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

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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

________________________

Answer 2

Answer:

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