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ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

পরীক্ষাব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্সতারিখতারিখ অনির্ধারিতসময়45 minutes২৭ বৈধ · অসম্পূর্ণ
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Math - 02 - Average, Problems on Ages
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স · তারিখ অনির্ধারিত · ২৮ প্রশ্ন

.
The average of 7 consecutive numbers is 20. The largest of these number is:
  1. ক) 21
  2. খ) 22
  3. গ) 23
  4. ঘ) 24
  5. ঙ) 25
সঠিক উত্তর:
গ) 23
উত্তর
সঠিক উত্তর:
গ) 23
ব্যাখ্যা

Let the number be,
x, x + 1, x + 2, x + 3, x + 4, x + 5 and x + 6,
Then (x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6)) / 7 = 20.
or 7x + 21 = 140
or 7x = 119
or x =17.
Latest number = x + 6 = 23.

.
Mr. Danny spends Tk.10000 monthly on average for the first four months and Tk.12000 monthly for the next eight months and saves Tk.26000 a year. His average monthly income is-
  1. ক) TK. 12500
  2. খ) TK. 14500
  3. গ) TK. 13500
  4. ঘ) TK.14000
  5. ঙ) TK.13800
সঠিক উত্তর:
গ) TK. 13500
উত্তর
সঠিক উত্তর:
গ) TK. 13500
ব্যাখ্যা

Total annual income
= TK (10000 X 4 + 12000 X 8 + 26000)
= TK. 162000
Average monthly income = TK 16200012 = TK. 13500

.
Find averages of the first 97 natural numbers.
  1. ক) 47
  2. খ) 37
  3. গ) 48
  4. ঘ) 49.5
  5. ঙ) 49
সঠিক উত্তর:
ঙ) 49
উত্তর
সঠিক উত্তর:
ঙ) 49
ব্যাখ্যা
Shot Cut: to solve this type of problem, sum up the first number and last number of the series and divide by 2.
So, ( 1 + 97)/2 = 49
.
The average age of a group of men is increased by 5 year when an 18 year old man is replaced by a 38 year old person. How many men were there in the group?
  1. ক) 3
  2. খ) 4
  3. গ) 5
  4. ঘ) 6
  5. ঙ) 7
সঠিক উত্তর:
খ) 4
উত্তর
সঠিক উত্তর:
খ) 4
ব্যাখ্যা

Let N be the no. of persons in the group.
Required number of person is given by;
Member in group × aged increased = difference of replacement
N × 5 = 38 - 18
Or, 5N = 20
Or, N = 4

.
The average weight of A, B and C is 45 kg. If the average weight of A and B is 40 kg and that of B and C be 43 kg, then the weight of B is:
  1. ক) 17 kg
  2. খ) 20 kg
  3. গ) 26 kg
  4. ঘ) 30kg
  5. ঙ) 31 kg
সঠিক উত্তর:
ঙ) 31 kg
উত্তর
সঠিক উত্তর:
ঙ) 31 kg
ব্যাখ্যা

Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 x 3) = 135 .... (i)
A + B = (40 x 2) = 80 .... (ii)
B + C = (43 x 2) = 86 ....(iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)
Subtracting (i) from (iv), we get : B = 31.
B's weight = 31 kg.

.
A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is:
  1. ক) 10
  2. খ) 20
  3. গ) 40
  4. ঘ) 73
  5. ঙ) 30
সঠিক উত্তর:
গ) 40
উত্তর
সঠিক উত্তর:
গ) 40
ব্যাখ্যা

Let there be x pupils in the class.
Total increase in marks = x . 1/2
= x/2
∴ x/2 = 83 - 63
=> x/2 = 20
=> x = 40

.
The average monthly income of P and Q is TK. 5050. The average monthly income of Q and R is TK. 6250 and the average monthly income of P and R is TK. 5200. The monthly income of P is:
  1. ক) 3500
  2. খ) 4050
  3. গ) 5000
  4. ঘ) 5050
  5. ঙ) 4000
সঠিক উত্তর:
ঙ) 4000
উত্তর
সঠিক উত্তর:
ঙ) 4000
ব্যাখ্যা

Let P, Q and R represent their respective monthly incomes. Then, we have:

P + Q = (5050 x 2) = 10100 .... (i)
Q + R = (6250 x 2) = 12500 .... (ii)
P + R = (5200 x 2) = 10400 .... (iii)

Adding (i), (ii) and (iii), we get:
2(P + Q + R) = 33000 or P + Q + R = 16500 .... (iv)

Subtracting (ii) from (iv), we get,
P = 4000.
∴ P's monthly income = TK. 4000.

