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Ratio & Proportion, Partnership [ব্যাংকের সকল পরীক্ষা যেকোনো প্যাকেজের জন্য ফ্রি]
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ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স · তারিখ অনির্ধারিত · ১৮ প্রশ্ন

১.
200 litres of a mixture contains milk and water in the ratio 17 : 3. After the addition of some more milk to it, the ratio of milk to water in the resulting mixture becomes 7 : 1. The quantity of milk added to it was?
  1. ক
    ক) 20 Litres
  2. খ
    খ) 40 Litres
  3. গ
    গ) 60 Litres
  4. ঘ
    ঘ) 80 Litres
ব্যাখ্যা

Milk : water = 17:3 = 17x : 3x
∴ 17x + 3x = 200
⇒ x =10litre
so, Milk = 170 litre and water = 30 litre in initial mixture.
Let 'y' litre of milk added in mixture
i.e. (170+y) : 30 = 7:1
⇒ (170 + y)/ 30= 7/1
∴ y = 210 - 170 = 40 litres

২.
A barrel contains a mixture of wine and water in the ratio 3:1. How much fraction of the mixture must be drawn off and substituted by water so that the ratio of wine and water in the resultant mixture becomes 1:1 = ?
  1. ক
    ক) 1/4
  2. খ
    খ) 1/3
  3. গ
    গ) 3/4
  4. ঘ
    ঘ) 2/3
ব্যাখ্যা

Original ratio of the mixture 3:1
Taking out the mixture actually means just taking out the wine because the water anyways is going to be added back.
If we remove 1 part of wine, it makes the ratio 2:2 (1 part water is added to keep the volume constant )
so, what we have actually done is remove 1 part wine from 3 part Wine. i.e. 1/3.
So, 1/3 mixture drawn.

৩.
In a proportion the product of 1st and 4th terms is 40 and that of 2nd and 3rd terms is 2.5x. Then the value of x is.
  1. ক
    ক) 16
  2. খ
    খ) 26
  3. গ
    গ) 75
  4. ঘ
    ঘ) 90
ব্যাখ্যা

Product of 1st and 4th terms (extremes) = product of 2nd and 3rd terms (means)
⇒ 2.5x = 40        
⇒ x = 40/2.5 = 16

৪.
Two numbers are in ratio 4:5 and their LCM is 180. The smaller number is-
  1. ক
    ক) 9
  2. খ
    খ) 15
  3. গ
    গ) 36
  4. ঘ
    ঘ) 45
ব্যাখ্যা

Numbers are in the ratio 4:5
Let the numbers be 4x and 5x
Hence, LCM = 20x
Hence, 20x = 180
Hence, x = 180/20 = 9
Hence the numbers are 36 and 45

৫.
Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is
  1. ক
    ক) 2:5
  2. খ
    খ) 3:5
  3. গ
    গ) 4:5
  4. ঘ
    ঘ) 6:5
ব্যাখ্যা

Let the third number be x.
First Number (120/100) × x = 6x/5
Second Number (150/100) × x = 3x/2
Ratio = 6x/5 : 3x/2
=> 4:5

৬.
If three numbers in the ratio 3:2:5 be such that the sum of their squares is 1862, the middle number will be-
  1. ক
    ক) 10
  2. খ
    খ) 14
  3. গ
    গ) 18
  4. ঘ
    ঘ) 22
ব্যাখ্যা

Let the numbers be 3x, 2x and 5x.
Then,
9x2 + 4x2 + 25x2=1862
=> 38x2 = 1862
=> x2 = 49
so, here x = 7.
So, middle number = 2x = 14

৭.
A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is-
  1. ক
    ক) 4:5
  2. খ
    খ) 9:5
  3. গ
    গ) 8:5
  4. ঘ
    ঘ) 9:2
ব্যাখ্যা

Dog : Hare
= (3 × 3) leaps of hare : (5×1) leaps of hare
= 9 : 5

৮.
A, B and C entered into a partnership by investing Tk 15400, Tk.18200 and Tk. 12600 respectively. B left after 6 months. If after 8 months, there was a profit of Tk. 28790, then what is the share of C in the profit?
  1. ক
    ক) 8710
  2. খ
    খ) 9432
  3. গ
    গ) 8352
  4. ঘ
    ঘ) 8568
ব্যাখ্যা

Investment of A for 8 months=Tk 15400
Investment of B for 6 months=Tk. 18200
Investment of C for 8 months= Tk.12600
Ratio of the share of A, B and C
= 15400×8:18200×6:12600×8
= 154×8:182×6:126×8
= 44:39:36
Sum of the terms of ratio
= 44+39+36 = 119
∴ Share of C
= Tk.(36/119 × 28790) ≈ Tk 8710 

৯.
A, B and C share the profit in the ratio of 2:3:7. If the average gain is Tk. 8000, then B's share is?
  1. ক
    ক) 2000
  2. খ
    খ) 1000
  3. গ
    গ) 1500
  4. ঘ
    ঘ) 6000
ব্যাখ্যা

