Question

when an article is sold at certain profit and certain loss then the ratio of profit and loss is 3 : 4 and ratio of respective selling price is 5:4. find loss percentage​

Answer 1

Given info : When an article is sold at certain profit and certain loss then ratio of profit and loss is 3 : 4. and the ratio of respective selling price is 5 : 4.

To find : The loss percentage is ..

solution : let cost price of an article was x

proportionality constant of profit and loss ratio is k

and proportionality constant of selling prices ratio is l.

for profit = selling price - cost price

⇒3k = 5l - x ...(1)

for loss = cost price - selling price

⇒4k = x - 4l ...(2)

adding equations (1) and (2) we get,

⇒7k = l ...(3)

from equation (1), 3(l/7) = 5l - x

⇒x = 5l - 3l/7 = 32l/7

now, percentage loss = loss/cost price × 100

= 4k/x × 100

= 4(l/7)/(32l/7) × 100

= 4/32 × 100

= 100/8

= 12 1/2 % or 12.5 %

Therefore the percentage loss is 12.5 %