.
The average of 11 numbers is 60. If the average of the first six numbers is 58 and that of the last six numbers is 63, then the middle number is:
  1. ক) 58
  2. খ) 60
  3. গ) 62
  4. ঘ) 64
  5. ঙ) 66
সঠিক উত্তর:
ঙ) 66
উত্তর
সঠিক উত্তর:
ঙ) 66
ব্যাখ্যা
Middle numbers = [(58 × 6 + 63 × 6) - 60 × 11]
= 66
.
A certain factory employed 600 men and 400 women and the average wage was TK. 25.50 per day, If a woman got TK. 5 less than a man, then what are their daily wages?
  1. ক) m:25.50 w:27.50
  2. খ) m:27.50 w:22.50
  3. গ) m:26.50 w:27.50
  4. ঘ) m: 24.50 w:26.50
  5. ঙ) m:26.00 w:27.00
সঠিক উত্তর:
খ) m:27.50 w:22.50
উত্তর
সঠিক উত্তর:
খ) m:27.50 w:22.50
ব্যাখ্যা

Then, daily wage of a woman = TK. (x - 5).
Now,
600x + 400 (x - 5) = 25.50 × (600 + 400)
=> 1000x = 27500
=> x = 27.50.
Man's daily wages = TK. 27.50;
Woman's daily wages = (x - 5)
= TK. 22.50.

১০.
The average age of A, B, C, D & E is 40 years. The average age of A and B is 35 years and the average of C and D is 42 years. Age of E is
  1. ক) 48
  2. খ) 46
  3. গ) 42
  4. ঘ) 45
  5. ঙ) 47
সঠিক উত্তর:
খ) 46
উত্তর
সঠিক উত্তর:
খ) 46
ব্যাখ্যা

Sum of their ages = 40 × 5 = 200 years
Sum of A & B’s ages = 35 × 2 = 70 years
Sum of C & D’s ages = 42 × 2 = 84
So, Age of E = 200 - (70 + 84) = 46

১১.
The average of four numbers 13, 27, 35, and X is 25. Find the number X.
  1. ক) 20
  2. খ) 25
  3. গ) 30
  4. ঘ) 35
  5. ঙ) None of above
সঠিক উত্তর:
খ) 25
উত্তর
সঠিক উত্তর:
খ) 25
ব্যাখ্যা

Average = (13 + 27 + 35 + X)/4 = 25
Or, X + 75 = 100
So, X = 25

১২.
The present ages of Samba and Bambi are in the ratio of 6:4. Five years ago their ages were in the ratio of 5:3. How old is samba?
  1. ক) 30
  2. খ) 36
  3. গ) 42
  4. ঘ) 48
  5. ঙ) 46
সঠিক উত্তর:
ক) 30
উত্তর
সঠিক উত্তর:
ক) 30
ব্যাখ্যা

Bambi’s present age = 6x,
Samba’s present age = 4x
Therefore,
(6x - 5)/(4x - 5) = 5/3
Or, 20x - 25 = 18x - 15
So, x = 5
And samba’s age = 6 × 5 = 30

১৩.
The average of 12 children is 15 years. If another child comes, the average age comes to 14. What is the age of the new child?
  1. ক) 5years
  2. খ) 7 years
  3. গ) 9 years
  4. ঘ) 11 years
  5. ঙ) 2 years
অনির্ধারিত
ব্যাখ্যা

Sum of 12 children ages = 12 × 15 = 180
Sum of the 13 children ages = 14 × 13 = 182
So age of new children = 182-180 = 2

লাইভ পরীক্ষার প্রশ্নে new average 14 এর পরিবর্তে 13 ছিলো। তাই উত্তর তুলে দেওয়া হয়েছে।

১৪.
The average of two numbers is 6.5 and the square root of their product is 6. What are the numbers?
  1. ক) 11 and 2
  2. খ) 8 and 5
  3. গ) 10 and 3
  4. ঘ) 9 and 4
  5. ঙ) 9 and 5
সঠিক উত্তর:
ঘ) 9 and 4
উত্তর
সঠিক উত্তর:
ঘ) 9 and 4
ব্যাখ্যা

According to the question,
(x + y)/2 = 6.5,
or, x + y = 13 and
xy = 36,
Now substitute the value of x and y from the option and find the answer.

