ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: The number of students in 3 classes is in the ratio of 2 : 3 : 4. If 12 students are increased in each class, this ratio changes to 8 : 11 : 14. The total number of students in the three classes at the start was-

Solution:
The number of students in 3 classes is in the ratio of 2 : 3 : 4.
Let the number of students in 3 classes be as follows 2x, 3x, 4x.
Total students = 9x.
According to the question, 2x + 12 : 3x + 12 : 4x + 12 = 8 : 11 : 14

Equating the ratio,
(2x + 12)/(3x + 12) = 8/11
→ 22x + 132 = 24x + 96
→ 2x = 36
→ x= 18
 
So, the total number of students in the three classes at the start was- 9 × 18 = 162.

Question: The salaries of A, B and C are in the ratio 1 : 3 : 4. If the salaries are increased by 5%, 10% and 15% 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 15%,
C's new Salary = (400 + 15% of 400) = Tk. 460

Then, ratio of increased Salary,
A : B : C = 105 : 330 : 460 = 21 : 66 : 92

Question: If A and B are in the ratio 3:4 and B and C are in the ratio 12:13, then A and C will be in the ratio.

Solution:
A and B are in the ratio 3:4 and B and C are in the ratio 12:13.



Another way,
Given, A and B are in the ratio = 3:4 -------(1)
B and C are in the ratio = 12:13.       --------(2)

To combine, make B's value the same (LCM of 4 and 12 is 12).

Thus, multiplying (1) by 3, we get,
 A:B = 9:12
and B:C = 12:13
Equating two ratios, we can achieve
→ A:C = 9:13

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%, then to get the average increased by 5%, C will be increased by-

Solution:
 Let
A= x, B = 2x, C = 3x.
Then,
x + 2x + 3x = 600 × 3
→ 6x = 1800
→ 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 = 105% of 600 = 630

∴ New value of C = (630 × 3) - (330 + 480)=1080
→ Increase in value of C = 1080 - 900 = 180 Tk.

Question: A bag contains red, blue, and green balls in the ratio 3 : 5 : 7. If there are 45 blue balls, how many total balls are there in the bag?

Solution: Given ratio = Red : Blue : Green = 3 : 5 : 7
Let the numbers be:
Red = 3x, Blue = 5x, Green = 7x

Given:
5x = 45
⇒ x = 45 ÷ 5 = 9

Now calculate total balls:
= 3x + 5x + 7x
= (3 + 5 + 7)x = 15x
= 15 × 9 = 135

Question: A jar contains black and white marbles. If there are ten marbles in the jar, then which of the following could not be the ratio of black to white marbles?

Solution:
Since the number of black and white marbles are whole numbers,
So the sum of the terms of the ratio must be a factor of 10.
ক) 1:4 = 1+4 = 5 a factor of 10.
খ) 1:10 = 1+10 = 11 not a factor of 10.
গ) 7:3 = 7+3 =10 a factor of 10.
ঘ) 9:1 = 9+1 = 10 a fac tor of 10.

Here we can see that the sum of only the second option is not a factor of 10

Question: The sum of money is divided among 160 males and some females in the ratio 16 : 21. Individually, each male gets Tk 4 and a female Tk 3. The number of females is-

Solution:
Let the number of females be x.
Then,
(160 × 4)/3x = 16/21
→ 48x = 160 × 4 × 21
→ x = 280

Question: If A invests Tk 5,000 for 12 months and B invests Tk 6,000 for 10 months, what is the ratio of their profits?

Solution:
We know, profit = (investment × time)
A has a profit of 5,000 × 12 = 60,000
B has a profit of  6,000 × 10 = 60,000
∴ So ratio of A's profit to B's profit = 60,000 : 60,000 = 1 : 1

Question: The sides of a triangle are in the ratio (1/2) : (1/3) : (1/4), and its perimeter is 104 cm. The length of the long side is-

Solution:
The sides of a triangle are in the ratio 1/2 : 1/3 : 1/4,
we multiply each term by 12 we get 6 : 4 : 3,
Let the sides be 6x, 4x, 3x 

Then, 13x=104
→ x= 8
• The length of the long side = 48.

Question: A and B start a business. A invests Tk 1,00,000 and B invests Tk 50,000. A works, B is a sleeping partner. A gets 20% of the profit for management. If total profit is Tk 30,000, what is A’s total share?

Solution:
First, A gets 20% of profit = 0.20 × 30,000 = Tk 6,000
Remaining = 24,000

→ This will be divided in the ratio of their investments: A : B = 100000 : 50000 
→ divided in 2 : 1 ratio

A’s share from this = (2/3) × 24,000 = 16,000
Total A = 6,000 + 16,000 = Tk 22,000

Question: A man distributes Tk.16500 among his daughter, wife and son in such a manner that the daughter's share and the wife's share are of 1 : 2 ratio, and the son gets half of the total amount. Find 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 = 16500/2
= 8250 Tk

→ Rest of the share = 3x
According to the question,
→ 3x= 8250
→ x= 2750

→ daughter's share = x = 2750 Tk