Bank Math

A's 5 days work = 50%
B's 5 days work = 33.33%
C's 2 days work = 16.66% [100 - (50 + 33.33)]

Ratio of contribution of work of A, B and C = 50: 33(1/3) : 16(2/3)
= 3 : 2 : 1

A's total share = Tk. 1500
B's total share = Tk. 1000
C's total share = Tk. 500

A's one day's earning = Tk.300
B's one day's earning = Tk.200
C's one day's earning = Tk.250

Question: A sum of money at simple interest doubles in 10 years. In how many years, at the same rate, will it be tripled?

Solution:
Given that,
Principal = P
Simple interest doubles the money in 10 years
 ∴ SI = P in 10 years.

We know,
SI = Prn/100
⇒ P = Prn/100
⇒ r × 10 = 100
⇒ r = 100/10
∴ r = 10% per annum 

Again,
To triple, total amount = 3P,  SI = 2P
2P = (P × 10 × n)/100
⇒ 2 = n/10
∴ n = 20

∴ Time taken to triple the amount is 20 years.

Question: A wire can be bent in the form of a circle of radius 21 cm. If it is bent in the form of a square, then its area will be -

Solution:
Given,
radius of the circle r = 21 cm

Circumference of the circle = 2πr 
 = 2 × (22/7) × 21 
= 2 × 22 × 3
= 132 cm 

The length of one side of the square = 132/4 = 33 cm

Area of the ​​square = (33)² cm²
= 1089 cm²

Question: If n(A) = 39, n(B) = 23 and n(A ∩ B) = 19, then n(A ∪ B) = ?

Solution:
We know that,
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
= 39 + 23 - 19
= 62 - 19
= 43

There are total 7 digits given - 2, 3, 4, 5, 6, 8 and 0
Between 500 and 1000 means from 501 to 999.

All of them are 3 digit numbers.
First digit - 5, 6 or 8 i.e. 3 possibilities (1 digit gets used here)
Second digit - Any one from 7-1 = 6 remaining digits i.e. 6 possibilities
Third digit - Any one from 6-1 = 5 remaining digits i.e. 5 possibilities

∴ Total numbers possible = 3 x 6 x 5 = 90.

Given, cosθ + sinθ = 1
Or, (cosθ + sin)² = 1² 
Or, cos²θ + sin²θ + 2cosθsinθ = 1
Or, 2cosθsinθ = 0 [As, cos²θ + sin²θ = 1]
Or, cosθsinθ = 0

So, either cosθ = 0 = cos90° or, sinθ = 0 = sin0°
⇒ θ = 90° or, 0°

Question: Play : Actor :: Concert : ?

Solution:
সঠিক উত্তর: খ) Musician

- Play (নাটক) এর মূল ব্যক্তি বা পারফর্মার হলো Actor (যে অভিনয় করে)
- ঠিক একইভাবে Concert (সঙ্গীতানুষ্ঠান) এর মূল ব্যক্তি বা পারফর্মার হলো Musician (যে সঙ্গীত পরিবেশন করে)

অতএব, Play : Actor :: Concert : Musician

• Noun যদি subject হিসেবে ব্যবহার করা হয় tag question করার নিয়ম:
- কখনো কখনো common noun ব্যবহার করে abstract noun বুঝানো হয়।
- The morning এখানে abstarct noun হিসেবে ব্যবহার করা হয়েছে।
- তাই The Morning এর অর্থ ধরে এর পরিবর্তে it- pronoun বসাতে হবে।
- Statement টি positive হলে tag question টি negative হবে।

• Complete Sentence: The morning greets us with fresh air, doesn't it?

Source: A Passage to the English Language S. M. Zakir Hussain, Live MCQ English Wizard.

Question: Find the difference of amount if 40% discount is given on Tk. 1000 and two consecutive discounts 30% and 10% are given on the same amount.

