Question

The sum of the ages of A and B is 85 years. 5 years ago, the age of A was twice that of B. Find the present ages.

Answer 1

Hint: Now to solve the question we will consider the ages of A and B to be x and y respectively. Now we know that the sum of their ages is 85 years. Hence with this we get our first equation. Now age 5 years ago age of A was x – 5, similarly 5 years ago age of B was y – 5. Now we are given that 5 years ago the age of A was twice the age of B. Hence we get our second condition. Now using these conditions we get our second equation. Now we will solve the equations simultaneously to find the values of x and y.

Complete step by step answer:
Now first let us consider the present age of A to be x and present age of B to be y.
Now we are given that the sum of their ages is 85.
Hence we have x + y = 85. ……………………….. (1)
Now since their present age is x and y, their age 5 years before would have been x – 5 and y – 5 respectively.
Now we are given that 5 years ago the age of A was twice the age of B.
Hence we have (x – 5) = 2 (y – 5) ………………………. (2)
Simplifying equation (2) we get
x – 5 = 2y – 10
Rearranging the terms we get
x – 2y = - 5 ………………………………….. (3)
Now subtracting equation (3) from equation (1) we get.
x + y – x + 2y = 85 – (– 5)
3y = 90.
Hence we get 3y = 90
Dividing the equation by 3 we get
y = 30.
Now substituting y = 30 in equation (1) we have
30 + x = 85
Hence x = 85 – 30 = 55.
Hence x = 55 and y = 30
Now we have the sum of ages as 55 + 30 = 85
And 5 years ago age of A was 50 and age of B was 25. And we have 25 × 2 = 50.
Age of A is 55 and B is 30.

Note:
Now in the condition where the age of A was twice that of B note that this means age of A = 2 × age of B and not 2 × age of A = age of B. Also in such problems always substitute the values I equation and check if the conditions are satisfied.