Test: Average- 2

SUm of 5 odd numbers = 255
Average = 255/5 = 51
47…..49…..51……53……55
Average = 51
Sum of largest and small number = 47+55 = 102

Average = sum/n
Average of 9 students = x
n = 9

Seven of them give Rs. 5 = 7 x 5 = 35
35+(5+x)+(9+x)
∴ other two give Rs. 5 and Rs. 9 more than the average contribution

9x = 49 + 2x
9x - 2x = 49
7x = 49
x = 7

Let the original number be (10b+a)

  ​​ ​​​​ Because of interchange, the mistaken number is (10a+b)

  ​​ ​​​​ Given that, 10b+a = 10a+b +(2.7*10) => 9b-9a = 27 => b-a = 3

So, the correct answer is A. 

Option (2) 5:7 is correct✅answer. 

Explanation:-

Let age of A = 5 x

                   B=  4x

                   C = 6x 

Then, according to the question;

( 5x+5) + (6x+5) = 54

11x + 10   = 54

=> 11x  = 54-10

=> 11x = 44

=> x =  4

B's age after 4 years;

 = 4x +4 

=> 4*4+4 

=>  20 years. 

C's age after 4 years ;

= 6x+4 

=>6*4+4

=  28 years 

Therefore,  ratio = 20/28

=>       ratio = 5:7

 Let the rice quantity of Rs. 60 /kg rice be x.

Price for Rs. 40 /kg = 200*40

Price for Rs. 60/kg = x*60

After mixing the two types of rice the price = 50*(200+x)

The price will remain same after and before mixing, hence the equation becomes:

200*40 + x*60 = 50(200+x)

x(60-50) = 200*(50-40)

10x = 200*10

X = 200 kg​​ 
 

So, the correct answer is A.

Let the present age of the father be x 

∴ The present age of the son is (45−x) 

Five years ago Age of father =(x−5)
Age of son =((45−x)−5)=(40−x) 

⇒(x−5)(40−x)=4×(x−5)
⇒40x−200−x2+5x=4x−20
⇒x2−41x+180=0
⇒(x−36)(x−5)=0

⇒x=36 or x=5 (Not possible)
∴x=36 years   

∴ Present age of father =36 years  

∴ Present age of son =45−36=9 years

So, the correct answer is B.

Let Kamla's age 6 years ago be x years.
So, Kamla's present age = (x + 6) years
∴ x + 6 = 5x / 4
⇒ 4x + 24 = 5x
⇒ x = 24
So, Kamla's Present age = (x + 6) years = 30 years
∴ Son's present age = 30/10 = 3 years

So, the correct answer is B

Let x be the amount invested in bonds then 200000-x will be saved by John.

As per the questions, the interest earned is 20400 which includes both bonds and savings. Hence x*11/100 + 9*(200000-x) /100 = 20400

2x = 2040000-1800000 =​​ 240000

X= 120000 (Invested in bonds)

Savings = 200000-120000 = 80000 ​​​​ 

So, the correct option is A.

Let the father's age be 7x
and son's age be 3x
So, 7x*3x=756
21x^2=756
X^2=756/21
X^2=36
X=6
Father's age=7x=6*7=42
Son's age=3x=3*6=18
Father's age 6 year hence =42+6=48
Son's age 6 year hence=18+6=24
So, ratio of their ages after 6 years will be 48/24=2=2:1

Let the age of the Vimal and Arun be 3x, 5x resp.
From the given condition, we get
3x+5x=80 ⇒8x=80 ⇒ x=80/8=10Then, Vimal′s age is 3x=3×10=30 and Arun′s age is 5x=5×10=50
After ten years, Vimal's age will be 30 + 10 = 40
Arun’s age will be 50 + 10 = 60
Then their ratio = 40 : 60 = 2 : 3

So, the correct answer is A. 

