Question

The average monthly income of p and q is rs. 7,050/. the average monthly income of q and r is rs.7,700/and that of p and r is rs.8,250/. what is the monthly income of p

Answer 1

p+q=7700------->1
q+r=7700------->2
p+r=8250------->3
eqn(3-2)
p-q=0550------->4
eqn(4+1)
2p=7600
p=3800

Answer 2

Answer:

Rs.7600

Step-by-step explanation:

Let the monthly income of p be p

Let monthly income of q be q

Let monthly income of r be r

Now we are given that The average monthly income of p and q is rs. 7,050

$\Rightarrow \frac{p+q}{2}=7050$

$\Rightarrow p+q=7050 \times 2$

$\Rightarrow p+q=14100$   --1

Now we are given that the average monthly income of q and r is rs.7,700

$\Rightarrow \frac{q+r}{2}=7700$

$\Rightarrow q+r=7700 \times 2$

$\Rightarrow q+r=15400$   --2

Now we are given that the average monthly income of p and r is rs.8,250

$\Rightarrow \frac{p+r}{2}=8250$

$\Rightarrow p+r=8250 \times 2$

$\Rightarrow p+r=16500$  --3

Now solve 1 ,2 and 3

Substitute the value of pq from 1 in 3

$\Rightarrow 14100-q+r=16500$

$\Rightarrow r-q=16500-14100$

$\Rightarrow r-q=2400$ ---4

Add 2 and 4

$\Rightarrow q+r+r-q=15400+2400$

$\Rightarrow 2r=17800$

$\Rightarrow r=\frac{17800}{2}$

$\Rightarrow r=8900$

Now substitute the value of r in 3

$\Rightarrow p+8900=16500$

$\Rightarrow p=7600$

Hence the monthly income of p is Rs.7600.