Question

5 years ago A' age was four times the age of b.5 years hence ,A' age will be twice the age of B.find their present age

Answer 1

(a-5) =4(b-5)
a-5=4b-20
a-4b = -15----(1)

5 year hence..

a+5= (b+5)×2
a+5=2b +10
a-2b= 5----(2)

from 1 n 2

b=10 and a =25

Answer 2

Let the age of A be 'x' yrs and the age of B be 'y' yrs.....

5 yrs ago,
Age of A = x - 5
Age of B = y - 5

x - 5 = 4(y - 5)
x - 5 = 4y - 20
x - 4y = - 20 +5
x - 4y = - 15..............(i)

5 yrs hence,
Age of A = x +5
Age of B = y +5

x + 5 = 2(y +5)
x + 5 = 2y +10
x - 2y = 10 - 5
x - 2y = 5.............(ii)

Solving (i) and (ii) using elimination method,

x - 4y = - 15
x - 2y = 5
....................
- 2y = - 20
y = 10

Substituting y = 10 in (i)

x - 2*10 = 5
x - 20 = 5
x = 5 +20
x = 25

Therefore, present age of A is 25 yrs and B is 10 yrs....

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