Percentages
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Q.

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 items?

 A.

$15\%$

 B.

$12.16\%$

 C.

$13.4\%$

 D.

$12.5\%$

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Solution:
Option(B) is correct

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 $P =0.79p$
SP of the item $Q =0.89q$
SP of the item $R =0.9r$
Overall loss percentage of the 1st two items = $14.33\%$

\(\Rightarrow \dfrac{0.21p+0.11q}{p+q}=0.1433\)

\(\Rightarrow \dfrac{p}{q}=\dfrac{1}{2}\)

Overall loss percentage of the 2nd and 3rd item =$10.4\%$

\(\Rightarrow \dfrac{0.11q+0.1r}{q+r}=0.104\)

\(\Rightarrow \dfrac{q}{r}=\dfrac{2}{3}\)

Overall loss percentage:

\(\Rightarrow \dfrac{0.21p+0.11q+0.1r}{p+q+r}\times 100\)

\(\Rightarrow \dfrac{1(0.21)+2(0.11)+3(0.1)}{1+2+3}\times 100\)

$⇒ 0.1216×100$

$= 12.16\%$


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