Trading Up Real Estate

C.P of the land rs 1500.So the c.p of 1/3 of land = 5000

The farmer sold 1/3 of land at 6 % loss so Sp= (5000)-(6/100*5000)=4700

The Desired sp of land to acquire 10 % profit = (1500)+(10/100*1500)=16500

The cost of land to be sold after selling 1/3 of it at a profit of 10 % on the whole = 16500-4700=11800

The cp of 2/3 of land = 10000

So the profit amount to be made in order to make a 10 % profit on the whole = 11800-10000=1800

And the percent of 1800 of 10000 = (1800/10000) *100 ==18 % ...

The land is divided into 3 parts so each part costs you 5000. he sold 1 part at 6% loss that means he sold it at 4700 (6% of 5000 is 300). Now that to be at par he needs 10300 and to earn a extra profit of 10% he needs 1500 more. so by selling his remaining land he needs to sell it at 11800. 2 parts is 10000 so he needs 1800 more that is 18% of 10000.

First, we must find how much did the farmer loss

He first sold $\frac{1}{3}\times15000 = 5000$

He lost $6$ % of it, which means that he sold it with the price of $5000\times\frac{100-6}{100} = 5000 \times \frac{94}{100} = 4700$

So, in order to gain $10$ % of the whole deal, we must first know how much is the sum of $10$ % of the whole deal and the original price

$\frac{110}{100}\times15000 = 16500$

The farmer must get $16500$ in total to earn $10$ %

We already had known how much is the $\frac{1}{3}$ of the land, now we have to know the price of the remaining land

Let the percentage profit be $x$

$4700+(\frac{2}{3}\times15000\times\frac{100+x}{100})=16500$

$4700+(100\times(100+x))=16500$

Subtract $4700$ at both sides,

$100\times(100+x)=11800$

Divide by $100$ at both sides,

$100+x=118$

$x=\boxed{18}$

1/3(-6) + 2/3(x) = 10

2/3(x) = 10 + 2

x = 12(3/2)

x=18

target profit 1500 so entire sale value = 16500, 1/3 rd part sale value comes as 4700 (6% loss=300), so remaining money to earn =11800, 2/3rd value of land = 10000 that means we will earn 1800 on sale 2/3rd that means total sale value = 11800+4700 =16500 (10% profit)

3.3=2x+0.94 thus x=1.18 then 1.18-1 equal to 0.18 :)

15000/3=5000 loss of 1/3 of land = 5000 6% =300 the required profit = 15000 10% = 1500 the profit from 2/3 of land will be equal to 1500+300 = 1800 in the term of percentage (1800/10000) = 18%

15000 * 1/3 = 5000. The cost of 1/3 of the land is 5000

(1.06 * 5000) - 5000 = 300. You have a loss of 300

5000 - 300 = 4700. You sold 1/3 of the land at 4700

15000 * 1.10 = 16500. To get a profit of 10%, the whole land must be sold at 16500.

16500 - 4700 = 11800. You must sell the remaining piece of land at 11800

11800 - 10000 = 1800

1800/10000 = .18

The percentage profit is 18%

with 6% loss of one third land, i sold (100-6)*5000=4700 RS

for 10 % profit of whole land, i have to sell (100+10)*15000=165000 RS

so, i will sell the remaining piece of land for 165000-4700 = 118000 RS

then my percentage of profite will be = (118000-10000)/100 = 18%

100 + 200 = 300 100 × (1 - 0.06) = 94 300 × (1 + 0.10) = 330 330 - 94 = 236 = 200 × (1 + 0.18)

O agricultor vendeu um terço de suas terras com um prejuízo de 6% em relação ao valor de compra, logo, ele obteve:

1/3 . 5000 . 0,94 = 4700

Vendendo o restante de suas terras, ele quer obter 10% de lucro sobre o preço de compra, logo, ele quer:

15000 . 1,1 = 16500

O agricultor precisa conseguir 11800 (valor que falta para obter 10% de lucro sobre o preço de compra), portanto, deve vender o restante das terras por esse valor.

Como o valor de compra foi de 10000, a porcentagem de lucro da venda das terras restantes é:

11800/10000 = 1,18

Logo, a porcentagem de lucro deve ser de 18%.

he sold one third @ loss of 6%. so he earned Rs.(5000-6% of 5000)= Rs. 4,700. Now let he sold rest @ x% profit i.e.
@Rs.(10,000+ 100x). so we have the linear equation 4,700+10,000+100x= 15000+10% of 15000 which gives x= 18...i.e. he has to sold @18%

15000/3=5000

5000*6%=300

15000*10%=1500

300+1500=1800

10000*18%=1800

The farmer bought $x$ land for Rs 15000. He sold $\dfrac{1}{3}$ of the land for a $6\%$ loss.

Now, he had initially bought $\dfrac{1}{3}$ of the land for $\dfrac{15000}{3} = 5000$ rupees. He sold it for a loss of $6\%$ . Thus, he sold it for $5000 - \left( 0.06 \times 5000 \right) = 4700$ rupees.

