ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: Two numbers X and Y are in the ratio 5 : 8 and their sum is 52. Then Y is-

Solution: 
let X = 5a and Y = 8a

∴ 5a + 8a = 52
13a = 52
a = 4

X = 20
Y = 32

Question: In what ratio must a mixture of 30% alcohol strength be mixed with that of 50% alcohol strength so as to get a mixture of 45% alcohol strength?

Solution: 
Let, X contains 30% alcohol strength and
Y contains 50% alcohol strength 

ATQ,
(30% of X) + (50% of Y) = 45% of (X + Y)
30X + 50Y = 45X + 45Y
15X = 5Y
X : Y = 1 : 3

Question: The number of students in 3 classes is in the ratio 2 : 3 : 4. If 10 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
According to the question,
(2x+10) : (3x+10) = 8 : 11
or, 11(2x+10) = 8(3x+10)
or, 22x + 110 = 24x + 80
or, 2x = 30
or, x = 15

Hence,
Original number of students,
9x = 9×15 = 135

Question: A, B and C enter into a partnership. A invests some money at the beginning, B invests double the amount after six months and C invest thrice the amount after eight months. If the annual profit be Tk. 27000; C's profit share is

Solution: 
ধরি,
A এর বিনিয়োগ X, লাভ পাবে 12 মাসের।
B এর বিনিয়োগ 2X, লাভ পাবে 6 মাসের।
C এর বিনিয়োগ 3X, লাভ পাবে 4 মাসের।

তাহলে,
A : B : C = (X × 12) : (2X × 6) : (3X × 4)
= 12X : 12X : 12X
= 1 : 1 : 1

∴ C এর লাভ হবে = (27000 এর 1/3)
= 9000 টাকা

question: A, B, C have the total money of Tk. 1400. B have half of A and C have half of B. The amount of C is 

Solution: 
Let A have X

then, 
B have X/2 and
C have X/4

so,
X + (X/2) + (X/4) = 1400
7X/4 = 1400
X = 800

hence, 
the amount of C is (800/4) or, 200

Question: In a mixture, the ratio of milk and water is 6 : 5. When 22 liter mixture is replaced by water, the ratio become 9 : 13. Find the quantity of water after replacement.

Solution: 
Let milk = 6X, water = 5X
so, 
total mixture = 6X + 5X = 11X

When 22 liter of mixture is replaced with water, then remaining milk is = 6X - (22 × 6X/11X) = 6X - 12

remaining water = 5X - (22 × 5X/11X) + 22  = 5X +  12

ATQ,
6X - 12 : 5X + 12 = 9 : 13
13(6X - 12) = 9(5X + 12)
78X - 156 = 45X + 108
78X - 45X = 156 + 108
33X = 164
X = 8

∴ water after replacement = 5X + 12 = 40 + 12 = 52 liters 

Question: A and B together have Tk. 500. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does A have?

Solution: 
Here,
(4/15)A = (2/5)B
A/B = 30/20
A : B = 3 : 2

Hence,
The amount of A = (500 × 3/5)
= 1500/5
= 300

Question: P, Q, R three friends invested in a business. Q invested twice of R and P invested half of R. what is the profit ratio of Q, P, R?

Solution: 
Let P invested x 
Then,
investment of R is 2x and
Investment of Q is (2 × 2x) or, 4x

∴ The profit ratio of Q, P, R will be 4x : x : 2x = 4 : 1 : 2

Solution: 
2/3 = 0.66
1/3 = 0.33
1/5 = 0.2
2/5 = 0.4

hance the lowest ratio is 1 : 5

Question: A and B invest in a business in the ratio 5 : 2. If 10% of the total profit goes to charity and A's share is Tk.9000 , the total profit is -

Solution: 
ধরি, মোট লাভ = ১০০ টাকা
১০% দান করার পর থাকে  = ১০০ - ১০০ এর ১০% = ৯০ টাকা

