Question

There are 3 persons sudhir, arvind, and gauri. Sudhir lent cars to arvind and gauri as many as they had already. After some time arvind gave as many cars to sudhir and gauri as many as they have. After sometime gauri did the same thing. At the end of this transaction each one of them had 24. Find the cars each originally had.

Answer 1

Answer:

Sudhir = 39

Arvind = 21

Gauriv = 12

Step-by-step explanation:

Suppose the number of cars with Sudhir, Arvind and Gauri initially be: X, Y, Z.

After the first transaction, number of cars with:

Sudhir = X - Y - Z

Arvind = 2Y

Gauri = 2X

After second transaction, number of cars with:

Sudhir = 2X - 2Y - 2Z

Arvind = 2Y - X + Y + Z - 2C = 3Y - X - Z

Gauri = 4Z

And finally after third transaction, number of cars with:

Sudhir = 4X - 4Y - 4Z            …..Eq (i)

Arvind = 6Y - 2X - 2Z           …….Eq (ii)

Gauri = 4Z - 2X + 2Y + 2Z - 3Y + A + Z = 7Z - X - Y        ……Eq (iii)

Each of  Eq (i), (ii) and (iii) are equal to 24. So, taking

(i) and (ii), we obtain, Y - Z = 9..(iv)

(i) and (iii), we obtain 3Z - Y = 15..(v)

Solving (iv) and (v), we get,

Z = 12

Then, Y = 21 and X = 39

So,

Sudhir = 39

Arvind = 21

Gauriv = 12