Multiple choice

Mr. X, a business man had the income in the year $2000$, such that he earned a profit of $20$% n his investment in the business. In the year $2001$, his investment was less by Rs. $5000$ but still had the same income (Income=Investment+Profit) as that in $2000$. Thus, the percent profit earned in $2001$ increased by $6$%. What was his investment in $2000$?

  1. Rs. $1,02,000$
  2. Rs. $1,05,000$
  3. Rs. $1,50,500$

  4. Data inadequate

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let investment in 2000 be I. Profit in 2000 is 0.2I, so income is 1.2I. In 2001, investment is I - 5000 and income is 1.2I. The profit percent in 2001 is (1.2I - (I - 5000)) / (I - 5000) = 0.26. Solving 0.2I + 5000 = 0.26I - 1300 gives 0.06I = 6300, so I = 105,000.

AI explanation

Let the investment in 2000 be x, making his total income 1.20x. In 2001, his investment was (x - 5000) and his profit percentage increased by 6% to become 26%, while the income remained 1.20x. Setting up the equation, (x - 5000) * 1.26 = 1.20x, which simplifies to 1.26x - 6300 = 1.20x. Solving this gives 0.06x = 6300, so x = 105000. His investment in 2000 was Rs. 1,05,000.

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