৯০ টাকার মধ্যে A পাবে ৯০ × (৫/৭) টাকা
= ৬৪.২৮৫৭ টাকা

৬৪.২৮৫৭ টাকা পায় যখন মোট লাভ ১০০ টাকা
∴ ৯০০০ টাকা পায় যখন মোট লাভ = (৯০০০ × ১০০)/৬৪.২৮৫৭ 
= ১৪০০০ টাকা

Question: A wheel that has 5 cogs is meshed with a larger wheel of 15 cogs. When the smaller wheel has made 21 revolutions, the number of revolutions made by the larger wheel will be-

Solution: 

smaller wheel cross = 5 × 21 = 105 cogs by 21 revolutions.
so, 
larger wheel will made = 105/15 = 7 revolutions.

Shortcut: 
cogs of A : cogs of B = reolution of B : revolution of A
hense,
5 : 15 = X : 21
X = 7

Question: A and B invested in the ratio of 11 : 12. B invested for 11 month. If the profit ratio of A and B is 2 : 3, for how much time A invested the money?

Solution: 
Let A and B invested 11p and 12p, 
A invested for Y month

Then,
(11p × Y) : (12p × 11) = 2 : 3
11Y : 132 = 2 : 3
33Y = 264
Y = 8

Question: In a ratio which is equal to 5 : 6, if the antecedent is 45, what is the consequent?

Solution: 
Let the consequent is x.

then, 
5 : 6 = 45 : x
5x = 270
x = 54

Question: In a zoo, there are Rabbits and Pigeons. If heads are counted, there are 200 and if legs are counted, there are 580. Find the ratio of number of Rabbits and Pigeons?

Solution: 
ধরি,
খরগোশ আছে X টি
তাহলে, কবুতর আছে (200 - X) টি

প্রশ্নমতে,
4X + 2(200 - X) = 580
4X + 400 - 2X = 580
2X = 180
X = 90টি

∴ কবুতর আছে = (200 - 90) বা, 110 টি


 Rabbits : Pigeons = 90 : 110 = 9 : 11

Question: The sides of a triangle are in the ratio 4 : 5 : 6. The smallest angle is-

Solution: 
we know that, the sum of the angles of a triangle is 180°

Hence, 
The smallest angle is (180° × 4/15) = 48°

Question: A, B, C subscribe Tk. 50,000 for 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.

Then,
B = x + 5000 and
A = x + 5000 + 4000
= x + 9000

So,
x + x + 5000 + x + 9000 = 50000
⇒ 3x = 36000
⇒ x = 12000

A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12

So A's Share = 35000×(21/50)
= 14700

Question: What is the ratio of one third of 7/15 and two third of the same number?

Solution:
one third of 7/15 is {(1/3) × (7/15)} = 7/45
two third of 7/15 is {(2/3) × (7/15)} = 14/45

ratio = 7/45 : 14/45 = 1 : 2

Question: A milkman wants to gain 25% on selling the mixture at cost price, then in what ratio must he mix water with milk?

Solution: 
Let, the milkman has milk of 100 Tk.
after mixing he sold it in = 100 + 25 = 125 Tk.

In 125, milk is of 100 Tk. and water is of 25 Tk.

∴ The ratio of water and milk is 25 : 100 = 1 : 4

Question: If a : b : c = 2 : 3 : 4 and 2a - 2b + 4c = 42, then the value of c is 

Solution: 
let, 
a = 2x
b = 3x
c = 4x

so,
2a - 2b + 4c = 4x - 6x + 16x = 42
14x = 42
x = 3

∴ c = 4x = 4 × 3 = 12

Question: Find the ratio in which rice at Tk. 7.20 a kg be mixed with rice at Tk. 5.70 a kg to produce a mixture worth Tk. 6.30 a kg-

Solution: 
Let, Tk. 7.20 per kg rice is X kg
and Tk. 5.70 per kg rice is Y kg

ATQ,
7.2X + 5.7Y = 6.3(X + Y)
7.2X + 5.7Y = 6.3X + 6.3Y
0.9X = 0.6Y

X : Y = 0.6 : 0.9 = 2 : 3

Question: What number has to be added to the terms of 3 : 5 to make the ratio 5 : 6?

