At what percentage above the cost price must an article be marked so as to gain $33 %$ after allowing a customer a discount of $5 %$ ?

35 %

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38 %

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40 %

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42 %

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Solution

The correct option is C $40 %$
Let the cost price $= R s . 100$
Gain $= 33 % = 33 %$ of $100 = R s . 33$
$S P = C P + G a i n = 100 + 33 = R s . 133$
Now, Marked Price $= S P + D i s c o u n t$
$M P = 133 + 5 %$ of MP
$M P - \frac{5}{100} M P = 133$
$M P = \frac{133 \times 100}{5} = R s . 140$
Hence as per the given condition, the artile must be marked at $40 %$ above its CP.

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A shopkeeper fixes the marked price of an item $35 %$ above its cost price. Calculate the percentage of discount allowed to gain $8 %$

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