Question

33. Ahmed buys a plot of land for 480000. He sells of it at a loss of 6%. At what gain percent
should he sell the remaining part of the plot to gain 10% on the whole?​

Answer 1

Given :

Cost price of a plot of land : ₹480000

Loss obtained for some part : 6%

Gain obtained for whole land : 10%

To find :

The gain percentage obtained while selling the other part of land.

Solution :

First, we should find the selling price of both part of lands.

Selling price of first part :

$\sf \dashrightarrow \dfrac{(100 - Loss\%)}{100} \times CP$

$\sf \dashrightarrow \dfrac{(100 - 6)}{100} \times 480000$

$\sf \dashrightarrow \dfrac{94}{100} \times 480000$

$\sf \dashrightarrow \dfrac{47}{50} \times 480000$

$\sf \dashrightarrow \dfrac{47 \times 480000}{50} = \dfrac{22560000}{50}$

$\sf \dashrightarrow \cancel \dfrac{22560000}{50} = 451200$

Selling price of second part :

Let the gain percent be x%.

$\sf \dashrightarrow \dfrac{(100 + Gain\%)}{100} \times CP$

$\sf \dashrightarrow \dfrac{(100 + x)}{100} \times 480000$

$\sf \dashrightarrow \dfrac{100 + x}{100} \times 480000$

$\sf \dashrightarrow \dfrac{100 + x}{1} \times 4800$

$\sf \dashrightarrow 4800 (100 + x)$

$\sf \dashrightarrow 480000 + 4800x$

Now, we should find the total cost and selling prices.

Total cost price :

$\sf \dashrightarrow 480000 + 480000$

$\dashrightarrow$₹$\sf 960000$

Total selling price :

$\sf \dashrightarrow 451200 + (480000 + 4800x)$

$\dashrightarrow$₹$\sf 931200 + x$

Now, let's find the value of x i.e, the profit of second part.

Gain percent of second part :

$\sf \dashrightarrow Total \: Gain\% = \dfrac{Gain}{Cost \: price} \times 100$

$\sf \dashrightarrow 10\% = \dfrac{931200 + 4800x - 960000}{960000} \times 100$

$\sf \dashrightarrow 10\% = \dfrac{-28800 + 4800x}{960000} \times 100$

$\sf \dashrightarrow 10\% = \dfrac{-28800 + 4800x}{9600}$

$\sf \dashrightarrow -28800 + 4800x = 9600 \times 10$

$\sf \dashrightarrow -28800 + x = 96000$

$\sf \dashrightarrow 4800x = 96000 + 28800$

$\sf \dashrightarrow 4800x = 124800$

$\sf \dashrightarrow x = \dfrac{124800}{4800}$

$\sf \dashrightarrow x = 26\%$

Hence, the gain percentage of second part of land is 26%.