Question

If a shopkeeper sold 8 items at the cost price of 7 items, how much profit/loss does he make?​

Answer 1

SOLUTION

GIVEN

A shopkeeper sold 8 items at the cost price of 7 items

TO DETERMINE

The profit / loss percentage

EVALUATION

Let price of each item = Rs x

∴ Cost price = Rs 8x

Selling price = Rs 7x

Since Selling price < Cost price

So loss occurs

∴ Loss = Rs ( 8x - 7x ) = Rs x

So the required loss percentage

$\displaystyle\sf{ = \frac{x}{8x} \times 100 \%}$

$\displaystyle\sf{ = \frac{100}{8} \: \%}$

$\displaystyle\sf{ = \frac{25}{2} \: \%}$

$\displaystyle\sf{ = 12.5 \: \%}$

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Answer 2

Given :- If a shopkeeper sold 8 items at the cost price of 7 items, how much profit/loss does he make ?

Answer :-

Method (1) :- Basic Method .

Let us assume that, CP of 1 item is Rs.x .

so,

→ CP of 7 items = 7 * x = Rs.7x .

now, given that,

→ SP of 8 items = CP of 7 items

→ SP of 8 items = Rs.7x

→ SP of 1 item = Rs.(7x/8)

since

→ (7x/8) < x .

→ SP < CP .

The shopkeeper have lose .

→ Loss = CP - SP = x - (7x/8)

→ Loss = (8x - 7x)/8 = Rs.(x/8)

therefore,

→ Loss % = (Loss * 100)/CP = {(x/8) * 100} / x = (x * 100)/8x = 12.5% (Ans.)

Method (2) :- Ratio Method .

given that,

→ 8SP = 7CP

→ SP/CP = 7/8 .

→ SP : CP = 7 : 8 .

so,

→ Loss = CP - SP = 8 - 7 = 1 item .

then,

→ Loss % = (1 * 100)/8 = 12.5% (Ans.)

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