The average age of 11 players of a cricket team is decreased by 2 months when two of them aged 17 ye

M4maths Previous Puzzles

03 Nov 2015 Age Problem

The average age of 11 players of a cricket team is decreased by 2 months when two of them aged 17 years and 20 years are replaced by two reserves. The average age of the reserves

OPtion

1) 17 years 1 months
2) 17 years 10 months
3) 17 years 7 months
4) 18 years 8 months
5) 18 years 2 months
6) 17 years 11 months
7) 18 years 9 months
8) 17 years 6 months
9) 18 years 3 months
10)None of these

Solution

Decrease in total age = (11*2) months = 1 years 10 months
Total age of reserves = 17+20 years - 1 years 10 momnths
= 35 years 2 months
Therefore Average age of reserves = 17 years 7 months

Option 3)

Correct Option: 3 Best Solution (25)

Sushmita Ghanty   9 years AGO

total age decreased =11*2=22 months
total age of previous 2 players= 20+17=37
total age of new players= 37yr-22 months = 35 yrs 2 months
average age= 17 yrs 7 months

Like? Yes (21) | No (4)  

Kethineni Vinodh   9 years AGO

11*2=22 months
17+20=37 years
37 yrs- 22 months=35 yrs 2 months
avg= 34 yrs 14 months/2= 17 yrs 7 months

Like? Yes (20) | No (8)  

ABHINAV PUSHPAM   9 years AGO

Let x be the average age of 11 players, and y be the average of the reserve players

(11x + 2y - 17 - 20)/11 = x - 2/12 or y = 211/12
So, 17 years 7 months
Option 3)

Like? Yes (12) | No (1)  

vamsi krishna   9 years AGO

the average age of new player = 17 yrs 7 months.
If initial average age of 11 players was x and average age of 2 new players is y, then
11x-11*(x-2/12) = 17+20-2y
y = 17 7/12 yrs = 17 yrs 7 months

Like? Yes (7) | No (2)  

PRAGATHI G   9 years AGO

let sum of ages be s
s/11=x
where x is average
after replacement.. (s-17yrs-20yrs+a)=(x-2months)
where a is the average of reserves
now substitute x=s/11
and solve..
we get avg as 17 and 7 momths

Like? Yes (5) | No   

RANJAN FADIA   9 years AGO

total decrease in age= 11* 2= 22 month
age of reserves = (17+ 20)year - (22 month)
= 37 year - 1 year 10 month
= 35 year 2 month

=> average age of reserve = 35 yr 2 month / 2
= 17 year 7 month

Like? Yes (8) | No (4)  

RAHUL KUMAR   9 years AGO

the average age of new player = 17 yrs 7
months.
If initial average age of 11 players was x
and average age of 2 new players is y, then
11x-11*(x-2/12) = 17+20-2y
y = 17 7/12 yrs = 17 yrs 7 months
Option (3) is correct answer.

Like? Yes (3) | No   

Dinni   9 years AGO

the average age of new player = 17 yrs 7 months.
If initial average age of 11 players was x and average age of 2 new players is y, then
11x-11*(x-2/12) = 17+20-2y
2y= 37-11/6= 211/6 yrs
y=211/12 yrs = 17 7/12 yrs = 17 yrs 7 months

Like? Yes (3) | No   

premlata   9 years AGO

Decrease = (11 * 2) months = 1 year 10 months

Total age of reserves
(17 + 20) years - (1 year 10 months) = 35 years 2 months

Avg. age of the reserves
(1/2) 35 years 2 months = 17 years 7 months

Like? Yes (3) | No   

Raghul Krishnan   9 years AGO

let x be the sum of 9 members out of that 11.
When 2 members of age, 17 and 20 are replaced, then the change in the sum of the ages of 9 members will be unchanged.
But, according to the given condition the initial average age decreases by two months after the replacement.
Hence, Considering a loss of 2 months in the age of each members will give
11 * 2 = 22(months)
22 months = 1 year 10 months
This ' 1 year 10 months ' will be the age reduced from the sum of those two members 17 & 20.
So, When " 1 year 10 months "
is subtracted from the 37 years (17+20),
then it will be
35 years 2 months
then the average of 35 years is ' 17 years 6 months '
and the average of 2 months is ' 1 month '
Then the total average age of 2 reserves is
'17 years 6 months ' + ' 1 month ' = ' 17 years 7 months '

Like? Yes (4) | No (1)  

chetan   9 years AGO

Decreased age=11*2=1year and 10 months
Total age of reserves is (17+20)-(1year 10 months)=35years 2 months
avg of reserves =0.5*35 yrs 10 months=17 years 7 months.
So option 3 is correct.