Solution:
40% discount on 1000 = 1000 × 40% = 400
 
Two consecutive discounts on 1000.
30% discount on 1000 = 30% of 1000
= 300

After 30% discount on 1000 = 1000 - 300
= 700

Again,
After 10% discount on 700 = 10% of 700
= 70

Total discount = 300 + 70
= Tk. 370
So, the difference = 400 - 370
= Tk. 30

Let original CP = Rs. 100
Then, the Marked Price = 40% of 100 + 100 = 140
SP = 140 - 25% of 140 = 105
%Profit = (5×100)/100 = 5%

Net Graphic Change Method:
100 == 40% UP ⇒ 140 == 25% discount ⇒ 105 So, % Profit = 5%

Question: Two pipes can fill a tank with water in 15 and 12 hours respectively and a third pipe can empty it in 4 hours. If the three pipes be opened, the tank will be emptied in-

Solution:
Part of the tank filled by two pipes in 1 hour = 1/15 + 1/12
= (4 + 5)/60 part
= 9/60 part
= 3/20
Part of the tank emptied by the third pipe in 1 hour = 1/4

∴ Net part of the tank emptied in 1 hour = (1/4 - 3/20) part
= (5 - 3)/20 part
= 2/20 part
= 1/10 part

1/10 Part of tank can be emptied in 1 hour
∴ The whole tank will be emptied in = 10 hours

Question: The ratio between the perimeter and the length of a rectangle is 3 : 1. If the area of the rectangle is 50 sq. cm, what is the breadth of the rectangle?

Solution:
Let the length and breadth be x and y respectively

So, 2(x + y) : x = 3 : 1
⇒ (2x + 2y)/x = 3/1
⇒ 2x + 2y = 3x
⇒ 2y = 3x - 2x
⇒ 2y = x
∴ x = 2y

Then,
Area = 50
⇒ x × y = 50
⇒ 2y × y = 50
⇒ 2y² = 50
⇒ y² = 25 = 5²
∴ y = 5

So the breadth of the rectangle is 5 cm.

By investing Tk. 1500, the man obtained an income of Tk. 130.
So, by investing Tk. 95, the income will be = (130/1500) × 96
= Tk 8.32
So, the divided = 8.32%

Question: If 20% of A = 30% of B, and B = 400, find A.

Solution:
the equation;
20% of A = 30% of B
⇒ (20/100) × A = (30/100) × B
⇒ 0.2A = 0.3 × 400 [Substitute B = 400]
⇒ 0.2A = 120
⇒ A = 120/0.2
⇒ A = 600

∴ A = 600

When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.
At 7 o'clock, they are 25 min. spaces apart.
∴ Minute hand will have to gain only 5 min. spaces.
55 min. spaces are gained in 60 min.
5 min. spaces are gained in
=(60/55)×5min.
= 5(5/11) min.
∴ Required time = 5 (5/11) min. past 7

Question: If secA + tanA = 7/3, then what is the value of secA - tanA?

Solution:
দেয়া আছে,
secA + tanA = 7/3

আমরা জানি,
sec²A - tan²A = 1
⇒ (secA + tanA)(secA - tanA) = 1
⇒ 7/3 (secA - tanA) = 1
∴ secA - tanA = 3/7

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

Solution: 
cost price 45 chocolates = 40/0.8 = 50 taka 

selling price after 20% gain = 50 + 50 × .2 = 60 taka

he should he sell for Tk. 24 = (24 × 45)/60 = 18 chocolates 

A/D = (A/(B × B))/((C × C)/D)
= (2/(3 × 4))/((5 × 5)/9)
= (2 × 4 × 5)/(3 × 5 × 9)
= 8/27
= 8 : 27

Question: If x = 7 - 4√3, then 

Solution: 
Given,
x = 7 - 4√3
⇒ x = 4 + 3 - 4√3
⇒ x = 2² + (√3)² - 2 × 2√3
⇒ x = (2 - √3)²  [ a² - 2ab + b² = (a - b)² ]
∴ √x = 2 - √3

Again,
√x = 2 - √3
⇒ 1/√x = 1/(2 - √3)
⇒ 1/√x = (2 + √3)/{(2 - √3) (2 + √3)}
⇒ 1/√x = (2 + √3)/(4 - 3)
∴ 1/√x = 2 + √3

∴ √x + (1/√x) = 2 - √3 + 2 + √3
∴ √x + (1/√x) = 4

Question: A train is moving at a speed of 132 km/hour. If the length of the train is 110 meters, how long will it take to cross a railway platform 165 meters long.

