Final answer:
To solve this problem, set up equations based on the given information. Simplify the equations and solve the system to find the values of x and y. Substitute the values back into one of the equations to find their sum.
Step-by-step explanation:
To solve this problem, we need to set up equations based on the given information. Let's assume Krishna's age is x and Ganesh's age is y.
From the first part of the problem, we can write the equation:
1/3 x + 1/4 y = 2/3 x
Next, we're told that the sum of their ages is 7 years more than twice Krishna's age:
x + y = 2x + 7
We have two equations with two variables, so we can solve the system of equations to find the values of x and y. Let's simplify the equations:
4/12 x + 3/12 y = 8/12 x
x + y = 2x + 7
Multiplying the first equation by 12 to get rid of fractions, we have:
4x + 3y = 8x
x + y = 2x + 7
Simplifying further:
3y = 4x
y = 4/3x
x + y = 2x + 7
Now we substitute the value of y from the second equation into the third equation:
x + 4/3x = 2x + 7
Simplifying:
3x + 4x/3 = 2x + 7
Multiplying through by 3 to get rid of the fraction:
9x + 4x = 6x + 21
13x = 6x + 21
Subtracting 6x from both sides:
7x = 21
Dividing both sides by 7:
x = 3
Now we can substitute the value of x back into one of the equations to find y:
3 + y = 2(3) + 7
3 + y = 6 + 7
y = 10
The sum of their ages is x + y = 3 + 10 = 13.