Question

a man buys a plot of land at Rs 360000 he sells one third of the plot at a loss of 20% again he sells two third of the plot left at a profit of 25% at what price should he sell the remaining plot in order to get a profit of 10% on the whole

Answer 1

Since plots divided as 1/3rd first and 2/3rd of remaining in second phase we estimate number of plots in total first.

1/3rd : 2/3rd of 2/3rd : remaining 1/3rd of 2/3rd

(1/3) : (2/3) x (2/3) : (2/3) x (1/3)

1/3 : 4/9 : 2/9

Make denominator common as 9 by multiplying first ratio with 3/3

3/9 : 4/9 : 2/9

So in total 9 plots purchased at Rs. 360000

Cost of 1 plot = Rs. 360000/9 = Rs. 40000

To get 10% whole profit a man get back Rs. 360000 + Rs 36000 = 396000

1/3 rd of plots sold with 20% loss

1/3rd of plots is = 9 x 1/3 = 3 plots

Cost of 3 plots = Rs. 40000 x 3 = 120000

Loss of 20% of 120000 = Rs.24000

So man got Rs. (120000 - 24000) in hand for 1/3rd plot sales

⇒ Rs. 96,000

Remaining plots in hand 9 - 3 = 6 plots

2/3rd of remaining plot = 6 x 2/3 = 4 Plots

Cost of 4 plots = Rs. 40000 x 4 = Rs. 160000

Sold with 25% profit of Rs. 160000 = Rs. 40,000

Man got Rs ( 160000 + 40000) on remaining 2/3 of 2/3rd plots

⇒ Rs. 200000

Man has to get Rs. 396000 to achieve 10% profit on whole

So far he received Rs. (96000 + 200000) = Rs. 296000

Remaining plot to be sold at Rs. (396000 - 296000)

⇒ Rs. 100000