১৫.
8 years ago, the ratio of A’s age to B’s age was 4:5. At present the ratio of B’s age to C’s age is 4:5. At present, the difference between A’s age and C’s age is 30 years, then what is the sum of the ages of A, B and c?
  1. ক) 138 years
  2. খ) 160 years
  3. গ) 148 years
  4. ঘ) 152 years
  5. ঙ) 164 years
সঠিক উত্তর:
গ) 148 years
উত্তর
সঠিক উত্তর:
গ) 148 years
ব্যাখ্যা

Let, 8 years ago,
the age of A and B was 4x and 5x respectively. Age of C = y
so, the present age of A and B is 4x + 8 and 5x + 8 respectively 

A/Q,
5x + 8 : y = 4 : 5 ------------ (1)
y - (4x + 8) = 20 ----------- (2)
Solving this equation we will get x = 8 and y = 60

So, present age of Age of A = 4×8 + 8
= 40
and present age of B = 5×8 + 8 
= 48
From equation (1),
C = {(5x + 8) × 5} ÷ 4 = 60

So, the total age of A, B & C= 40 + 48 + 60
= 148

১৬.
The average height of girls in a class is 5 feet and that of boys is 5.7 feet. If the average height of the students in class is 5.5 feet. What could be the possible strength of boys and girls respectively in the class:
  1. ক) 50, 25
  2. খ) 30, 20
  3. গ) 20, 30
  4. ঘ) 60, 50
  5. ঙ) 50, 20
সঠিক উত্তর:
ঙ) 50, 20
উত্তর
সঠিক উত্তর:
ঙ) 50, 20
ব্যাখ্যা

The number of boys = B
The number of Girls = G
According to question, 5G + 5.7B = 5.5(B + G)
Or, 0.2B = 0.5G
Or, B:G = 5:2
Now, sum of the ratio= 7.
Sum of one option is divisible by 7 that is = 50 + 20
= 70

১৭.
7 years ago, son’s age was 1/5th of the father’s age. If the ratio of their present ages is 1:3, what will be the ratio of their ages after 7 years?
  1. ক) 2:5
  2. খ) 3:5
  3. গ) 5:11
  4. ঘ) 3:7
  5. ঙ) None of above
সঠিক উত্তর:
ঘ) 3:7
উত্তর
সঠিক উত্তর:
ঘ) 3:7
ব্যাখ্যা

Let,
7 years ago son’s age was x years old and father’s age was 5x year.
Now,
(x+7)/(5x+7) = 1/3,
so x = 7
Son’s age = 7 + 7 = 14
Father’s age= 5 × 7 + 7 = 42
After 7 years,
Son’s age : Father’s age = 21:49 = 3:7

১৮.
Father is aged three times more than his son Roni. After 8 years, he would be two and a half times of Roni's age. After another 8 years, how many times would he be of Ronit's age?
  1. ক) 2 times
  2. খ) 2.5 times
  3. গ) 2.75 times
  4. ঘ) 3 times
  5. ঙ) 3.5 times
সঠিক উত্তর:
ক) 2 times
উত্তর
সঠিক উত্তর:
ক) 2 times
ব্যাখ্যা

Let Roni's present age be x years. Then, father's present age =(x + 3x) years = 4x years.
there4 (4x + 8) = (5/2)(x + 8)
=> 8x + 16 = 5x + 40
=> 3x = 24
=> x = 8.

Hence, required ratio = (4x + 16)/(x + 16)
= 48/24
= 2

১৯.
A father said to his son, ''I was as old as you are at the present at the time of your birth''. If the father's age is 38 years now, the son's age five years back was:
  1. ক) 14 years
  2. খ) 19 years
  3. গ) 33 years
  4. ঘ) 38 years
  5. ঙ) 40 years
সঠিক উত্তর:
ক) 14 years
উত্তর
সঠিক উত্তর:
ক) 14 years
ব্যাখ্যা

Let the son's present age be x years.
Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back = (19 - 5)
= 14 years.

২০.
Sum of the ages of 5 children born in regular intervals of 3 years each is 50 years. What is the age of the youngest children?
  1. ক) 4 years
  2. খ) 8 years
  3. গ) 10 years.
  4. ঘ) 6 years
  5. ঙ) None of these
সঠিক উত্তর:
ক) 4 years
উত্তর
সঠিক উত্তর:
ক) 4 years
ব্যাখ্যা

Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
⇒ 5x = 20
⇒ x = 4.
∴ Age of the youngest child = x = 4 years.

২১.
The average age of a group of 10 students is 15 years. When 5 more students join the group, the average age increases by 1 year. The average age of the new students is?
  1. ক) 12 years
  2. খ) 16 years
  3. গ) 18 years
  4. ঘ) 20 years
  5. ঙ) 22 years
সঠিক উত্তর:
গ) 18 years
উত্তর
সঠিক উত্তর:
গ) 18 years
ব্যাখ্যা

Total age of 10 students = 150 years
Total age of 15 students = 240 years
Total age of 5 new students = 240 - 150 = 90 years
Therefore,
Average age of 5 new students = 90/5 = 18 years

২২.
20 years ago, my age was 1/3 of what it is now. What is my present age?
  1. ক) 66 years
  2. খ) 36 years
  3. গ) 33 years
  4. ঘ) 35 years
  5. ঙ) 30 years
সঠিক উত্তর:
ঙ) 30 years
উত্তর
সঠিক উত্তর:
ঙ) 30 years
ব্যাখ্যা

Let the present age be x years.
20 years ago my age was x - 20.

