Question

an article sold at a certain fixed price. by selling it at 2/3 of that price, one loses 10%. the gain % on selling it at original price is ?

a.20
b.33 1/3
c.35
d.40

Answer 1

If he sells at 2/3 of the price, that means that 1/3 is the 10% he lost.

Answer 2

We are interested in the gain, 1/3 would be the gain, if he sells at the original price, therefore gain = 33 1/3 %

Answer 3

how u saying 1/3 is gain?

Answer 4

He sells at 2/3, original price is 1
2/3 -> 1 = +1/3

Answer 5

if he sells at 2/3rd of the price, it leads to 10% lost.. so if he sells for original price, he wont get 1/3rd gain.. am i right??

Answer 6

Think about it this way.
P is price. M is margin (what you gain).

(P + M) * 2/3 = P * (1-0.1)

P(1-0.1) means you only get back 90% of what you paid for it. You lose 10. So you solve for M.

Answer 7

Should leave you with M = 7/5 P, which is the same as M = 140/100 P, or M = 140% P

Your gain should be 40%

Answer 8

Umm, didn't think of that D:

Answer 9

I understand, its not very intuitive :(

Answer 10

ans s 35%

Answer 11

let cp = 100
sp * 2/3 = 90
so sp = (90*2)/3 = 135
so 35% gain... but i cant understand it properly

Answer 12

Define cp, sp.

Answer 13

cost price, selling price

Answer 14

Its not that straight forward. The cost price is P. The selling price is P plus a margin M. The margin is your profit. So from your problem you get that (P + M), when that is 2/3, you get back 90% of P. Which means 0 margin, and 10% less of what you paid for. So 10% loss.

In the end the equation should be
\[(P + M ) {2 \over 3} = P * 0.9\]

Answer 15

Which you want to solve for M, as above

Answer 16

Let the original selling price be : x

And now the new selling price is : (2/3) of x = 2x/3

Now the formula for Cost Price is:

\[CP = \frac{100}{(100 - Loss)} \times SP\]

Where SP is Selling Price..

Here, Loss = 10% and SP = 2x/3

Put in the formula for find the Cost Price:

\[CP = \frac{100}{90} \times \frac{2x}{3}\]

\[CP = \frac{20x}{27}\]

This is the Cost Price for that article..

Selling Price is : x (we have assumed it earlier)

Gain = Cost Price - Selling Price

\[Gain = x - \frac{20x}{27}\]

\[Gain = \frac{7x}{27}\]

Now find the Gain Percentage:

Gain% =

\[= \frac{\frac{7x}{27}}{\frac{20x}{27}} \times 100 = \frac{7x \times 27}{27 \times 20x}\]

= 35%

Answer 17

Sorry, there I have written wrong..

Gain = Selling Price - Cost Price...