Question

The average monthly income of X and Y is Rs \[5050\] . The average monthly income of Y Rs $6250$ and the average monthly income X and Z is the Rs $5200$ . The monthly income of X and Z is is
A) Rs $4050$
B) Rs $3500$
C ) Rs $4000$
D) Rs $5000$

Answer 1

Hint:
As it is given that the average income of X and Y , Y and Z and Z and X using this, find out the sum of the income of X , Y , Z that is equal to Rs $16500$ now subtract the sum of income of Y and Z we get the income of X .

Complete step by step solution:
As in the question it is given that the average monthly income of X and Y is Rs \[5050\] , The average monthly income of Y and Z is Rs $6250$ and the average monthly income X and Z is the Rs $5200$
Hence we know that the
Average = $\dfrac{{{\text{Sum of income }}}}{{{\text{Total number of person}}}}$
Let the monthly income of X ,Y , Z is x , y , z respectively
So the average monthly income of X and Y is Rs \[5050\] mean that ,
$\dfrac{{{\text{x + y}}}}{2} = 5050$
$x + y = 10100$ ..... equation (i)
The average monthly income of Y and Z is Rs $6250$ mean that
$\dfrac{{y + z}}{2} = 6250$
$y + z = 12500$ ....... equation (ii)
The average monthly income X and Z is the Rs $5200$
$\dfrac{{x + z}}{2} = 5200$
$x + z = 10400$ .......equation (iii)

Adding the equation (i) , equation (ii) and equation (iii) we get ,
$x + y + y + z + x + z = 10100 + 12500 + 10400$
$2\left( {x + y + z} \right) = 33000$
Divide by $2$ on both side
$x + y + z = 16500$
hence sum of income of all three person is $16500$
So we have to find the income of X as we know that the sum of income of all three person is $16500$ and we also know the sum of income of Y and Z that is $12500$ ( from equation (ii) )
Hence
$x + y + z = 16500$
Put the value of $y + z = 12500$ in above equation
$x + 12500 = 16500$
$x = 16500 - 12500$
$x = 4000$

Hence the income of X is Rs $4000$ or option C is correct.

Note:
Whenever this type of question will come always try to find out the sum of total income of X, Y, Z from the given conditions and after that try out find the value of Y and Z or find the out relation among Y and Z and then put it in the equation of total income of X , Y , Z so we get the value of X .