Question

A shopkeeper allows a discount of 10% on his goods and still makes a profit of
20%. Find the Cost Price of an item whose marked price is Rs.1700.

Answer 1

Step-by-step explanation:

Let M.P. be 100.

Discount =10% of M.P.

=

100

10

of M.P. =

100

10

×100

= 10

S.P. = M.P. − Discount

=100−10= 90

Gain =20% of C.P.

=

100

20

×450= 90

S.P. = C.P. + Gain

=450+90= 540

If S.P. is 90, then M.P. is 100.

When S.P. is 540,

M.P. =

90

540×100

= 600

∴ The M.P. of an article = 600

OR

Vimal used the formula method:

Discount =10%, Gain =20%,

C.P. = 450, M.P. = ?

M.P. =

100−Discount%

100+Gain%

× C.P.

=

(100−10)

(100+20)

×450

=

90

120

×450

= 600

Answer 2

Given:

✰ Discount percent d% = 10%

✰ Profit (gain)% = 20%

✰ Marked price ( M.P. ) = Rs. 1700

To find:

✠ The Cost Price ( C.P. ) of an item.

Solution:

First we will assume that the C.P of an item as x. Then, by using appropriate formulas we will find the required C.P of an item.

Let the Cost Price ( C.P. ) of an item be x.

Profit (gain)% = 20%

✭ S.P = (100 + gain%)/100 × C.P. ✭

Putting the values in the formula, we have:

➛ S.P = (100 + 20)/100 × x

➛ S.P = 120/100 × x

➛ S.P = 12/10 x

➛ S.P = Rs. 6/5 x ...①

Discount percent d% = 10%

Marked price ( M.P. ) = Rs. 1700

✭ Discount ( d ) = d% of M.P. ✭

➛ Discount ( d ) = 10% × 1700

➛ Discount ( d ) = 10/100 × 1700

➛ Discount ( d ) = 1 × 170

➛ Discount ( d ) = Rs. 170

✭ S.P. = M.P. - d ✭

➛ S.P. = 1700 - 170

➛ S.P. = Rs. 1530 ...②

Now, we can both the S.P. in eq① and eq② to get the value of x, which is equal to the Cost Price ( C.P. ) of an item.

➤ 6/5 x = 1530

➤ 6x = 1530 × 5

➤ 6x = 7650

➤ x = 7650/6

➤ x = 1275

∴ The Cost Price ( C.P. ) of an item = Rs. 1275

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