Question

A merchant gets 17percent profit after giving 10% discount on the marked price of certain item by what percentage should the marked price be increased so that he will get 20% profit

Answer 1

Answer:3%

Step-by-step explanation

Answer 2

Answer:

Marked price would be increased by 2.56% ( approx)

Step-by-step explanation:

Let x be the marked price of the item,

Discount percentage = 10%,

So, selling price = x - 10% of x

= x - 0.1x

= 0.9x

Now, we have profit% = 17 %,

We know that,

Profit% = $\frac{SP-CP}{CP}\times 100$

$17 = \frac{0.9x-CP}{CP}\times 100$

$17CP = 90x - 100CP$

$117CP = 90x$

$\implies CP = \frac{90x}{117}=\frac{10x}{13}$

If profit% = 20 %,

$20 = \frac{SP-CP}{CP}\times 100$

$20=\frac{SP-\frac{10x}{13}}{\frac{10x}{13}}\times 100$

$20=\frac{13SP-10x}{10x}\times 100$

$\frac{1}{5} =\frac{13SP-10x}{10x}$

$2x = 13SP - 10x$

$12x =13SP$

$\implies SP = \frac{12x}{13}$

∵ 90% of MP = SP

$\frac{90}{100}\times MP = \frac{12x}{13}$

$MP=\frac{1200x}{1170}=\frac{40x}{39}$

$\because \frac{\text{New MP-Original MP}}{\text{Original MP}}\times 100$

$=\frac{\frac{40x}{39}-x}{x}\times 100$

$=\frac{40-39}{39}\times 100$

$=\frac{1}{39}\times 100$

≈ 2.56%

Hence, the MP would be increased by approximate 2.56%

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