According to given data,
x - 20 = x/3
=> 2x = 60
=> x = 30

২৩.
When I was married 10 years ago my wife became the 6th member of the family. Today my father died and a baby born to me. The average age of my family during my marriage is the same as today. What was the age of Father when he died?
  1. ক) 50 yrs
  2. খ) 60 yrs
  3. গ) 70 yrs
  4. ঘ) 65 yrs
  5. ঙ) 70 yrs
সঠিক উত্তর:
খ) 60 yrs
উত্তর
সঠিক উত্তর:
খ) 60 yrs
ব্যাখ্যা

Let the Father be x years when he died.
Average Age 10 years ago be A.
Total Age 10 years ago = 6 × A
Total Age after 10 years(Just before father's Death) = 6A + 6 × 10 = 6A + 60
Father Died and Baby was born => the Total number of people in the family is Same (6)
Baby born today so age of baby = 0
(6A + 60 - x)/6 = 6A/6
=> A + 10 -(x/6) = A
=> x/6 = 10
=> x = 60
Therefore we can conclude that the father was 60 years old when he died.

২৪.
The ratio of the ages of Maala and Kala is 4 : 3. The total of their ages is 2.8 decades. The proportion of their ages after 0.8 decades will be- [1 Decade = 10 years]
  1. ক) 4:3
  2. খ) 12:11
  3. গ) 7:4
  4. ঘ) 6:5
  5. ঙ) None of the above
সঠিক উত্তর:
ঘ) 6:5
উত্তর
সঠিক উত্তর:
ঘ) 6:5
ব্যাখ্যা

Let,
Maala’s age = 4A and
Kala’s age = 3A
Then,
4A + 3A = 28
A = 4
Maala’s age = 16 years
and Kala’s age = 12 years
Proportion of their ages after 8 is = (16 + 8) : (12 + 8)
= 24 : 20
= 6 : 5

২৫.
Six years ago Anika was P times as old as Benu was. If Anika is now 17 years old, how old is Benu now in terms of P?
  1. ক) (11/P) + 6
  2. খ) (P/11) + 6
  3. গ) 17 - (P/6)
  4. ঘ) 17/P
  5. ঙ) 17p - 6
সঠিক উত্তর:
ক) (11/P) + 6
উত্তর
সঠিক উত্তর:
ক) (11/P) + 6
ব্যাখ্যা

Let Benu’s age now be B.
Anika’s age now is A.
(A - 6) = P(B - 6)
But A is 17 and therefore 11 = P(B - 6)
11/P = B - 6
(11/P) + 6 = B

২৬.
Sahin is younger than Ratul by 7 years. If the ratio of their ages is 7:9, find the age of Sahin.
  1. ক) 24.0
  2. খ) 25.5
  3. গ) 26.5
  4. ঘ) 27.5
  5. ঙ) 24.5
সঠিক উত্তর:
ঙ) 24.5
উত্তর
সঠিক উত্তর:
ঙ) 24.5
ব্যাখ্যা

If Ratul age is x,
then Sahin age is x - 7,
so, (x - 7)/x = 7/9
9x - 63 = 7x
2x = 63
x = 31.5
So, Sahin age is = 31.5 - 7
= 24.5

২৭.
A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is-
  1. ক) 20
  2. খ) 21
  3. গ) 22
  4. ঘ) 23
  5. ঙ) 25
সঠিক উত্তর:
গ) 22
উত্তর
সঠিক উত্তর:
গ) 22
ব্যাখ্যা

Let the son's present age be x years.
Then, man's present age = (x + 24) years
=> (x + 24) + 2 = 2(x + 2)
=> x + 26 = 2x + 4
So, x = 22

২৮.
Raju decided to marry 3 years after he got a job. He was 17 years old when he passed class 12th. After passing class 12th, he completed his graduation course in 3 years and PG course in 2 years. He got the job exactly 1 year after completing his PG course. At what age will he get married?
  1. ক) 27 yr
  2. খ) 26 yr
  3. গ) 28 yr
  4. ঘ) 23 yr
  5. ঙ) None
সঠিক উত্তর:
খ) 26 yr
উত্তর
সঠিক উত্তর:
খ) 26 yr
ব্যাখ্যা

Age of Raju when he got the job = 17 + 3 + 2 + 1 = 23 yr

Age of Raju at the time of marriage = 23 + 3 = 26 yr