Aptitude Discussion

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. |
$12.5\%$ |

**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:

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

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

$⇒ 0.1216×100$

$= 12.16\%$