Miscellaneous Question 30
- A shopkeeper marks two items $A$ and $B$ - $ 40 \%$ and $25 \%$ respectively above their cost prices. He give a discount of $25 \%$ on item A and a discount of $10 \%$ on item $B$. The selling price of both the items A and B is the same.
I. Cost price of item A
II. Cost price of item $B$
(1) I $<$ II
(2) $I=I I$
(3) I $>$ II
(4) I $\geq$ II
(5) No relation
(IBPS Bank PO/MT CWE (Main) 18.11.2016)
Show Answer
Correct Answer: 30. (3)
Solution: 30. (3) Let the C.P. of items A and $B$ be $x$ and $y$ respectively.
Marked Price $: 1.40 x = 1.25 y$
S.P. : $ 1.40 x \times \frac{75}{100} = 1.25 y \times \frac{90}{100} $
$=1.050 x =1.125 y$
According to the question,
$1.050 x=1.125 y$
$\Rightarrow \frac{x}{y}=\frac{1125}{1050}>1$
$\Rightarrow x>y$
$\therefore$ I $>$ II
Aliter : Using overall $\%$ gain
$=\left(x+y+\frac{x y}{100}\right) \%$,
Overall $\%$ gain on $\mathrm{A}$
$=\left[40-25-\frac{40 \times 25}{100}\right] \%=5 \%$
Overall $\%$ gain on $\mathrm{B}$
$=\left[25-10-\frac{25 \times 10}{100}\right] \%=12.5 \%$
$\Rightarrow 1.05 x=1.125 y$
$\Rightarrow \frac{x}{y}=\frac{1.125}{1.050}>1$
$\therefore \quad$ I $>$ II