The combined ages 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 do they have?
Answers
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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