ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: If 25% of (A + B) = 50% of (A - B), then find B : A - 

Solution: 
25% of (A + B) = 50% of (A - B)
⇒ (A + B) × 25/100 = (A - B) × 50/100
⇒ (A + B)/4 = (A - B)/2
⇒ 2 (A + B) = 4 (A - B)
⇒ 2A + 2B = 4A - 4B 
⇒ 4A - 2A = 2B + 4B
⇒ 2A = 6B
⇒ A/B = 6/2 = 3/1
∴ B/A = 1/3
= 1 : 3

Question: The salaries of A, B and C are in the ratio 1 : 3 : 4. If the salaries are increased by 5%, 10% and 10% respectively, then the increased salaries will be in the ratio -

Solution:
Given that
Salary has  in 1 : 3 : 4 ratio
Let
A's Salary = Tk. 100
B's Salary = Tk. 300
C's Salary = Tk. 400

Now,
5% increase in A's Salary,
A's new Salary = (100 + 5% of 100) = Tk. 105

B's Salary increases by 10%, Then,
B's new Salary = (300 + 10% of 300) = Tk. 330

C's Salary increases by 10%,
C's new Salary = (400 + 10% of 400) = Tk. 440

Then, ratio of increased Salary,
A : B : C = 105 : 330 : 440 = 21 : 66 : 88

Question: The ratio of income and expenditure of a person is 5 : 2, If he saves Tk. 3000 per month, what is his monthly income?

Solution: 
Let, income = 5x
and expenditure = 2x 
Then,
Savings = 5x - 2x = 3000
⇒ 3x = 3000
∴ x = 1000

∴ monthly income = 5x = 5 × 1000 = Tk. 5000

Question: Three numbers A, B, and C are in the ratio 1 : 2 : 3. Their average is 600. If A is increased by 10% and B is decreased by 20%, by what amount should C be increased so that the new average becomes 3% higher?

Solution:
Let
A = x, B = 2x, C = 3x.
Then,
x + 2x + 3x = 600 × 3
Or, 6x = 1800
Or, x = 300

So, A = 300, B = 600, C = 900.
New value of A = 110% of 300 = 330
New value of B = 80% of 600 = 480 
New average = 103% of 600 = 618

∴ New value of C = (618 × 3) - (330 + 480)
= 1854 - 810
= 1044

∴ Increase in value of C = 1044 - 900
= 144 Tk.

Question: Rafsan and Karim entered into a business partnership by investing Tk. 20,000 and Tk. 30,000 respectively. If the total profit earned is Tk. 7,000, what is Rafsan’s share of the profit?

Solution:
Given,
Investment ratio = 20000 : 30000
= 2 : 3
Sum of the ratio's = 2 + 3 = 5

∴ Rafsan's share = 7000 × (2/5)
= Tk. 2800

Question: A bag contains red, blue, and green balls in the ratio 2 : 3 : 5. If there are 15 blue balls, how many total balls are there in the bag?

Solution: Given ratio = Red : Blue : Green = 2 : 3 : 5
Let the numbers be:
Red = 2x, Blue = 3x, Green = 5x

Given,
Blue balls, 3x = 15
∴ x = 5

Now calculate total balls:
= 2x + 3x + 5x
= (2 + 3 + 5)x 
= 10x
= 10 × 5 
= 50

Question: A, B, and C invest in a business in the ratio 2 : 1 : 3. If the total profit is Tk 30,000, how much more did C get than A?

Solution:
Let the invested shares ratio = 2x : x : 3x

Now
2x + x + 3x = 30000
Or, 6x = 30,000
∴ x = 5,000

∴ A’s share = 2 × 5,000 = 10,000
∴ C’s share = 3 × 5,000 = 15,000
∴ Difference = 15,000 - 10,000
= Tk 5,000

∴ C gets 5000 Tk more than A.

Question: A sum of money is divided among 6 males and some females in the ratio of the total money received by males to total money received by females as 3 : 1. If each male gets Tk. 600 and each female gets Tk. 1200, how many females are there?

Solution:
Let the number of females be x.

Then,
(600 × 6)/1200x = 3/1
Or, 6/2x = 3/1
Or, 3/x = 3/1

So, 3x = 3
∴ x = 1

Question: P and Q started a business in the ratio of 2 : 3. After, 1 year P left the business but Q continued. After 2 years they had the profit of Tk. 26,000. What is the profit of Q?

Solution:
Let the initial capital of P and Q be 2x and 3x, respectively.

Then, ratio of profits
= 2x × 12 : 3x × 24
= 24x : 72x
= 1 : 3

∴ Q's share of profit
= 26000 × (3/4)
= Tk. 19500.

Question: 40% of a number A is equal to 1/5 of another number B. Find the ratio A : B.

Solution:
ATQ,
40% of A = 1/5 of B
Or, (40/100) × A = (1/5) × B
Or, (2/5) A = (1/5) B
Or, 2A = B
∴ Ratio A : B = 1 : 2

Question: If a : b = 3 : 1, find ratio (3a + 5b) : (3a - 5b).

Solution: 
(3a + 5b) : (3a - 5b)
= b(3a/b + 5) : b (3a/b - 5)
= (3 × 3/1 + 5) : (3 × 3/1 - 5)
= (9 + 5) : (9 - 5)
= 14 : 4
= 7 : 2

Question: Rafi, Nabil, and Hasan started a business together. Rafi invested one-fourth of the total capital, Nabil invested one-sixth, and the remaining capital was invested by Hasan. What is the ratio of their profits?

Solution:
Let the total capital be 12x
Then, Rafi's share = 12x × (1/4) = 3x
Nabil's share = 12x × (1/6) = 2x
Hasan's share = 12x - (3x + 2x) = 7x

So, required ratio = 3x : 2x : 7x = 3 : 2 : 7

Question: Rafi and Nabil started a business. Rafi invested Tk. 15,000 for 12 months, while Nabil invested Tk. 10,000 for 6 months. After 6 months, Nabil added another Tk. 5,000. If the total profit is Tk. 11,000, what is Nabil’s share of the profit?

Solution:
Rafi's share 15,000 × 12 = 180,000
Nabil's share (10,000 × 6) + (15,000 × 6)
= 60,000 + 90,000
= 150,000

Ratio of Rafi : Nabil = 180,000 : 150,000 = 6 : 5

∴ Nabil's profit = (5/11) × 11,000
= Tk 5,000

Question: A man distributes Tk. 16,000 among his daughter, wife, and son such that the daughter’s and wife’s shares are in the ratio 1 : 2, and the son receives half of the total amount. What is the daughter’s share?

Solution:
The daughter's share and the wife's share are of 1 : 2 ratio
daughter's share = x
wife's share = 2x

As the son gets half of the total amount
∴ son's share = 16000/2
= 8000 Tk

∴ Rest of the share = 3x
∴ According to the question,
Or, 3x = 8000
Or, x = 8000/3
∴ x = 2666.66

∴ daughter's share = x = 2666.66 Tk

Question: Arif and Samir started a business in partnership by investing Tk. 20,000 and Tk. 15,000 respectively. After six months, Tanvir joined them with Tk. 20,000. If the total profit earned at the end of 2 years from the start of the business is Tk. 25,000, what is Samir’s share?

Solution:
Here,
Arif : Samir : Tanvir
= (20,000 x 24) : (15,000 x 24) : (20,000 x 18)
= 4 : 3 : 3.

So, Samir's share = 25000 x 3/10 = 7,500.