Question

Roopa is twice as old as kiran.If 10 yr ago,roopa was 4 times as old as kiran, then the present age of roopa and kiran?

Answer 1

let present age of roopa be x and that of kiran be y
it is given that roopa is twice as old as kiran. therefore,
x=2y
x-2y=0.....................(eq1)
ten years ago,
roopa=x-10
kiran=y-10
it is given that ten years ago roopa was four times as old as kiran
x-10=4(y-10)
x-10=4y-40
x-4y=-40+10
x-4y=-30..........................(eq2)
from eq 1 and 2
by using substitution method

x−2y=0;x−4y=−30Step: Solvex−2y=0for x:x−2y+2y=0+2y(Add 2y to both sides)x=2yStep: Substitute2yforxinx−4y=−30:x−4y=−302y−4y=−30−2y=−30(Simplify both sides of the equation)−2y−2=−30−2(Divide both sides by -2)y=15Step: Substitute15foryinx=2y:x=2yx=(2)(15)x=30(Simplify both sides of the equation)Answer:x=30 and y=15
therefore
roopa= 30 years
kiran= 15 years

Answer 2

Let Kiran's present age be x
therefore, 
Present age of Roopa=2x
10 years ago........(flashback......)
Kiran's age then,
x-10
Roopa's age then,
2x-10

the, it is given that 
at that time Roopa's age was 4 times Kiran's age then
therefore,
4(x-10)=2x-10
4x-40=2x-10
4x-2x=40-10
2x=30
=>x=15
Therefore Kiran's present age is 15 years and Roopa's present age is 30 years