Like? Yes (1) | No   

M Sreekanth Yadav   9 years AGO

the average age of new player = 17 yrs 7 months.
If initial average age of 11 players was x and average age of 2 new players is y, then
11x-11*(x-2/12) = 17+20-2y
y = 17 7/12 yrs = 17 yrs 7 months

Like? Yes (1) | No   

harshavi   9 years AGO

if avg is considered p then the sum of all ages of sum=11p---(1)
then the new avg is sum-17-20+(x+y)=11q----(2)
then (1)-(2) we get
37-(x+y)=22
and (x+y)=422 months
and thus avg of reserves would be 211 months which means 17 years 7 months

Like? Yes (1) | No   

Dr.Dipin Singh   9 years AGO

If x is initial average age and R is average age of two reserves, then
11(x-2/12)= 11x-37+2R
R= 17 yrs 7 months

Like? Yes (1) | No   

chinu singla   9 years AGO

the average age of new player = 17 yrs 7 months.
If initial average age of 11 players was x and average age of 2 new players is y, then
11x-11*(x-2/12) = 17+20-2y
y = 17 7/12 yrs = 17 yrs 7 months

Like? Yes (1) | No   

Abhishek Jaiswal   9 years AGO

37 is equal to sum of reserves plus total decrement in age , 22 months

Like? Yes (1) | No   

MADHUBABU   9 years AGO

Let x be the average age of 11 players, and y be the average of the reserve players

(11x + 2y - 17 - 20)/11 = x - 2/12 or y = 211/12

So, 17 years 7 months

Like? Yes (1) | No   

tarun   9 years AGO

total decrease in sum= 11*2=22 months
so sum of reserve players age= 37years-22months=35 years 2 months
so average of reserves=35years 2 months/2=17years 7 months

Like? Yes (2) | No (1)  

ROHIT   9 years AGO

because the total age of two players is 37
from this age subtract 2*11=22 months
after that the age of two reserves is 35 years 2 months divided by 2= 17 years 7 months

Like? Yes (1) | No   

Venkateswarlu   9 years AGO

avg of 17 and 20 years players=18 years 6 moths
by replacing reserves avg decreased by 2 months.
18 years 6 months-11 months=17years 7 months

Like? Yes (1) | No   

Vaithiyanaathan   9 years AGO

Let the age of 9 players be a1 to a9.
(a1+a2+a3+a4+a5+a6+a7+a8+a9+17+20)/11=x
Therefore a1+a2+a3+a4+a5+a6+a7+a8+a9=11x-37
Now they are replaced by two reserves.
Let the age of reserves be a10 and a11.
(a1+a2+a3+a4+a5+a6+a7+ a8+a9+a10+a11)/11= x-(2/12).
substituting for sum of a1 to a9 we get
(11x-37 +a10+a11)/11 = x-0.166
simplifying
a10+a11= 35.174
divide by 2
a10+a11=17.587

0.5 of year is 6 months.
0.587 is 7.2 months.
rounding it
we get 17 years 7 months

Like? Yes (2) | No (2)  

Jaikumar Bhatia   9 years AGO

Sum of age of original 11 players=S
av age of original 11 players =S/11=x

S/11=x.............................(i)
sum of two reserve players =y

By subtracting two original players age of 17yrs(204months)&20yrs(240months)
and adding two reserve players age
the av. age becomes=x-2

formula for this would be
(S-204-240+y)=x-2.....................(ii)

By substituting value of S from (i) into (ii)
and simply (ii)

Y=422 months..sum of ages of two reseves

therefore av =y/2
=422/2
=211months
=17years and 7 months
option (3)

Like? Yes (3) | No (3)  

Priya Verma   9 years AGO

1year 10 months is to be subtracted from (20+17) years & to find average of two reserves divide the obtained result I.e. 35 years 2months so answer is 17 years 7 months...

Like? Yes (3) | No (3)  

anju sukumaran   9 years AGO

the average age of new player = 17 yrs 7 months.
If initial average age of 11 players was x and average age of 2 new players is y, then
11x-11*(x-2/12) = 17+20-2y
2y= 37-11/6= 211/6 yrs
y=211/12 yrs = 17 7/12 yrs = 17 yrs 7 months

Like? Yes (1) | No (1)  

JENSI KARUNYA.S   9 years AGO

correct answer is option 3) 17 years and 7months

Like? Yes (1) | No (2)