Multiple choice

Annual expenses of A and B are in the ratio $5:3$. The saving of Aand B are in the ratio $1:2$. Find the expenses of A. given that the income of A is $Rs. 8000$ and that of B is $Rs.9000$.

  1. $3000$
  2. $4000$
  3. $4500$
  4. $5000$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the expenses of A and B be 5x and 3x. Their savings are 8000 - 5x and 9000 - 3x, and these have ratio 1:2. Solving gives x = 1000, so A's expenses are 5000 rupees.

AI explanation

Let the expenses of A and B be 5x and 3x, and their savings be y and 2y respectively. We can write the income equations as 5x + y = 8000 and 3x + 2y = 9000. Multiplying the first equation by 2 gives 10x + 2y = 16000, and subtracting the second equation yields 7x = 7000, so x = 1000. The expenses of A are 5 multiplied by 1000, which equals Rs. 5000.

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