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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

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & {\text{First}}\,{\text{Method}}: \cr & {\text{CP}} = 360000 \cr & {\text{To}}\,{\text{gain}}\,10\% \,{\text{on}}\,{\text{whole}}\,{\text{land}}, \cr & SP = 360000 + 10\% \,\text{of}\,360000 \cr & \,\,\,\,\,\,\,\, = Rs.\,396000 \cr & \frac{1}{3}\,{\text{of}}\,{\text{the}}\,{\text{land}}\,{\text{sold}}\,{\text{on}}\,20\% \,{\text{loss}}. \cr & {\text{SP}}\,{\text{of}}\,\frac{1}{3}\,{\text{land}} \cr & = {\frac{{360000}}{3}} - 20\% \,{\text{of}}\,\, {\frac{{360000}}{3}} \cr & = Rs.\,96000 \cr & {\text{SP}}\,{\text{of}}\,\frac{2}{5}\,{\text{of}}\,{\text{the}}\,{\text{land}} \cr & = \frac{{ {360000 \times 2} }}{5} + 25\% \,{\text{of}}\,\,\frac{{ {360000 \times 2} }}{5} \cr & = Rs.\,180000 \cr & {\text{Thus}}, \cr & {\text{SP}}\,{\text{of}}\,{\text{the}}\,{\text{remaining}}\,{\text{land}} \cr & = 396000 - 96000 - 180000 \cr & = Rs.\,120000 \cr & \cr & {\text{Second}}\,{\text{Method:}} \cr & {\text{SP of total agricultural }} \cr & {\text{field at a profit of}} \cr & 10\% = \frac{{ {360000 \times 110} )}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\, = Rs.\,396000 \cr & {\text{So,}}\,{\text{SP}}\,{\text{of}}\,\frac{1}{3}\,{\text{of}}\,{\text{field}} \cr & = {\frac{{360000}}{3}} \times {\frac{{80}}{{100}}} \cr & = Rs.\,96000 \cr & {\text{SP}}\,{\text{of}}\,\frac{2}{5}th\,{\text{of}}\,{\text{the}}\,{\text{field}} \cr & = \frac{{ {2 \times 360000 \times 125} }}{{ {5 \times 100} }} \cr & = Rs.\,180000 \cr & {\text{Hence}}, \cr & {\text{SP}}\,{\text{of}}\,{\text{the}}\,{\text{remaining}}\,{\text{field}} \cr & = Rs.\,\left( {396000 - 96000 - 180000} \right) \cr & = Rs.\,120000 \cr} $$

This Question Belongs to Arithmetic Ability >> Profit And Loss

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Comments ( 2 )

  1. Md Helal
    Md Helal :
    5 years ago

    Applying equation method :
    360000*(1/3)*(4/5) + 360000*(2/5)*(5/4) + R = 360000*(11/10)
    ⇒ 96000 + 180000 + R = 396000
    ⇒ R = 120000

  2. Sudhakar Prajapati
    Sudhakar Prajapati :
    8 years ago

    Correct Answer = C

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