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1. A man buys a field of agricultural land for Rs. 3,60,000. He sells one-third at a loss of 20% and two-fifths at a gain of 25%. At what price must he sell the remaining field so as to make an overall profit of 10%?

A. Rs.1,00,000

B. Rs. 1,15,000

C. Rs. 1,20,000

D. Rs. 1,25,000

Solution:

\begin{aligned} First Method : \\ CP = 360000 \\ To gain 10 % on whole land, \\ S P = 360000 + 10 % of 360000 \\ = R s . 396000 \\ \frac{1}{3} of the land sold on 20 % loss . \\ SP of \frac{1}{3} land \\ = \frac{360000}{3} - 20 % of \frac{360000}{3} \\ = R s . 96000 \\ SP of \frac{2}{5} of the land \\ = \frac{360000 \times 2}{5} + 25 % of \frac{360000 \times 2}{5} \\ = R s . 180000 \\ Thus, \\ SP of the remaining land \\ = 396000 - 96000 - 180000 \\ = R s . 120000 \\ Second Method: \\ SP of total agricultural \\ field at a profit of \\ 10 % = \frac{360000 \times 110)}{100} \\ = R s . 396000 \\ So, SP of \frac{1}{3} of field \\ = \frac{360000}{3} \times \frac{80}{100} \\ = R s . 96000 \\ SP of \frac{2}{5} t h of the field \\ = \frac{2 \times 360000 \times 125}{5 \times 100} \\ = R s . 180000 \\ Hence, \\ SP of the remaining field \\ = R s . (396000 - 96000 - 180000) \\ = R s . 120000 \end{aligned}

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