ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: If on a test, three people answered 90% of the questions correctly and two people answered 80% correctly, then the average for the group of five people is-

Solution:
- ৩ জন পরীক্ষার্থী ৯০% সঠিক উত্তর দিয়েছে
- ২ জন পরীক্ষার্থী ৮০% সঠিক উত্তর দিয়েছে
- Total students (মোট পরীক্ষার্থী) = 3+2=5

- মোট শতাংশ:
3×90 %+2×80%
=(270+160)%
=430%

- গড় শতাংশ নির্ণয়:
430%÷5 (মোট ৫ জন পরীক্ষার্থী)
=86%

- তাই গড় হবে: 86%.

Question: In 2007, the arithmetic mean of the annual incomes of Jarif and Naim was Tk 3800. The arithmetic mean of the annual incomes of Naim and Jamil was Tk 4800, and the arithmetic mean of the annual incomes of Jamil and Jarif was Tk 5800. What is the arithmetic mean of the incomes of the three?

Solution: It is given that in 2007, the arithmetic mean of the annual income of,
Jarif and Naim = 3800 Tk.
Naim and Jamil = 4800 Tk.
Jamil and Jarif = 5800 Tk.

Let a, b, and c be the annual incomes of Jarif, Naim, and Jamil, respectively.

Now, we are given that the arithmetic mean of the annual incomes of Jarif and Naim was Tk 3800.
Hence, (a + b)/2 = 3800
⇒ a + b = 2 × 3800 = 7600   -----------------------(1)

The arithmetic mean of the annual incomes of Naim and Jamil was Tk 4800.
Hence, (b + c)/2 = 4800
⇒ b + c = 2 × 4800 = 9600  -------------------------(2)
The arithmetic mean of the annual incomes of Jarif and Jamil was Tk 5800.
Hence, (c + a)/2 = 5800
⇒ c + a = 2 × 5800 = 11,600 -------------------------(3)

Summing these three equations(1+2+3) yields,  
⇒ (a + b) + (b + c) + (c + a) = 7600 + 9600 + 11,600
⇒ 2a + 2b + 2c = 28,800
⇒ a + b + c = 14,400
The average of the incomes of the three equals the sum of the incomes divided by 3:
⇒ (a + b + c)/3 = 14,400/3 = 4800

Question: Find the Arithmetic mean of 3, 6, 7, and 4.

Solution:
The mean is calculated first by taking the sum of all the values 3+6+7+4 = 20
- and then dividing it by, 4 (as we have a total of 4 terms.)
∴ Arithmetic mean =  20/4 = 5
Thus, the arithmetic mean of the given value is 5.

Question: The sum of the present ages of a mother and daughter is 50 years. Five years ago, the mother was seven times as old as the daughter. How much older is the mother than the daughter?

Solution:
Let mother’s age = M, daughter’s age = D.
Given:
⟹ M+D=50 --------------------------(1)
Five years ago:
⟹ M−5=7(D−5)  
⟹  M−5=7D−35 
⟹  M=7D−30 ---------------------(2)

Substitute Equation 2 into Equation 1:
(7D−30)+D=50 
⟹  8D=80 
⟹ D=10 (Daughter's age)

Then,
M=50−10=40. (Mother's age)
Age difference: 40−10=30
Answer: 30

Question: Today, Jakir is twice as old as Moin. In 5 years, Jakir will be 1.5 times as old as Moin. How old is Jakir today?

Solution:
Let Jakir’s age = J, Moin’s age = M.
Given:
⇒ J=2M --------------------(Equation 1)
In 5 years:
⇒ J+5=1.5(M+5)J+5=1.5(M+5) ---(Equation 2)

Substitute J=2M (equation 1) in equation (2),
⇒ 2M+5=1.5M+7.5  ⟹  0.5M=2.5  
⟹  M=5
Then, J=2×5=10
Answer: 10

Question: A group of 30 employees of Cadre A has a mean age of 27. A different group of 70 employees of Cadre B has a mean age of 23. What is the mean age of the employees of the two groups together?

Solution:
• Cadre A has a mean age = 27
- Total employees = 30
- Total age = 27×30 = 810 years

On the other hand,
• Cadre B has a mean age = 23
- Total employees = 70
- Total age = 1610 years

• From both the A and B cadre groups,
- Total employees = 100
- Total age = 2420 years
Now, Mean or Average = 2420/100 = 24.2 years.

Question: Ten years ago, the age of a father was four times his son's age. Ten years from now, the father will be twice as old as his son. What is the ratio of their current ages?

Solution:
Let father’s current age = F,
son’s current age = S
Ten years ago:
F−10=4(S - 10)  
⟹  F−10=4S - 40 
 ⟹  F=4S - 30 ------------(Equation 1)

Ten years later:
F+10=2(S+10)  
⟹  F+10=2S+20  
⟹  F=2S+10 ------------(Equation 2)

Set Equation 1 = Equation 2 (উভয় এই পিতার বয়স):
4S−30=2S+10  ⟹  2S=40 
 ⟹  S=20

Then, F=2(20)+10=50
Ratio:
F : S
=50 : 20 =5 : 2
Answer: 5 : 2

Question: A student scored 70, 80, 75, and 85 in four subjects. What score must he get in the fifth subject to have an average of 80?

Solution:
- If the average is 80, then
- Total marks needed = 80 × 5 = 400
- Marks so far obtained in 4 subjects = 70 + 80 + 75 + 85 = 310
- Marks Required to obtain desired average = 400 - 310 = 90

Question: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?

Solution:
Let the age of the initially born children = x years old,
Then, according to the question,(প্রতিটি বাচ্চার বয়সের পার্থক্য ৩ বছর করে তাই)
The ages of children be x, (x + 3), (x+3+3)= (x+6), (x+6+3)= (x + 9) and (x+9+3)=(x + 12) years.

Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
⇒ 5x+ 30 = 50
⇒ 5x = 20
⇒ x = 4

 Age of the youngest child ⇒ x = 4 years.

Question: The average of 6 consecutive numbers (integers) is 19.5. What is the largest of these numbers?

Solution:
Let the 6 consecutive integers be:
x, x+1, x+2, x+3, x+4, x+5.

Their sum is:
Sum=x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)=6x+15
To calculate the average, we use the average formula
Average: Summation/ total number
= 6x+15 / 6 = 19.5​

We multiply both sides by 6:
6x+15=117
⇒6x=102
⇒x=17

So the numbers are:
17, 18, 19, 20, 21, 22
- Largest number = 22.

Question: The average marks of 50 students was found to be 60. Later, it was found that a student’s marks were wrongly entered as 80 instead of 50. What is the correct average?

Solution :
Firstly, wrong total = 50 × 60 = 3000
An error happened in one student's mark = 80 - 50 = 30.
Correct total = 3000 - 30 = 2970
Correct average = 2970 ÷ 50 = 59.4

Question: Present ages of Sameer and Ananda are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Ananda's present age in years?

Solution:
Let the present ages of Sameer and Ananda be 5x years and 4x years respectively.

Then,

 
⇒ 9(5x + 3) = 11(4x + 3)
⇒ 45x + 27 = 44x + 33
⇒ 45x - 44x = 33 - 27
⇒ x = 6
 Anand's present age = 4x = 24 years

Question: The average age of a family of four members is 26 years. If the youngest member is 14 years old, what is the average age of the remaining members?

Solution:
Total age of all 4 members = 4 × 26 = 104 years
Youngest member's age = 14 years
Remaining total age = 104 - 14 = 90
Average age of 3 remaining = 90 ÷ 3 = 30 years