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

Step-by-step explanation:

Let p= present sum of the parents ages

Let c= present sum of the children's ages

Let n= number of children

THE SUM OF AGES OF HUSBAND AND HIS WIFE IS 4 TIMES THE SUM OF AGES OF THEIR CHILDREN.

∴ p=4c ....(1)

4 YEARS AGO THE RATIO OF THEIR AGES TO THE AGES OF THEIR CHILDREN WAS 18:1

That will reduce the sum of the parents ages by 8, the children's age by 4n

∴ p−8=18(c−4n)

∴ p−8=18c−72n .....(2)

replace p with 4c (From (1))

∴ 4c−8=18c−72n

subtract 18c from both sides and rearrange to:

∴ −14c+72n=8 .......(3)

2 YEARS HENCE THE RATIO WILL BE 3:1.

that will increase the parents age sum by 4, the children's age by 2n

∴ p+4=3(c+2n)

∴ p+4=3c+6n .....(4)

replace p with 4c (From (1))

∴ 4c+4=3c+6n

subtract 3c from both sides and rearrange to:

c=6n−4 .....(5)

In the (3) replace c with (6n−4)

∴ −14(6n−4)+72n=8

∴ −84n+56+72n=8

∴ −12n=8−56

∴ −12n=−48

∴ n=−48/−12

∴ n=4

Number if children's=4

Answer 2

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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

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