Now, he wants to make an overall profit of $10 \%$ on $15000$ , thus, he wants to make a total amount of $15000 + \left( 0.1 \times 15000 \right) = 16500$ .

To make a profit of $16500$ , he has to sell the $\dfrac{2}{3}$ land at $16500 - 4700 = 11800$ rupees.

But he had bought the land for $10000$ rupees.

Thus he has to sell it at a percentage profit of $\dfrac{11800 - 10000}{10000} \times 100 = \boxed{18 \%}$

I tracked his net investment. Basically, he starts at zero, and by purchasing the land he "loses" $15000. When know that he's trying to get to a profit of $1500 (The original 15000 plus ten percent would put him at that amount of profit.) So now he has to go from -15000 to +1500 (Which would be a total "movement" of 16,500). His first transaction gains him +4700, but he still has to gain $11,800 to get to +1500. So now he has to sell the remaining land, originally valued at $10,000 (Two thirds the land, originally valued at two thirds his original purchase price.) for $11,800 to get where he wants to be. That would be an 18% mark-up from $10,000. So we're done. 18% is the answer. :)

The farmer bought the land at a price of RS $15000$ . Then, price of $\frac{1}{3}$ rd of the land $=\frac{1}{3}\times 15000 = 5000$

Now, the farmer sold it at a $6$ % loss, so selling price of $\frac{1}{3}$ rd of the land $=5000-\frac{6}{100}\times 5000 = 5000-300=4700$ .

Now, the owner wants to gain $10$ % profit on the whole land, so whole land should be sold at a total of $=15000+\frac{10}{100}\times 15000 = 15000+1500=16500$

So, the owner has to sell the $\frac{2}{3}$ rd part of the land which had a cost price of RS $10000$ at RS $(16500-4700)=11800$ , i.e., at extra RS $1800$

So, he sold that part at a profit of $\frac{1800}{10000}\times 100 = \boxed{18}$ %

cant explain clearly ..........but i made this eqn.......2/3y-1/3x6=10......to get the answer(18%)........(wink)

1500+150000=5000-{[6*5000]/100}+10000+100x x=18 :D

from the problem total land price is 15000(5000+5000+5000) Since he sold 1/3 of the land with rate of 6% loss = 4700 and to get the 10% profit on the whole deal it will be like = 16500 and we get the 10% profit from the 2/3 of the land so : 16500 - 4700 = 11800 so for the 2/3 we are having 10000 and to get 11800 from that lets take 10000 ---- 100 and 11800 -----x then x=(100* 11800)/10000 = 118 x = 118-100 x=18

$\frac{1}{3}$ of land means that part of land should be sell at 5000 ( $\frac{1}{3}$ *15000) rupees if there should be no loss or no profit but he sold it at a loss of 6% means 6% of 5000=300 rupees loss. so,he sold $\frac{1}{3}$ of land at 4700 rs.

Now, to gain 10% on the whole deal mean 10% of 15000=1500rs means finally after selling whole farm he should have 15000+1500=16500 rs. now he is already have 4700 rs so he has to earn 16500-4700=11,800 rs .

now 10,000 is price of remaining $\frac{2}{3}$ of land so he need to gain profit of 1800 means 18 % profit on the remaining piece of land

C.P.(Cost Price=15000/-)

Suppose he buys $x$ area of land for Rs. $15000$ .

Then, $\frac {x}{3}$ costs $\frac {15000}{3}$ , that is Rs. $5000$ .

Then, we can say that $C.P.$ of $\frac {x}{3}$ land is Rs. $5000$ .

$S.P.$ (Selling price)= $\frac {100-loss}{100}$ * $C.P.$

$S.P.$ of the $\frac {x}{3}$ land for $6$ % loss= $\frac {100-6}{100}$ * $5000$

= $\frac {94}{100}$ * $5000$

= $4700$ /-

Now,

Remaining $\frac {2x}{3}$ land should be sold at a rate that the total profit is $10$ %.

Profit of $10$ % on $Rs.$ $15000$ = $\frac {10}{100}$ * $15000$ .

= $Rs.$ $1500$ .

Total C.P.= $Rs.$ $16500$ .

Let the rate at which he should sell the remaining $\frac {2x}{3}$ land be $R$ %.

Then,

By the formula for S.P.,

$S.P.$ = $\frac {100+gain}{100}$ * $C.P.$ (Rs. 10000 because Rs.15000-Rs.5000)

= $\frac {100+R\%}{100}$ * $10000$

= $100+R$ * $100$

= $10000+100R$

Total C.P.= $10000+100R$ + $4700$

Therefore, equating this we get,

=> $10000+100R+4700$ = $16500$

=> $100+R+47$ = $165$ (Cancelling Common Factor 100 both sides)

=> $147+R$ = $165$

=> $R$ =( $165-147$ )%

=> $R$ = $18\%$

Therefore, Rate% at which he should sell to gain $10$ % on the whole is $\boxed{18}$ .