Average of 5 numbers = 15

  ​​ ​​​​ Sum of these 5 numbers = 15*5 = 75

  ​​ ​​​​ Average of 3 of those numbers = 11

  ​​ ​​​​ Sum of these 3 numbers = 11*3 = 33

  ​​ ​​​​ Sum of remaining two numbers = 75-33 = 42

  ​​ ​​​​ Average of remaining two numbers = 42/2 = 21

So, the correct answer is B 

Given:

Present age

Age of father = 5 × Age of Son

3 years ago,

Age of father = 8 × Age of son

Calculation:

Let the age of father and son be F and S.

According to the question,

F = 5S      ----(1)

Again according to the question,

⇒ (F - 3) = 8(S - 3)      ----(2)

After equating the equation (1) and equation (2)

⇒ 5S - 3 = 8S - 24

⇒ -3S = -21

⇒ S = 7 years

From equation (1)

⇒ F = 5 × 7

⇒ F = 35 years

∴ The present age of the father is 35 years.

So, the correct option is A . 

Option (a) 49 is correct

Explanation:- 

  total run scored in 10 innings :-

=> 21.5 * 10 = 215

Total run he must score after 11 innings=  24*11 = 264

He must score in 11 th innings:-

( 264- 215) = 49

Let the ages of father and son be 4x and x respectively.

Product of ages = 196

4x X x = 196

4x^2 = 196

So, x^2 = 49

Thus x = 7

So, father's age and son's age = 28 and 7 respectively.

So, ratio after 5 years becomes;

28 + 5 : 7 + 5

= 33 : 12

= 11 : 4

So, the correct answer is C. 

According to the question,

We have the following statements:

The ratio of the ages of father and son at present is 6: 1. After 5 years the ratio will become 7:2

Now, let's take the age of the father to be 6x years and that of his son to be x years.

So, according to the second statement:

Using the cross multiplication method,

2(6x+5) = 7(x+5)

12x+10 = 7x+35

12x-7x = 35-10

5x = 25

x = 25/5

x = 5 years

Hence, the present age of the son is 5 years.

So, the correct option is C.

⠀⠀⠀⠀⠀

After 5 years, father's age = 3 × Son's age
5 years ago, father's age = 7 × Son's age

Calculation:
Let 5 years ago, son's age be s.
5 years ago, Father's age = 7 × s = 7s
After 5 years, son's age = s + 5 + 5 = s + 10
After 5 years, father's age = 7s + 5 + 5 = 7s + 10      ----(1)
After 5 years, father's age = 3 × Son's age = 3 × (s + 10)      ----(2)
Equating equation (1) and (2),
⇒ 7s + 10 = 3s + 30 
⇒ 7s – 3s = 30 – 10
⇒ 4s = 20
⇒ s = 20/4
⇒ s = 5
Present age of father = 7s + 5
⇒ 7 × 5 + 5
⇒ 35 + 5 = 40
∴ The present age of the father is 40 years.

Given:

Rahul's age 5 years ago : shiv's age 5 years hence = 3 : 5

Rahul : Riya = 5 : 4

(Shiv + Riya)'s average = 18 years

Calculation:

Let the present ages of Rahul and Riya be 5x and 4x.

Rahul's age 5 years ago = 5x - 5

so, Shiv's age after 5 years = 5/3(5x - 5)

∴ Shiv's present age = 5/3(5x - 5) - 5

A.T.Q

5/3(5x - 5) - 5 + 4x = 18 × 2 = 36

⇒ 25x/3 - 25/3 - 5 + 4x = 36

⇒ 37x/3 = 148/3

⇒ x = 148/37 = 4 years

Riya's present age = 4 × 4 = 16 years

∴ Riya's present age is 16 years.
 

So, the correct answer is E. 

Let the average age of board of consultants before replacement by a old consultant be a years. The sum of the ages of the consultants on the board = 10*a

The average age of the board of consultants 2 years age = a-2

The sum of the ages of the consultants on the board 2 years ago = 10(a-2)​​ 

After the older consultant was replaced with a younger man, the average remains the same as it was 2 yrs ago i.e., 10a hence, the younger man was 20 years younger to the old consultant.​​

So, the correct option is B.