লগ ইননিবন্ধন
পরীক্ষা আর্কাইভ

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

পরীক্ষাব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্সতারিখতারিখ অনির্ধারিতসময়25 minutes১৭ বৈধ · ১ অসম্পূর্ণ
মোট প্রশ্ন১৮
সিলেবাস
Math - 04: Ratio & Proportion, Partnership, Allegation or Mixture
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

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

১.
A mixture of 50 liters of milk and water contains 10% of water. How much water must be added to make the water 20% in the new mixture?
  1. ক
    ক) 6.25 litres
  2. খ
    খ) 7 litres
  3. গ
    গ) 7.25 litres
  4. ঘ
    ঘ) 8.25 litres
ব্যাখ্যা
Quantity of water in given mixture
=10 / 100 x 50=5 litres.

Quantity of milk in given mix.
= 50 - 5= 45 litres.

Let x litres of water be added to it.
Milk : 45 litres, water (5 + x) litres
Total mix = (50 + x) litres
(5+x)/ (50+ x ) = 20/100
⇒ (5 + x)5 = 50 + x
⇒ 4x = 25
⇒ x= 6.25
6.25 litres of water must be added.
২.
If a and b are integers greater than 200 such that a + b = 600, which of the following could be the exact ratio of a to b?
  1. ক
    ক) 3 to 2
  2. খ
    খ) 5 to 2
  3. গ
    গ) 7 to 3
  4. ঘ
    ঘ) 9 to 1
ব্যাখ্যা
for, 3 to 2, 
600 × 3/(3 + 2) = 360; which is greater than 200. This maybe the correct answer.

for, 5 to 2, 
600 × 2/(5 + 2) = 171.43; which is less than 200. This is not the correct answer.

for, 7 to 3, 
600 × 3/(7 + 3) = 180; which is less than 200. This is not the correct answer.

for, 9 to 1, 
600 × 1/(9 + 1) = 60; which is less than 200. This is not the correct answer.
৩.
If x : y = 5 : 3, then (11x + 2y) : (11x - 2y) = ?
  1. ক
    ক) 67 : 49
  2. খ
    খ) 57 : 43
  3. গ
    গ) 57 : 49
  4. ঘ
    ঘ) 61 : 49
ব্যাখ্যা
x : y = 5 : 3
⇒ x/y = 5/3
⇒ 11x/2y = (11 × 5)/(2 × 3)
⇒ 11x/2y = 55/6
⇒ (11x + 2y)/(11x - 2y) = (55 + 6)/(55 - 6)
⇒ (11x + 2y)/(11x - 2y) = 61/49
⇒ (11x + 2y) : (11x - 2y) = 61 : 49
৪.
If x/y = 3 and x + 3y - 10 = 0 then x is
  1. ক
    ক) 5
  2. খ
    খ) 7
  3. গ
    গ) 8
  4. ঘ
    ঘ) 9
ব্যাখ্যা
x/y = 3
⇒ x = 3y

x + 3y - 10 = 0
⇒  3y + 3y = 10
⇒  6y = 10
⇒  y = 10/6
⇒  y = 5/3

x = 3 × 5/3 = 5
৫.
The ratio of ages of Mary and Maria is 4 : 5. After 12 years their ratio becomes 5 : 6. What will be the age of Mary after 2 years?
  1. ক
    ক) 45 years
  2. খ
    খ) 48 years
  3. গ
    গ) 50 years
  4. ঘ
    ঘ) 56 years
ব্যাখ্যা
Since the ages of Mary and Maria are in the ratio 4 : 5,
the actual ages can be taken as 4x years and 5x years respectively.
After 12 years, their ages will be 4x + 12 years and 5x + 12 years.
Therefore, as per the problem (4x + 12)/(5x + 12) = 5/6 => x = 12
Mary's age now is 4x years = 48 years.
So after 2 years Mary will be 50 years.
৬.
If x : y = 7 : 3 and x/(13 - 2y) = 1 then y = ?
  1. ক
    ক) 9
  2. খ
    খ) 10
  3. গ
    গ) 12
  4. ঘ
    ঘ) 13
অনির্ধারিত
ব্যাখ্যা
x : y = 7 : 3
⇒ x/y = 7/3
⇒ x = 7y/3

x/(13 - 2y) = 1
⇒ (7y/3)/(13 - 2y) = 1
⇒ 7y/3 = 13 - 2y
⇒ 7y = 39 - 6y
⇒ 7y + 6y = 39
⇒ 13y = 39
⇒ y = 3

অপশনে সঠিক উত্তর নেই, তাই বাতিল করা হয়েছে।
৭.
The present age of Jamal and Kamal are in the ratio of 6 : 4. Five years ago, their ages were in the ratio of 5 : 3. How old is Jamal now?
  1. ক
    ক) 30 years
  2. খ
    খ) 35 years
  3. গ
    গ) 40 years
  4. ঘ
    ঘ) 45 years
ব্যাখ্যা
Let, the present ages of Jamal and Kamal are 6x and 4x respectively.
(6x - 5)/(4x - 5) = 5/3
20x - 25 = 18x - 15
2x = 10
x = 5

