Multiple choice

A and B started business by investing money in ratio 4 : 5. After 6 months, C joined them by investing Rs. 3,000 more than B. On completion of one year, they shared the profit in ratio 4 : 5 : 3. How much money was invested by A?

  1. Rs. 6,000

  2. Rs. 9,000

  3. Rs. 12,000

  4. Rs. 15,000

  5. Rs. 18,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A = 4x, B = 5x. C invests (5x + 3000) for 6 months. Profit ratio = (4x*12) : (5x*12) : ((5x+3000)*6) = 48x : 60x : (30x+18000) = 4 : 5 : 3. Solving 48x/60x = 4/5 (consistent) and 60x/(30x+18000) = 5/3 gives 180x = 150x + 90000, so 30x = 90000, x = 3000. A's investment = 4 * 3000 = 12000.

AI explanation

Let the investments of A and B be 4x and 5x; since C invests Rs. 3000 more than B, C's investment is 5x plus 3000. Using the profit formula of investment multiplied by time for one year, their profit ratio is (4x multiplied by 12) : (5x multiplied by 12) : ((5x plus 3000) multiplied by 6), which simplifies to 48x : 60x : 30x plus 18000. Equating this to the given profit ratio of 4 : 5 : 3, we get (30x plus 18000) divided by 48x equals 3 divided by 4. Solving this equation gives 12x equals 18000, so x equals 1500; therefore, A's investment is 4 multiplied by 1500, which is Rs. 12,000.

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