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? don't post unnecessary answer please .l​

Answer 1

Answer:

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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➤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

Number of children = 3