SOLUTION: sum of ages of man and wife is 6 times the sum of age of children 2 years ago sum was 10 time sum of ages of their children After 6 years sum of their ages will be 3 times sum of

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Question 940341: sum of ages of man and wife is 6 times the sum of age of children 2 years ago sum was 10 time sum of ages of their children After 6 years sum of their ages will be 3 times sum of ages of their find out how many children
Answer by krutarthas(22) (Show Source):
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sum of ages of man and wife is 6 times the sum of age of children 2 years ago sum was 10 time sum of ages of their children After 6 years sum of their ages will be 3 times sum of ages of their find out how many children?
Answer:-
ok letus take man age is x year
his wife age is y year
and sum of children age is z year
number of children = p nos
as per given condition
sum of ages of man and wife is 6 times the sum of age of children
x+y=6z ------(1)
2 years ago sum was 10 time sum of ages of their children
x-2+y-2=10(z-2p) (p times 2 years less than the sum of children age)
x+y-4=10z-20p------(2)
After 6 years sum of their ages will be 3 times sum of ages of their children
x+6+y+6=3(z+6p) (p times 6 years greater than the sum of children age)
x+y+12=3z+18p ------(3)
solving the equation (2) puting eq(1) result
x+y-4=10z-20p
⇒6z-4=10z-20p (where x+y=6z ----eq(1))
⇒20p-10z+6z-4=0
⇒20p-4z=4
⇒ -4z+20p =4 ------(4)
solving the equation (3) puting eq(1) result
x+y+12=3z+18p
⇒6z+12=3z+18p (where x+y=6z ----eq(1))
⇒6z-3z-18p+12=0
⇒3z-18p+12=0
⇒3(z-6p+4)=0
⇒z-6p+4=0
⇒z-6p=-4
⇒z=6p-4 ------(5)
solving the equation (4) puting eq(5) result
-4z+20p =4
⇒-4(6p-4)+20p=4 (where as per eq(5) z=6p-4 )
⇒-24p+16+20p=4
⇒-24p+20p=4-16
⇒-4p=-12
⇒p=-12/-4=3
⇒p=3
so, number of children are 3
answer
Krutartha