Percentages
Aptitude

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Q.

After offering a discount of $37.5%$, Pankaj sold the rice at a profit of $25%$. Had he offered a discount of $41.67%$, his profit or loss percent would have been:

 A.

$16.66\%$  profit

 B.

$12\%$ loss

 C.

$29.17\%$ loss

 D.

$8.33\%$ profit

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Solution:
Option(A) is correct

Let the marked price of the rice = $8p$

Discount

\(=37.5\%=\dfrac{3}{8}\times MP\)

Selling price

\(=8p-\dfrac{3}{8}\times 8p=5p\)

\(5p= CP +\dfrac{25}{100}\times 25\)

\(\Rightarrow CP =4p\)

If he had offered a discount of $41.67\%=\dfrac{5}{12}$

\(SP =8p-\dfrac{5}{12}\times 8p\)

\(=\dfrac{14p}{3}\)

Profit

\(=\dfrac{14p}{3}-4p\)

\(=\dfrac{2p}{3}\)

Profit percentage

\(=\dfrac{2p/3}{4p}\times 100\)

\(=\dfrac{100}{6}\%\)

\(=16.66\%\)

Edit: For shortcut method please see Thulasi's comment.


(4) Comment(s)


Vineet
 ()

A person gets 3 successive discounts of 28.56%, 12.5% and 60%. The net discount is?

.



Thulasi
 ()

let M.P $= 100$,

$100-37.5=62.5 =$ SP

$\dfrac{62.5}{5}\times 4=50=$ CP

Now $100-41.67=58.33=$ new SP

$\dfrac{8.33}{50} \times 100=16.67\%$


Raman
 ()

Wow that a cool short trick.

Ned Stark
 ()

wow good short cut