Question

Present age of Anu and Raj are in the ratio 4 : 5.Eight years from now the ratio of their ages will be 5 : 6.Find their present ages..

Answer 1

let present age of anu be x and raj's age be y.
x/y= 4/5
4y=5x
y= 5x/4

anu's age 8 years from now= x+8
raj's age 8 years from now= y+8
ratio
x+8=5
----- -----
y+8 6
6(x+8)=5(y+8)
6x+48= 5y+ 40
6x-5y= 40-48
6x-5y= - 8
6x-5(5x/4)= - 8
6x - 25x/4= -8
taking LCM 4
24x-25x/4= -8
-x/4= -8
-x= -32
x= 32

y= 5(32)/4
y= 40

therefore anu is 32years old while raj is 40 years old.

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Answer 2

let the age of Anu be "X" and the age of Raj be "y"
present ages = 4:5
X:Y = 4:5
X/Y = 4/5........ equation (1)

After '8' years , their ages become
X+18 : Y+18 = 5:6
x+8/y+8 = 5/6.......... equation (2)
X/Y = 4/5
5x= 4y
X=4y/5........ equation (3)
put this value in equation...(2)
X+8/y+8=5/6
4y/5+8/y+8=5/6
4y+40/5/y+8 = 5/6

4y+40/5 ÷y+8=5/6
4y+40/5 × 1/y+8 = 5/6

4y+40/5y+40=5/6

6(4y+40)=5(5y+40)
24y+240=25y+200
240-200=25y-24y
40=y or y=40..


X=4y/5=4(40)/5
X=32/5=32years..