The percentage profit earned by selling a pair of earphones for rs 1800 is equal to the percentage loss incurred by selling the same article for rs 1200 at what price should the article be sold to make 50% profit
Answers
Answer:
2250
Step-by-step explanation:
prfit equals lose
Given: Profit on selling earphones at Rs. 1,800 = Loss on selling at Rs. 1,200
Required profit% = 50%
To find: S.P. to make 50% profit
Let: Gain/Loss % = X
Solution: Case 1, when S.P. is 1,800 and seller had profit
Using the formula to calculate C.P. when gain % and S.P. are given
.: C.P. = 100/(100 + gain%) x S.P.
= 100/(100 + X) x 1,800 ...(1)
Case 2, when S.P. is 1,200 and seller had loss
Using the formula to calculate C.P. when loss% and S.P. are given
.: C.P. = 100/(100 - loss%) x S.P.
= 100/(100 - X) x 1,200 ...(2)
Since, C.P. is same in both cases, we can compare equation (1) and (2)
⇒ 100/(100 + X) x 1,800 = 100/(100 - X) x 1,200
⇒ (1,800 x 100)/(100 + X) = (1,200 x 100)/(100 - X)
⇒ =
⇒ (1,80,000) x (100 - X) = (1,20,000) x (100 + X)
⇒ 1,80,00,000 - 1,80,000X = 1,20,00,000 + 1,20,000X
⇒ 1,80,000X + 1,20,000X = 1,80,00,000 - 1,20,00,000
⇒ 3,00,000 X = 60,00,000
⇒ X = 60,00,000/3,00,000 = 20
Profit % = 20%
Putting value of X in equation (1)
C.P. = 100/(100 + 20) x 1,800
= 100/120 x 1,800 = 1500
Required profit % = 50%
.: Profit % = Profit/C.P. x 100
.: Profit = (Profit% x C.P.)/100
= (50 X 1,500)/100 = 750
.: S.P. = C.P. + Profit
= 1,500 + 750 = 2,250
Hence, the article should be sold at Rs. 2,250 to get 50% profit.