Solution: 
Let the number to be added is X.
Then,
(3 + X)/(5 + X) = 5/6
6(3 + X) = 5(5 + X)
18 + 6X = 25 + 5X
X = 7

Question: a : b = 3 : 5 and c : b = 7 : 3 then what is the ratio of c : b : a?

Solution:
here,
a : b = 3 : 5 = 9 : 15 [multiplying by 3]
c : b = 7 : 3 = 35 : 15 [multiplying by 5]

c : b : a = 35 : 15 : 9

Question: If 20% of A = 30% of B = 1/6 of c, then A : B : C = ?

Solution: 
20% of A = 30% of B = 1/6 of c
(1/5)A = (3/10)B = (1/6)C
A/5 = 3B/10 = C/6

∴ A/5 = 3B/10
A/B = 15/10

and,
A/5 = C/6
A/C = 5/6 = 15/18

hence, 
A : B : C = 15 : 10 : 18

Question: Father divides his property equally between his two sons and 150000 Tk left. If the remaining part is 7.5% of actual property than every brother owns Tk. - 

Solution: 
৭.৫% = ১৫০০০০ টাকা
∴ সম্পূর্ণ সম্পত্তি = ২০০০০০০ টাকা
২ পুত্র পেল = (২০০০০০০ -১৫০০০০) = ১৮৫০০০০

∴ প্রত্যেক পুত্র পেল = ১৮৫০০০০/২ = ৯২৫০০০ টাকা

Question: Which of the following represent ab = 64?

Solution: 
32 : a = b : 2
ab = 64

a : 8 = b : 8
a = b

a : 16 = b : 4
4a = 16b
a = 4b

8 : a = 8 : b
8a = 8b 
a = b

Question: The cost of a table and a chair are in the ratio of 4 : 5. If the cost of chair and table is increased by 20% and 10% respectively, then the new ratio of cost is 

Solution: 
let the cost of the table and chair are 4x and 5x.

After increasing 10% the new cost of the table is = (110% of 4x) = (11/10 of 4x) = 22x/5
After increasing 20% the new cost of the chair is = (120% of 5x) = (12/10 of 5x) = 6x

hance,
the new cost ratio is = (22x/5) : 6x
= (22/5) : 6
= 22 : 30
= 11 : 15

অপশনে সঠিক উত্তর না থাকায় প্রশ্নটি বাতিল করা হয়েছে।

Question: If m : n = 3 : 2, then find the ratio (4m + 5n) : (4m - 5n).

Solution: 
here, 
m : n = 3 : 2
2m = 3n
∴ 4m = 6n 

hence,
(4m + 5n) : (4m - 5n) = (6n + 5n) : (6n - 5n)
= 11n : n
= 11 : 1

Question: A container contains 64 litres of milk. From this container 16 litres of milk was taken out and replaced by water. This process was repeated overall three times. How much milk is now contained by the container?

Solution: 
After first replacement the ratio of milk and water is 48 : 16 = 3 : 1

After second replacement,
remaining milk = 48 - (3/4 of 16) = 48 - 12 = 36
water = 16 +12= 16 + 12 = 28
∴ ratio = 36 : 28 = 9 : 7

After third replacement,
remaining milk = 36 - (9/16 of 16) = 36 - 9 = 27
water = 28 + 9 = 37
∴ ratio = 27 : 37  

shortcut,
after three replacement the reamining milk will be = 64 × (3/4)³
= 64 × 27/64
= 27

Question: The fourth proportional to 5, 8, 15 is 

Solution: 
Let the fourth proportion is X.
then,
5 : 8 : : 15 : X
5X = 120
X = 24