calculate ages of all

@manish-r2Hoep • Oct 22, 2024

Oct 22, 2024

1.1K

Fifteen years back my neighbour mrs sareen had 3 daughter sudha ,seema and reema and their combined ages were half of hers.During next five years sonny was born and mrs sareen age equalled the total of all her children ages
after some years kishu was born and then sudha was as old as reema and sonny together .And now the combined age of al children is double mrs sareen age which is as matter of fact only equal to that of sudha and seema together .SUDHA age is equal to that of two sons
what is the age of each one of them?

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4M4N

@4m4n-jQmegc • Dec 25, 2010

kishu=9, reema=18, sudha=21, seema=18, sonny=12 and sareen=39,
correct me if wrong
Ankita Katdare

@abrakadabra • Dec 25, 2010

@4M4N: Please put the explanation or solving process.
Manish Goyal

@manish-r2Hoep • Dec 25, 2010

Please explain the answer
4M4N

@4m4n-jQmegc • Dec 25, 2010

sorry friends, i jst read the answer from a book , no explanation was given there
makru921

@makru921-Am65Ah • Dec 26, 2010

25 minutes and all i have is a bunch of nonsensical equations😔 Hope somebody can explain it if there is a correct answer..
Ankita Katdare

@abrakadabra • Dec 26, 2010

@Makru: Same here.
I am not able to build a relation between the equations.
Saandeep Sreerambatla

@saandeep-sreerambatla-hWHU1M • Dec 28, 2010

This is not a direct question which can be solved by equations.

We need to solve this using equations and by probable substitutions.

I got the solution after 1 hour of work, nice question goyal.

And yes, the answers are correct.
Saandeep Sreerambatla

@saandeep-sreerambatla-hWHU1M • Dec 28, 2010

Now let us assume the ages of everyone for variables.

Sareen = M , sudha = X , seema = Y , Reema = Z , sonny = a and Kishu = b.

Now few points to be noted are, Sonny age will be between 10 - 15 and that of Kishu will be below 10.

Now from the condition 1:

1/2(M-15) = X + Y+ Z - 45
which comes down to

M = 2(X + Y+ Z)-75 -----------------------------(1)

For condition 2:

M-10 = X + Y+ Z-30 + a – 10

Substituting 1 in the above equation we get

M = 2a + 15 -----------------------------(2)

Now from another condition ,

X + Y+ Z+a+b = 2M

And M = X+Y and X = a+b (all given)

Now, M+Z+X = 2M (a+b = X)

So, X+Z = M

And we also know that X + Y = M , which results in Y = Z.

So which states that Seema and Reema are twins and also states that Sudha is the eldest.

Now 1 will be modified as ,

M + 75 = 2(X + Y+ Z) , since X + Y = M

M + 75 = 2M + 2Z which gives

2Z = 75 – M ----------------------(F1)

Now, we go back to the equation 2.

As already stated Sonny’s age will be in 10 – 15, his age will be 11, 12, 13 and 14.

2(11) + 15 = M = 37

Putting this in F1 , will give Z = 19 , and Y = 19 as Y and Z are twins.

This results in X = 18 which is incorrect as Sudha is eldest.

Now, we will substitute Sonny’s age as 12.

Which results in M = 39

Which gives , Z = Y = 18

And X = 21

And X = a+b , which gives b = X – a = 21-12 = 9 J

Hence got the solution.

All other values of Sonny will result in b > 10 which is not valid.

Hope everyone understood.
Ankita Katdare

@abrakadabra • Dec 28, 2010

@ES: That was simply superb! You've got a knack. 😀
Sahithi Pallavi

@sahithi-oJZaYj • Dec 28, 2010

Fantastic ES! You are superb! 😀
makru921

@makru921-Am65Ah • Dec 28, 2010

Wow.. impressive! I reached the equations stage but then dint bother to substitute and all.. Got lazy😀 But this is perfectly done and explained.. Good job ES😀
Reya

@reya-SMihdC • Dec 28, 2010

@ES:Hats off to you!I was trying for a long time!