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One third of Krishna’s age is added to one fourth of Ganesh’s age is equal to two thirds of Krishna’s age. If the sum of their ages is 7 years more than twice the age of Krishna, find the sum of their ages.

a) 20
b) 22
c) 24
d) 26

User Pjvds
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1 Answer

6 votes

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.

User Haferje
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