ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: A and B are the two alloys of copper and brass prepared by mixing metals in the proportion of 7 : 2 and 7 : 11 respectively. If equal quantities of two alloys are melted to form a third alloy called C, then the proportion of copper and brass in C will be

Solution: 
Let, A is 18 kg
copper = 18 × (7/9)
= 14 kg 
brass = 4 kg

Let, B is 36 kg
copper = 36 × (7/18)
= 14 kg
brass = 22 kg

After mixing, total amount = 18 + 36 = 54 kg 

From part A, copper = (54/2) × (7/9) = 21 kg
brass = 27 - 21 = 6 kg

From part B, copper = (54/2) × (7/18) = 10.5 kg
brass = 27 - 10.5 = 16.5 kg

Ratio = (21 + 10.5) : (6 + 16.5)
= 31.5 : 22.5
= 315 : 225
= 63 : 45
= 7 : 5

Question: The incomes of X and Y are in the ratio of 3 : 2 and their expenditures are in the ratio of 5 : 3. If each of them saves Tk. 1000, then, X’s income can be

Solution: 
The incomes of X and Y are 3x, 2x
their expenditures are 5y, 3y 

3x - 5y = 1000 
2x - 3y = 1000

3x - 5y = 2x - 3y 
⇒ x = 2y

3 × 2y - 5y = 1000 
⇒ y = 1000
x = 2 × 1000 = 2000 taka

∴ X’s income = 3x
= 3 × 2000
= Tk. 6000

Question: In a zoo, there are deer and ducks. If the heads are counted, there are 180, while the legs are 448. What will be the number of ducks in the zoo?

Solution:
ধরি, হাঁসের সংখ্যা x টি ও হরিণের সংখ্যা  y টি  

x + y = 180 
⇒ 4x + 4y = 720

2x + 4y = 448

4x + 4y - 2x - 4y = 720 - 448
⇒ 2x = 272
∴ x = 136 

হাঁসের সংখ্যা ১৩৬ টি 

Question: A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture? 

Solution:         
Amount of water = 150 × 20/100
= 30 

Amount of wine = 120 liter

ATQ, 
(30 + x)/(150 + x) = 25/100
⇒ (30 + x)/(150 + x) = 1/4
⇒ 120 + 4x = 150 + x
⇒ 4x - x = 150 - 120
⇒ 3x = 30
⇒ x = 30/3 = 10 liters                    

Question: The students in three batches in school is in the ratio of 2 : 3 : 5. If 20 students in each batch are increased than the ratio changes to 4 : 5 : 7. The total number of students in the three before the increase was- 

Solution: 
Let, students in the three before the increase were 2x, 3x, 5x

After increase, 2x + 20, 3x + 20, 5x + 20

(2x + 20)/ (3x + 20) = 4/5
⇒ 10x + 100 = 12x + 80 
⇒ 2x = 20
⇒ x = 10

The total number of students in the three before the increase was = (2x + 5x + 3x)
= 10x
= 10 × 10
= 100

প্রশ্ন: If a : b = 2 : 3 and a : c = 4 : 7, then b : c =?

সমাধান:
 a : b = 2 : 3
⇒ a/b = 2/3

a : c = 4 : 7 
⇒ a/c = 4/7

(a/b) / (a/c) = (2/3)/(4/7)
⇒ c/b = 7/6
∴ b/c = 6/7
∴ b : c = 6 : 7

Question: A solution containing 10% sugar by weight is made sweeter by doubling the amount of sugar. The percent of sugar, by weight, in the new solution is-

Solution: 
let, solution is 100 unit
amount of sugar = 100 × 10%
= 100 × 10/100
= 10 unit 

by doubling, amount of sweet = 20 unit
solutin = 100 + 10 = 110 unit 

percent of sugar = 20 × 100%/110
= 18.18%

Question: If A : B = (1/2) : (1/3) and B : C = (1/2) : (1/3), then A : B : C =? 

Solution: 
A : B = (1/2) : (1/3)
⇒ A : B = (6/2) : (6/3)
= 3 : 2
= (3 × 3) : (3 × 2)
= 9 : 6

B : C = (1/2) : (1/3)
⇒ B : C = (6/2) : (6/3)
= 3 : 2
= (3 × 2) : (2 × 2)
= 6 : 4

then A : B : C = 9 : 6 : 4

Question: Tea worth Tk. 126 per kg and Tk. 135 per kg are mixed with a third variety in the ratio 1 : 2 : 2. If the mixture is worth Tk. 153 per kg, the price of the third variety per kg will be:

Solution: 
let, price of third variety x tk per kg 
126y + 135 × 2y + x × 2y = 153 (y + 2y + 2y)
⇒ 126 + 270 + 2x = 765
⇒ 2x = 369
∴ x = 184.5 tk

প্রশ্ন: Helal and Tonmoy share some sweets in a ratio of 7 : 5. Helal has 12 more sweets than Tonmoy. How many sweets were there altogether?

সমাধান: 
Let,
Helal has 7x sweets 
Tonmoy has 5x sweets 
∴ Total sweets 7x + 5x = 12x

ATQ,
7x - 5x = 12
⇒ 2x = 12
∴ x = 6

∴ There were 12 × 6 = 72 sweets altogether.

Question: The ratio of expenditure and savings is 3 : 2 . If the income increases by 15% and the savings increase by 6%, then by how much percent should his expenditure increases?

Solution: 
Let, expenditure 300 and savings be 200
Income = 300 + 200 
= 500 

New income = 500 + 500 × 15/100 
= 500 + 75
= 575 

New savings = 200 + 200 × 6/100
= 212 

 New expenditure = 575 - 212
= 363

% increase = {(363 - 300)/300} × 100%
= 21%

Question: A, B, C subscribe Tk. 50,000 for a business. A subscribes Tk. 4000 more than B and B Tk. 5000 more than C. Out of a total profit of Tk. 35,000, A receives- 

Solution: 
let, C subscribes x taka 
B subscribes x + 5000 taka 
A subscribes x + 5000 + 4000 
= x + 9000 taka 

x + x + 5000 + x + 9000 = 50000 
⇒ 3x + 14000 = 50000
⇒ 3x = 36000 
⇒ x = 12000 taka 

A receives = {(x + 9000)/50000} × 35000
= (21000/50000) × 35000
= 14700 taka 

Question: Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is-

Solution:
Let the third number be x

Then, first number = 120% of x = 120x/100 = 6x/5
Second number = 150% of x = 150x/100 = 3x/2

∴ Ratio of first two numbers = 6x/5 : 3x/2
= 12x : 15x
= 4 : 5

Question: A bag contains 50P, 25P and 10P coins in the ratio 5 : 9 : 4, amounting to Tk. 206. Find the number of coins of each type respectively.

Solution:
Number of 50P coins = 5x
Number of 25P coins = 9x
Number of 50P coins = 4x

ATQ, 
5x (1/2) + 9x (1/4) + 4x(1/10) = 206
⇒ (50x + 45x + 8x)/20 = 206
⇒ 103x = 206 × 20
⇒ x = 40


The number of coins of each type respectively = 200, 360, 160