Solution: 
Given that,
Length of train = 110 m
Length of platform = 165 m
∴ Total distance to be covered = 110 + 165 = 275 meters
Speed of train = 132 km/h
= 132 × (1000/3600) m/s
= 132 × (5/18) m/s
= 110/3 m/s

Time taken = Distance/Speed
= 275/(110/3)
= (275 × 3)/110 
= 7.5 seconds

So the train will take 7.5 seconds to cross the 165 meter long railway platform.

Question: The ratio of the present ages of a mother and son is 7 : 2. After 7 years, the ratio of their ages becomes 8 : 3. What will be the ratio of their ages after 11 years?

Solution:
Let,
The present age of the mother = 7x years
The present age of the son = 2x years

After 7 years, their ages will be:
Mother = (7x + 7) years
Son = (2x + 7) years

According to the question,
(7x + 7)/(2x + 7) = 8/3
⇒ 3(7x + 7) = 8(2x + 7)
⇒ 21x + 21 = 16x + 56
⇒ 21x - 16x = 56 - 21
⇒ 5x = 35
⇒ x = 35/5
∴ x = 7

Present age of mother = 7 × 7 = 49 years
Present age of son = 2 × 7 = 14 years

Now, after 11 years,
Mother's age = 49 + 11 = 60 years
Son's age = 14 + 11 = 25 years

∴ The ratio of their ages after 11 years,
= 60 : 25
= 12 : 5

Question: If the word PSYCHOLOGY is viewed in a mirror, what will be its reflected image?

Solution: 
PSYCHOLOGY -এর আয়নায় প্রতিফলিত রূপটি হবে:

Question: If the radius of a sphere is 3r, what is its volume?

Solution:
Given that,
Radius of sphere = 3r

We know,
Volume of a sphere = (4/3) × πr³
= (4/3) × π(3r)³
= (4/3) × π × 27 × r³
= 36πr³ 

Question: The selling price of a an article after giving two successive discounts of 10% and 5% on the marked price is Tk. 171. What is the marked price?

Solution: 
If the marked price Tk.100, then after giving discounts of 10%,
selling price of the article = (100 - 10) = Tk. 90

If discounts of 5% on Tk. 90,
selling price of the article = (90 - 90 × 5%) = 90 - 4.5 = Tk. 85.5.

If the selling price Tk. 85.5, marked price is Tk. 100
If the selling price Tk. 171, marked price is Tk. 100 × 171/85.5 = Tk. 200

Question: The series is: (2/√5), - 2, 2√5, - 10, ......... What is the seventh term of this series?

Solution:
Here,
First term, a = 2/√5
Common ratio, r = - 2/(2/√5)
= - 2 × √5/2
= - √5

We know that,
The nth term of a geometric progression is given by = ar^{n - 1}
∴ Seventh term = ar^{7 - 1}
= ar⁶
= (2/√5) × (-√5)⁶
= (2/√5) × {(-√5)2}3
= (2/√5) × (5)3
= (2/√5) × 125
= 250/√5
= (250 × √5)/5
= 50√5

∴ 7^th term = 50√5

Question: How many 8 letter words can be formed by rearranging the letters of the word TRENDING such that T and G occupy the first and last positions respectively?

Solution:
As T and G should occupy the first and last position, the first and last position can be filled in only one following way.
T _ _ _ _ _ _ G.

The remaining 6 positions can be filled in the remaining words (R, E, N, D, I, N) where "N" comes twice.

Total permutations of these 6 letters with one letter repeating = 6!/2! = 720/2 = 360 ways

Question: A bus travels 300 km in 5 hours. What is its average speed?

Solution:
ট্রেনটির অতিক্রান্ত দূরত্ব = 300 কি.মি.
মোট সময় = 5 ঘণ্টা

গড় গতিবেগ = 300/5 km/h
= 60 km/h

- 25 m/sec
- 1500 m/min = 1500/60 = 25 m/sec
- 90 km/hr = (90×1000)/3600 = 25 m/sec