Here,                    A   :   B    :   C
Ratio of Profit → 2   :   3    :    7
Average gain= (2+3+7)/3 = 4 units
According to the question,
4 units= Tk. 8000
1 unit= Tk. 2000
3 units=3×2000= Tk. 6000
∴Share of B= Tk. 6000

১০.
A, B, C started a business with their investments in the ratio 1:3:5. After 4 months, A invested the same amount as before and B as well as C withdrew half of their investments. The ratio of their profits at the end of the year is?
  1. ক
    ক) 4 : 3 : 5
  2. খ
    খ) 5 : 6 : 10
  3. গ
    গ) 6 : 5 : 10
  4. ঘ
    ঘ) 10 : 5 : 6
ব্যাখ্যা

Let their initial investments be x, 3x and 5x respectively
Then,
=A:B:C
= (x×4+2x×8) : {3x×4+(3x/2)×8} : {5x×4+(5x/2)×8}
= 20x:24x:40x
= 5:6:10

১১.
A, B and C enter into a partnership with capitals in the ratio 5:6:8. At the end of the business term, they received the profit in the ratio 5:3:12. Find the ratio of time for which they contributed their capitals?
  1. ক
    ক) 2 : 1 : 3
  2. খ
    খ) 1 : 2 : 3
  3. গ
    গ) 2 : 3 : 1
  4. ঘ
    ঘ) 3 : 2 : 1
ব্যাখ্যা

Profit= Time×Capital invested
Time= Profit/ Capital invested
Required ratio of time
=5/5:3/6:12/8
=1:1/2:3/2
=2:1:3

১২.
A started a business with tk 21,000 and is joined afterwards by B with tk 36,000. After how many months did B join if the profits at the end of the year are divided equally?
  1. ক
    ক) 4
  2. খ
    খ) 5
  3. গ
    গ) 6
  4. ঘ
    ঘ) 7
ব্যাখ্যা

Suppose B joined after x months
21000 × 12 = 36000 × (12 - x)
⇒ 36x = 180
⇒ x = 5

১৩.
A and B started a partnership business investing some amount in the ratio of 3:5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
  1. ক
    ক) 3 : 5 : 2
  2. খ
    খ) 3 : 5 : 5
  3. গ
    গ) 6 : 10 : 5
  4. ঘ
    ঘ) Data inadequate
ব্যাখ্যা

Let initial investment of A is 3x and B is 5x, then C investment is also 5x, but most important to note in this question is the time duration of investment
Like, A invested for 12 months, B invested for 12 months and C invested for 6 months.
A : B : C = (3x x 12) : (5x x 12) : (5x x 6)
= 36 : 60 : 30
= 6 : 10 : 5.

১৪.
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
  1. ক
    ক) 8,400
  2. খ
    খ) 11,900
  3. গ
    গ) 13,600
  4. ঘ
    ঘ) 14,700
ব্যাখ্যা

Let C = 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 
= Tk 35000× (21/50)
= Tk 14700

১৫.
In business, A and C invested amounts in the ratio 2:1, whereas the ratio between amounts invested by A and B was 3:2, If Tk 157300 was their profit, how much amount did B receive?
  1. ক
    ক) 48000
  2. খ
    খ) 47000
  3. গ
    গ) 47400
  4. ঘ
    ঘ) 48400
ব্যাখ্যা

A:B = 3:2 = 6:4
=> A:C = 2:1 = 6:3
=> A:B:C = 6:4:3
B share = (4/13)×157300
= 48400

১৬.
Nirmal and Kapil started a business investing Tk 9000 and Tk 12000 respectively. After 6 months, Kapil withdrew half of his investment. If after a year, the total profit was Tk 4600, what was Kapil’s share initially?
  1. ক
    ক) Tk 2300
  2. খ
    খ) Tk 2400
  3. গ
    গ) Tk 2500
  4. ঘ
    ঘ) None of above
ব্যাখ্যা

Nirmal:Kapil = 9000×12:(12000×6 + 6000×6)= 1:1
Kapil's share = Tk [4600 ×(1/2)) = Tk. 2300

১৭.
A,B and C enter into a partnership investing Tk 35000, Tk 45000 and Tk 55000. Find the their respective shares in annual profit of 40,500
  1. ক
    ক) 10500, 13500, 19500
  2. খ
    খ) 10500, 13500, 18500
  3. গ
    গ) 10500, 13500, 17500
  4. ঘ
    ঘ) 10500, 13500, 16500
ব্যাখ্যা

A:B:C = 35000:45000:55000 = 7:9:11
A's share = (7/27) ×40500 = Tk 10500
B's share = (9/27) ×40500 = Tk 13500
C's share = (11/27)×40500 = Tk 16500

১৮.
A starts business with tk. 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2:3. What is B's contribution in the capital?
  1. ক
    ক) 7500
  2. খ
    খ) 8000
  3. গ
    গ) 8500
  4. ঘ
    ঘ) 9000
ব্যাখ্যা

Let B's capital be tk. x.
Then, (3500 x 12)/7x = 2/3    
or, 14x = 126000
so, x = 9000 tk