Question 507242: Mary's age is 2/3 that of peter.2 years ago marys age was 1/2 of what petr age will be in5 years time,how old is peter know Answer by Maths68(1474) (Show Source):
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Present of age of Mary = m
Present of age of Peter = p
Mary's age is 2/3 that of Peter.
m=2/3 * p
m=2p/3 .............(1)
2 years ago means we have to subtract 2 from their present ages
m-2=p-2
then
Mayr's age was 1/2
m-2=1/2(p-2)
of what Peter age will be in 5 years time means we have add 5 to age of Peter what was it 2 years ago
m-2=1/2[(p-2)+5)]
Multiply by 2 both sides of the equation
2(m-2)=2*1/2[(p+5)-2)]
2m-4=(p+5)-2)
2m-4=p+5-2
2m-4=p+3
2m-p=3+4
2m-p=7
Put the value of m from (1)in above equation
2(2p/3)-p=7
(4p/3)-p=7
Multiply by 3 both sides of the equation
4p-3p=21
p=21
Put the value of p in (1)
m=2p/3 .............(1)
m=2(21)/3
m=2*7
m=14
Present of age of Mary = m = 14 years old
Present of age of Peter = p = 21 years old
Check
Mary' age = 2/3 Peters age
14 = 2/3 * 21
14 = 42/3
14 = 14
2 years ago Mary's age = 14-2 = 12
2 years ago Peter's age = 21-2 = 19
after 5 years Peter's age = 19 + 5 = 24 which is twice the age of Mary or Mary's age 1/2 of the Peter.
