Question

The combined age of husband and wife are three times the combined ages of their children. Three years ago the ratio of their ages was 4 : 1, while 5 years after the ratio will be 20:9. How many children have they?

Answer 1

Given : The combined age of husband and wife are three times the combined ages of their children. Three years ago the ratio of their ages was 4 : 1, while 5 years after the ratio will be 20:9.

To Find : How many children have they?

Solution:

Let say number of  children = n

Combined  Age of n Children  = A

combined age of husband and wife  = 3A

Three years ago combined age of husband and wife  = 3A - 2 * 3 = 3A - 6

Three years ago combined age Combined  Age of n Children  = A - n * 3 = A - 3n  

Three years ago the ratio of their ages was 4 : 1

=>  3A - 6 = 4(A - 3n)

=> 3A - 6 = 4A - 12n

=> A = 12n - 6

5 years After combined age of husband and wife  = 3A+ 2 * 5 = 3A+10

5 years After combined age Combined  Age of n Children  = A+ n * 5 = A +5n

5 years after the ratio will be 20:9

=>  9(3A + 10) = 20(A + 5n)

=> 27A +90 = 20A +100n

=> 7A = 100n-90

12n - 6

=> 7 (12n - 6) =  100n-90

=> 84n - 42 = 100n-90

=> 16n =48

=> n = 3

Number of children = 3

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Answer 2

$\huge\tt{\bold{\underline{\underline{Question᎓}}}}$

The combined age of husband and wife are three times the combined ages of their children. Three years ago the ratio of their ages was 4 : 1, while 5 years after the ratio will be 20:9. How many children have they?

$\huge\tt{\bold{\underline{\underline{Answer᎓}}}}$

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➤Let take number of children = n

➤Combined Age of n Children = x

➤combined age of husband and wife = 3x

➤Three years ago combined age of

➤husband and wife 3x -2 3= 3x 6

Three years ago combined age

Combined Age of n Children = x - n *3

x=3n

Three years ago the ratio of their ages

was 4:1

=3x-6= 4(x - 3n)

=>3x- 6 = 4x -12n

=>x=12n-6

5 years After combined age of husband

and wife = 3x+ 2×5= 3x+10

5 years After combined age Combined

Age of n Children = x+n×5= x+5n

5 years after the ratio will be 20:9

9(3x +10)= 20(x+5n)

=>27x +90= 20x +100n

=7x =10On-90

12n- 6

=>7 (12n- 6) =100n-90

=>84n -42 =100n-90

=>16n =48

=>n = 33

$\bold{Number \:of\: children = 3}$

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