ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: At present, the ratio of the age of Muna and Riya is 6 : 5 and fifteen years from now, the ratio will get changed to 9 : 8. Muna’s present age is-

Solution:
Let, Muna’s present age be = 6x years
and Riya’s present age be = 5x years.

After 15 years, Muna’s age be = (6x + 15) years
After 15 years, Riya’s age be = (5x + 15) years

ATQ,
(6x + 15)/(5x + 15) = 9/8
⇒ 48x + 120 = 45x + 135
⇒ 48x - 45x = 135 - 120
⇒ 3x = 15
⇒ x = 5

∴ Muna’s present age = 6x
= 6 × 5) = 30 years

Question: 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. 1425, the total profit is:

Solution:
Let,
the total profit be = Tk.100
After paying to charity, A's share = Tk. {95 × (3/5)}
= Tk. 57

If A's share is = Tk. 57
∴ Total profit = Tk. 100

If A's share = Tk. 1425
∴ Total profit = {(100/57) × 1425}
= 2500

Question: If a : b : c = 7 : 3 : 5, then (a + b + c) : (2a + b - c) is equal to-

Solution:
Given,
a : b : c = 7 : 3 : 5

Let,
(a/7) = (b/3) = (c/5) = k
a = 7k, b = 3k, c = 5k

Now, (a + b + c) : (2a + b - c)
= (7k + 3k + 5k) : {(2 × 7k) + 3k - 5k)
= 15 k : 12 k
= 5 : 4

Question: A and B start a business jointly. A invests Tk 32000 for 8 months and B remains in the business for 4 months. Out of the total profit, B claims 2/7 of the profit. How much money was contributed by B?

Solution:
Here,
Total profit = 7
B's profit = 2
So, A's profit = (7 - 2) = 5

So, ratio of A's and B's profit = 5 : 2

Let B's capital be = x

Then,
(32000 × 8)/(x × 4) = 5/2 
⇒ 20x = 32000 × 8 × 2
⇒ x = (32000 × 8 × 2)/20
⇒ x = 25600

Question: Tk. 180 is to be divided among 66 persons (men and women). The ratio of the total amount of money received by men and women is 5 : 4. But the ratio of the money received by each man and woman is 3 : 2. The number of men is:

Solution:
Let, amount received by men = 5x.
and amount received by women = 4x

ATQ,
5x + 4x = 180
⇒ 9x = 180
⇒ x = 20

Amount received by men = TK.100
Amount received by women = TK.80

Suppose, the number of men be y and that of women be = (66 - y).
∴ (100/y)/{80/(66 - y)} = 3/2
⇒ (100/y) × {(66 - y)/80} = 3/2
⇒ {5(66 - y)}/4y = 3/2
⇒ 660 - 10y = 12y
⇒ 22y = 660
⇒ y = 30

Question: Two friends invested Tk.1500 and Tk. 2500 in a business. They earned a profit of Tk. 800. One-half of the profit was divided equally between them and the other half was divided in proportion to their capitals. How much did each of them receive?

Solution:
Ratio of shares = 1500  : 2500
= 3 : 5

∴ Share of first friend = Tk. [(400/2) + {400 × (3/8)}]
= Tk. (200 + 150)
= Tk. 350

∴ Share of second friend = Tk. [(400/2) + {400 × (5/8)}]
= Tk. (200 + 250)
= Tk. 450

Question: A man spends a part of his monthly income and saves the rest. The ratio of his expenditure to the savings is 61 : 6. If his monthly income is Tk. 8710, the amount of his monthly savings is-

Solution:
Expenditure : Savings = 61 : 6

∴ Sum of the terms of ratio = (61 + 6) = 67

Given,
Total monthly salary = Tk. 8710

∴ Monthly savings = Tk.{(6/67) × 8710}
= Tk. 780

Question: A started a business with Tk. 4000 and is joined afterwards by B with Tk. 6000. After how many months did B join if the profits at the end of the year are divided equally?

