A shopkeeper sells three items P, Q and R and incurs a loss of 21 % , 11 % and 10 % respectively. The overall loss percentage on selling P and Q items is 14.33 % and that of Q and R items is 10.4% . Find the overall loss percentage on selling the three times ?

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Solution

Let the cost of the item P = Rs p.
Let the cost of the item Q = Rs q.
Let the cost of the item R = Rs r.
SP of the item P = $0.79$ p.
SP of the item Q = $0.89$ q.
SP of the item R = $0.9$ r.
Overall loss percentage of the 1st two items =14.33%.
$\frac{0.21p+0.11q}{p+q}=0.1433$ .

$\frac{p}{q}=\frac{1}{2}$ .

Overall loss percentage of the 2nd and 3rd item =10.4%.
$\frac{0.11q+0.1r}{q+r}=0.104$ .

$\frac{q}{r}=\frac{2}{3}$ .
Overall loss percentage:
$(\frac{0.21p+0.11q+0.1r}{p+q+r})\ast 100$ ,

$(\frac{10.21+20.11+3*0.1}{1+2+3})\ast 100$ ,
0.1216×100= 12.16%.

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