A dealer bought a merchandise at a% less than its marked price and the

In this question, both CP and SP are given to us in terms of MP. As per question data,

CP of the dealer = MP (1-\(\frac{a}{100}\)) and

SP of the dealer = MP (1-\(\frac{b}{100}\)).
We are to find the discount given to the customer. To do this, we will need to find the value of SP since Discount = MP – SP.

From statement I alone, a = 6%.
Let’s assume the MP to be $1000. 6% less on this is 940 which represents the CP of the dealer.
The value of b is unknown. Also, we do not know if the dealer made a profit or a loss or none. As such, the discount given can be less than, equal to or more than 6% of MP.
Statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.

From statement II alone, the dealer made a profit of 5%.
Remember that the profit percentage is always calculated on CP. Although we know the profit percentage value, we don’t know the CP.

We only know that SP = 105% of CP or SP = \(\frac{21 }{ 20}\) CP. Using the expressions given in the question data, we have

MP (1-\(\frac{b}{100}\)) = MP (1-\(\frac{a}{100}\)) (\(\frac{21}{20}\)). Simplifying and solving, we have,

21a – 20b = 100.

We have two unknowns but only one independent equation; hence, we cannot find unique values for the variables and hence the discount.
Statement II alone is insufficient. Answer option B can be eliminated. Possible answer options are C or E.

Combining statements I and II, we have the following:

From statement II, 21a – 20b = 100; from statement I, a = 6.

Substituting the value of a in the equation, we have b = 1.3. This means, the customer obtained a 1.3% discount on the marked price.

However, since we have to calculate the VALUE of the discount, the combination of statements is insufficient since we do not know the Marked price of the merchandise.
The combination of statements is insufficient. Answer option C can be eliminated.

The correct answer option is E.

Hope that helps!

A dealer bought a merchandise at a% less than its marked price and then sold at b% less that its marked price. What was the value of the discount offered to customers?

(1) a = 6%
(2) The dealer made a profit of 5%

1) value of b% is unknown, so cant find the value of profit
2) profit is 5%, but we dont know the profit of what amount (CP)
1+2)
we dont know the value of marked price, so we cant find the value of profit.
Ans E

buy: m(1-a)=x
sell: m(1-b)=y

(1) insufic
no info b

(2) insufic
x-y/y=0.05

(1/2) sufic
x-y/y=0.05
x=1.05y
m(1-0.06)=1.05(m-mb)
m0.94=1.05m-1.05mb
0.94=(1.05-1.05b)
b=..

ans (C)

Check your \(\frac{6 - b }{ 100 - 6} = 5\)
b = - 3.64%

B value is not right

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Bunuel
Isn't the question asking for the value of the discount, in that case I think the answer should be E
Please, clarify.