Habib's age = 6 × 5 = 30 years 
৮.
Two numbers are in the ratio 3 : 5. If 8 is added to both the numbers, their ratio becomes 2 : 3. The greater number is
  1. ক
    ক) 24
  2. খ
    খ) 36
  3. গ
    গ) 40
  4. ঘ
    ঘ) 45
ব্যাখ্যা
Two numbers are 3y and 5y
(3y + 8)/(5y + 8) = 2/3
10y + 16 = 9y + 24
y = 8
The greater number is 5 × 8 = 40
৯.
The ratio of spirit and water in two mixtures of 20 litres and 36 litres is 3 : 7 and 7 : 5 respectively. Both the mixtures are mixed together. Now the ratio of the spirit and water in the new mixture is ?
  1. ক
    ক) 18 : 29
  2. খ
    খ) 20 : 29
  3. গ
    গ) 23 : 25
  4. ঘ
    ঘ) 27 : 29
ব্যাখ্যা
In 20 litres mixture - 1; sum of ratio = 3 + 7 = 10
10 units = 20 litres
1 unit = 20/10 = 2

In 36 litres mixture - 1; sum of ratio = 5 + 7 = 12
12 units = 36 litres
1 unit = 36/12 = 3

In 20 litres mixture - 1; spirit : water = 3 × 2 : 7 × 2 = 6 : 14
In 36 litres mixture - 2; spirit : water = 7 × 3 : 5 × 3 = 21 : 15

spirit : water = (6 + 21) : (14 + 15) = 27 : 29
১০.
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. 100000, C receives
  1. ক
    ক) Tk. 24,000
  2. খ
    খ) Tk. 34,000
  3. গ
    গ) Tk. 42,000
  4. ঘ
    ঘ) Tk. 35,000
ব্যাখ্যা
Let C subscribes Tk. x
x + x + 5000 + x + 9000 = 50,000
x = 12,000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12
C's share = 100000 of 12/50 = 24,000
১১.
A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Tk. 1140, the total profit is:
  1. ক
    ক) Tk. 1000
  2. খ
    খ) Tk. 1200
  3. গ
    গ) Tk. 1440
  4. ঘ
    ঘ) Tk. 2000
ব্যাখ্যা
Let total profit be Tk. 100
After paying 5% to charity, A's share = 95 × 3/5 = 57
Total profit = 100/57 × 1140 = 2000
১২.
P and Q started a business investing Tk. 57000 and Tk. 33000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively.
  1. ক
    ক) 19 : 33
  2. খ
    খ) 17 : 31
  3. গ
    গ) 19 : 11
  4. ঘ
    ঘ) 12 : 31
ব্যাখ্যা
In this question as time frame for both investors is same as then just get the ratio of their investments.

P : Q
= 57000 : 33000
= 57 : 33
= 19 : 11
১৩.
A, B and C enter into a partnership investing Tk. 35000, Tk. 45000 and Tk. 55000 respectively. The share of A in an annual profit of Tk. 81,000 is
  1. ক
    ক) Tk. 21,000
  2. খ
    খ) Tk. 27,000
  3. গ
    গ) Tk. 33,000
  4. ঘ
    ঘ) Tk. 41,000
ব্যাখ্যা
A : B : C = 35000 : 45000 : 55000 = 7 : 9 : 11
sum of ratio = 7 + 9 + 11 = 27
A's share = 81,000 × 7/27 = 21,000
১৪.
A and B are two partners in a firm sharing the profit in the ratio 4 : 5. If the firm earns a profit of Tk. 72000, then profit to be received by B ?
  1. ক
    ক) Tk. 40,000
  2. খ
    খ) Tk. 32,000
  3. গ
    গ) Tk. 48,000
  4. ঘ
    ঘ) Tk. 56,000
ব্যাখ্যা
Sum of 4 and 5 is 9
Share of B = 72000 × 5/9 = Tk. 40,000
১৫.
If a : b : c = 3 : 4 : 7, then the ratio (a + b + c) : 5c is equal to
  1. ক
    ক) 1 : 3
  2. খ
    খ) 2 : 1
  3. গ
    গ) 4 : 1
  4. ঘ
    ঘ) 2 : 5
ব্যাখ্যা
(a + b + c) : 5c = (3 + 4 + 7) : 5 × 7 = 14 : 35 = 2 : 5
১৬.
  1. ক
    ক) 9 : 11 : 13
  2. খ
    খ) 9 : 8 : 13
  3. গ
    গ) 9 : 8 : 10
  4. ঘ
    ঘ) 7 : 8 : 12
ব্যাখ্যা
2A/3 = 75B/100 = 6C/10
A/B = 9/8
B/C = 8/10
A : B : C = 9 : 8 : 10
১৭.
A bucket contains a mixture of two liquids A & B in the proportion 5 : 3. If 16 liters of the mixture is replaced by 16 liters of liquid B, then the ratio of the two liquids becomes 3 : 5. How much of the liquid B was there in the bucket?
  1. ক
    ক) 4
  2. খ
    খ) 7
  3. গ
    গ) 10
  4. ঘ
    ঘ) None of these
ব্যাখ্যা
Let bucket contains 5x and 3x of liquids A and B respectively.
Quantity of A in 16 liters = 16 × (5x / 8x) = 10
Quantity of B in 16 liters = 16 - 10 = 6
(5x - 10)/(3x - 6 + 16) = 3/5
Upon solving, x = 5
So initial quantity of B = 15 liters
১৮.
The present ratio of ages of A and B is 4 : 5. 18 years ago, this ratio was 11 : 16. Find the sum of their present ages.
  1. ক
    ক) 70 years
  2. খ
    খ) 64 years
  3. গ
    গ) 90 years
  4. ঘ
    ঘ) 75 years
ব্যাখ্যা
Let present age of A and B be 4x and 5x
18 years ago their ages
(4x - 18)/(5x - 18) = 11/16
x = 10
Sum of the present ages = 40 + 50 = 90 years