Solution:
Let,
B joined after = x months

Then,
4000 × 12 = 6000 × (12 - x)
⇒ 48000 = 72000 - 6000x
⇒ 480 = 720 - 60x
⇒ 60x = 240
∴ x = 4

∴ B joined after 4 months.

Question: A mixture contains acid and water in the ratio 7 : 5. If 6 liters of water is added to the mixture, the ratio becomes 7 : 8. Find the quantity of acid in the given mixture.

Solution:
Let, the quantity of acid and water be 7x liters and 5x liters respectively

ATQ,
7x/(5x + 6) = 7/8
⇒ 56x = 7(5x + 6)
⇒ 56x = 35x + 42
⇒ 56x - 35x = 42
⇒ 21x = 42
∴ x = 2

So, Quantity of acid = (7 × 2) liters
= 14 liters

Question: A and B started a business investing amounts in the ratio of 2 : 3. If A has invested an additional amount of Tk. 12000, their ratio of investment would have been 3 : 2. The amount invested by A was?

Solution:
Let, their respective investments are 2x and 3x

If A added Tk. 12000 to his investment
Then the new ratio = 3 : 2

∴ (2x + 12000) : 3x = 3 : 2
⇒ 9x = 4x + 24000
⇒ 5x = 24000
⇒ x = 4800

Hence, the investment of A is = (2 × 4800)
= 9600

Question: Tk. 1500 is divided into three parts in the ratio (2/3) : (3/4) : (5/6), the 2nd part is-

Solution:
A : B : C = (2/3) : (3/4) : (5/6)
= {(2/3) × 12} : {(3/4) × 12} : {(5/6) × 12}
= 8 : 9 : 10

∴ Sum of the terms of ratio = (8 + 9 + 10)
= 27

So, First part = Tk.{(9/27) × 1500}
= Tk. 500

Question: A jar contains a total of 400 coins of 5 cents and 10 cents that add up to Tk 30. Find the number of 10-cent coins.

Solution:
Let,
the number of 10-cent coins be = x
So, the number of 5-cent coins is = (400 - x)

ATQ,
10x + {5 × (400 - x)} = (30 × 100)
⇒ 10x + 2000 - 5x = 3000
⇒ 5x = 1000
∴ x = 200

Therefore, there are 200 coins of 10 cents.

Question: In a regiment the ratio between the number of officers to soldiers was 3 : 31 before. In a battle 6 officers and 22 soldiers were killed and the ratio become 1 : 13, the number of officers in the regiment before battle was?

Solution:
Let, the number of officers and soldiers = 3x, 31x

ATQ,
(3x - 6)/(31x - 22) = 1/13
⇒ 39x - 78 = 31x - 22
⇒ 39x - 31x = - 22 + 78
⇒ 8x = 56
∴ x = 7

So, number of officer before = 3x
= 3 × 7
= 21

Question: Three friends P, Q, and R share the cost of renting a storage unit. P stores goods weighing 300 kg for 4 months, Q stores 200 kg for 6 months, and R stores 400 kg for 3 months. If the total rent is Tk 840, how much should R pay as their share of rent?

Solution:
Here,
P : Q : R = (300 × 4) : (200 × 6) : (400 × 3)
= 1200 : 1200 : 1200
= 1 : 1 : 1

∴ R's rent = {840 × (1/3)}
= Tk 280

Question: If two numbers are in the ratio 2 : 3 and the ratio becomes 3 : 4 when 8 is added to both the numbers, then the sum of the two numbers is-

Solution:
Let, the numbers be 2x and 3x respectively.

ATQ,
(2x + 8)/(3x + 8) = 3/4
⇒ 9x + 24 = 8x + 32
⇒ 9x - 8x = 32 - 24
⇒ x = 8

∴ Sum of numbers = 2x + 3x
= 5x
= 5 × 8
= 40