পানিতে গতিবেগ - স্রোতের গতিবেগ
= (13.5 - 3.5) কিমি/ঘন্টা
= 10 কিমি/ঘন্টা

সুতরাং, স্রোতের বিপরীতে নৌকার গতিবেগ 10 কিমি/ঘন্টা।

১৩,০৯৮.

A high-speed train running at 102 km/hr passes a person walking in the opposite direction at 6 km/hr. If the train takes 8 seconds to pass the person, what is the length of the train (in meter)?

ক
180 m
খ
220 m
গ
240 m
ঘ
260 m

ব্যাখ্যা

Question: A high-speed train running at 102 km/hr passes a person walking in the opposite direction at 6 km/hr. If the train takes 8 seconds to pass the person, what is the length of the train (in meter)?

Solution:
ধরি,
ট্রেনের দৈর্ঘ্য = x মিটার
ট্রেনের গতিবেগ = 102 km/hr
মানুষের গতিবেগ = 6 km/hr

যেহেতু তারা বিপরীত দিক থেকে আসছে, তাই আপেক্ষিক গতিবেগ = (102 + 6) km/hr
= 108 km/hr
= 108 × (5/18) = 30 m/s

আমরা জানি, অতিক্রান্ত দূরত্ব (ট্রেনের দৈর্ঘ্য) = আপেক্ষিক গতিবেগ × সময়

প্রশ্নমতে,
x = 30 × 8
∴ x = 240

সুতরাং, ট্রেনটির দৈর্ঘ্য 240 মিটার।

১৩,০৯৯.

Solve for x: log₃(x - 1) = 3

ক
20
খ
25
গ
28
ঘ
12

ব্যাখ্যা

Question: Solve for x: log₃(x - 1) = 3

Solution:
Given that,
log₃ (x - 1) = 3
⇒ x - 1 = 3³
⇒ x - 1 = 27
⇒ x = 27 + 1
∴ x = 28

১৩,১০০.

The average age of three boys is 15 years. If their ages are in ratio 3 : 5 : 7, the age of the youngest boy is:

ক
12 years
খ
10 years
গ
9 years
ঘ
8 years

ব্যাখ্যা

Question: The average age of three boys is 15 years. If their ages are in ratio 3 : 5 : 7, the age of the youngest boy is:

Solution:

The sum of the ages of three boys = 45 years

Now, (3x + 5x + 7x) = 45

⇒ 15x = 45

⇒ x = 3

So, the age of the youngest boy = 3x

= (3 × 3) years

= 9 years