Question 561108: The ratio of the ages of John and Janet is 3:4. In four years time the ratio of their ages will be 4:5. Find their present ages? Answer by Maths68(1474) (Show Source):
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Let
Present age of John = j
Present age of Janet = t
The ratio of the ages of John and Janet is 3:4
j:t=3:4
j/t=3/4
j=3t/4...........(1)
In four years time
John will be = j+4
Janet will be = t+4
Then
the ratio of their ages will be 4:5
(j+4):(t+4)=4:5
(j+4)/(t+4)=4/5
5(j+4)=4(t+4)
5j+20=4t+16
5j=4t+16-20
5j=4t-4.............(2)
Put the value of j from (1) to (2)
5(3t/4)=4t-4
15t/4=4t-4
15t=4(4t-4)
15t=16t-16
15t-16t=-16
-t=-16
Multiply by -1 both sides of above equation
t=16
Put the value of t in (1)
j=3t/4...........(1)
j=3(16)/4
j=3*4
j=12
Present age of John = j = 12 years old
Present age of Janet = t = 16 years old
