Question

17. As a sales gimmick, a merchant began measuring with a metric stick thatwas x centimeters too long. If this reduced his profits from 50% of his cost to 20% of his cost. Find x​

Answer 1

Answer:

x=25 cm

Step-by-step explanation:

Let the cost of 1 m cloth is X Rs.

Earlier profit = 50%

Thus the merchant was selling the 1m cloth in

$X+X\times \frac{50}{100}$

$=X+\frac{X}{2}$

$=\frac{3X}{2}$

Now his profit is reduced to 20%

The selling price is still 3X/2 but the profit is only 20%

If the cloth he is selling has Cost Price Y then

$y+20\times\frac{y}{100}=\frac{3X}{2}$

$\implies \frac{6Y}{5}=\frac{3X}{2}$

$\implies Y=\frac{5X}{4}$

$\implies Y=1.25X$

Thus the actual cost price of his cloth now is 1.25 times the original cost price because of faulty metric stick

i.e. he is selling 0.25 m price of cloth extra

Thus x = 25 cm

Hope this helps.

Answer 2

Answer:

x = 25

Step-by-step explanation:

Let say cost price = Rs 100C per m

if He sells M meter

then Cost Price = 100CM

Profit = 50CM

Selling Price = 150CM

Now Let say he Measured x  cm extra

then cost price on selling M meters

= 100C( M + Mx/100)

= 100CM + MCx

profit = 20%

Selling price = (100CM + MCx) 1.2   =  150CM

=> 120CM + 1.2MCx  = 150CM

=> 1.2MCx = 30CM

=> 1.2x = 30

=> x = 25