Question

a shopkeeper wishes to offer a discount of 5% on the list price of an item and still makes a profit of 10% at what percentage above the cost price should shopkeeper mark the item​
plz answer....

Answer 1

Answer:

Hence, the percentage above the cost price should shopkeeper mark the item​ is:

15.79%

Step-by-step explanation:

Let the marked price(MP) of the item be=₹ 100.

a shopkeeper wishes to offer a discount of 5% on the list price of an item .

i.e. selling price(SP) of an item is:

95% of 100

= $\dfrac{95}{100}\times 100=95$

Also after selling the item he receives a profit of 10%.

i.e. Cost price(CP) of item is:

110% of CP=SP

$\dfrac{110}{100}\times CP=95\\\\CP=86.3636$

Now,

The percentage above the cost price should shopkeeper mark the item​ is:

$\dfrac{MP-CP}{CP}\times 100\\\\=\dfrac{100-86.3636}{86.3636}\times 100\\\\=15.79\%$

Hence, the percentage above the cost price should shopkeeper mark the item​ is:

15.79%

Answer 2

QUESTION

A shopkeeper wishes to offer a discount of 5% on the list price of an item and still makes a profit of 10% at what percentage above the cost price should shopkeeper mark the item.

SOLUTION

Let the cost price, CP of the item be ₹x. Since, the profit% is 10%.

The selling price SP

= ₹ (x+10/100×x)

= ₹(x+x/10)

= ₹11x/10

Also, SP = MP - discount

= 11x/10 = MP - (5/100×MP) ---------- (Discount is 5%)

= 11x/10 = 19/20 × MP

= MP =

$\sf \: \frac{11 \times 20}{10 \times 19} x$ = 22/19x

MP = (19+3/19)x

= (1+3/19)x = x+3/19x

Now, 3/19x = (3/19×100)% of x =

$\rm \: 15 \frac{15}{19} \% \: of \: x$

Thus , the shopkeeper marks the item at

$\sf \: 15 \times \frac{15}{19} \% \: more \: than \: the \: cost \: price$

Alternatively

Let the cost price of the item = ₹100

Since the profit is 10% the SP = ₹100+₹10 = ₹110

Discount offered = 5%

Also, SP = MP - (5/100×MP)

= 110 = (1-1/20) MP

= 110 = 19/20 MP

= MP = (20×110)/19

= MP = 2200/19

= 1900/19+300/19

$\rm : \to\: 100 \: + 15\times \frac{15}{19}$

MP will be

$\rm \: 15 \frac{15}{19} \% \: more \: thn \: the \: cost \: price$