Question

Five years ago age of Nuri was thrice as old as Sona. Ten years later Nuri will be twice as old as Sona. How old are Nuri and Sona?

Answer 1

Hint: Now to solve this question let us assume the age of Nuri and Sona to be x and y respectively. Now 5 years ago the age of Nuri and Sona was x – 5 and y – 5. Now we are given that 5 years ago Nuri was thrice as old as Sona. Hence we get the first equation. Now 10 years later the age of Nuri and Sona will be 10 + x and 10 + y respectively and it is given that 10 years later Nuri will be twice as old as Sona. Hence we get the second equation as well. Now we will solve these two equations simultaneously to find x and y.

Complete step by step answer:
Now let us say the age of Nuri is x and the age of Sona is y.
This means 5 years ago the age of Nuri was x – 5 and the age of Sona was y – 5.
Now it is given that 5 years ago the age of Nuri and Sona was x – 5 and y – 5.
Now we know that 5 years ago Nuri was thrice as old as Sona
Hence x – 5 = 3(y – 5)
Opening the bracket we get x – 5 = 3y – 15
Rearranging the terms we get x – 3y = 5 – 15
Hence we have x – 3y = –10 ………………………………… (1)
Now 10 years later the age of Nuri and Sona was 10 + x and 10 + y respectively.
We know that Ten years later Nuri will be twice as old as Sona.
Hence we have 10 + x = 2(10 + y)
Now opening the bracket we get
10 + x = 20 + 2y.
Rearranging the terms we get x – 2y = 20 – 10
Hence we get x – 2y = 10 …………………………….. (2).
Now subtracting equation (1) from equation (2) we get
x – 2y – (x – 3y) = 10 – (–10)
hence we have y = 20.
Now substituting y = 20 in equation (2) we get
x – 20(2) = 10
x = 10 + 40
Hence we have x = 50.
Now hence we can say that the age of Nuri was 50 and the age of Sona was 20.

Note:
Now while calculating ages always remember which variables are chosen for which person also use the conditions very carefully. Now while solving the simultaneous equation we can solve it with different methods. For example, we can write x in terms of y from the first equation and then substitute that x in equation (2) to find the value of y. Now after solving the simultaneous equation always check if the values of x and y satisfy both the equations to be sure.